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BEGIN:VEVENT
SUMMARY:Eivind Schneider (Hradec Kralove University)
DTSTART:20200415T093000Z
DTEND:20200415T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/1
DESCRIPTION:Title: Differential invariants in thermodynamics\nby Ei
vind Schneider (Hradec Kralove University) as part of Prague-Hradec Kralov
e seminar Cohomology in algebra\, geometry\, physics and statistics\n\nLec
ture held in ZOOM meeting ID 895-276-2498.\n\nAbstract\nIt is well know
n that contact geometry gives the appropriate framework for formulating th
ermodynamics: Thermodynamic states can be interpreted as Legendrian subman
ifolds of a certain contact manifold. The existence of a metric on thermod
ynamic states has also received some attention in the last decades. The me
tric can be interpreted as the variance of an underlying probability measu
re. Less studied is the action of the affine group that appears naturally
in this context as the group preserving the variance. We study this group
action by finding generators of its algebra of scalar differential invaria
nts\, which intuitively can be thought of as the observables in the theory
. In the end\, we discuss the relation between the invariants and some wel
l-known physical quantities in thermodynamics.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Galaev (Hradec Kralove University)
DTSTART:20200422T093000Z
DTEND:20200422T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/2
DESCRIPTION:Title: Non-diffeomorphic Reeb foliations and modified Godbi
llon-Vey class\nby Anton Galaev (Hradec Kralove University) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\n\nAbstract\nThe definition of the Reeb foliation depends
upon two real functions satisfying certain conditions. All these foliatio
ns are pairwise homeomorphic and have trivial Godbillon-Vey class. We cons
truct explicit examples of the Reeb foliations that are not diffeomorphic.
For this purpose we show that a modified Godbillon-Vey class defined by L
osik is non-trivial for some Reeb foliations and trivial for some other Re
eb foliations. This characteristic class takes values in the second order
frame bundle of the leaf space of the foliation. This is a joint work with
Ya. Bazaikin and P. Gumenyuk.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Khavkine (Institute of Mathematics\, Czech Academy of Scien
ces)
DTSTART:20200429T093000Z
DTEND:20200429T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/3
DESCRIPTION:Title: Triangular decoupling of systems of differential equ
ations\, with application to separation of variables on Schwarzschild spac
etime\nby Igor Khavkine (Institute of Mathematics\, Czech Academy of
Sciences) as part of Prague-Hradec Kralove seminar Cohomology in algebra\
, geometry\, physics and statistics\n\n\nAbstract\nCertain tensor wave equ
ations admit a complete separation of variables on the Schwarzschild space
time (static\, spherically symmetric black hole)\, resulting in complicate
d systems of radial mode ODEs. The spectral theory of these systems has im
portant applications to the stability analysis electromagnetic and gravita
tional perturbations of the black hole. However\, almost none of the impor
tant questions about the radial mode equations can be answered in their or
iginal form. I will discuss a drastic simplification of these ODE systems
to sparse upper triangular form that is directly susceptible to spectral a
nalysis. Essential to this simplification are geometric properties of the
original tensor wave equations\, ideas from homological algebra and from t
he theory of ODEs with rational coefficients. Based on [arXiv:1711.00585\,
1801.09800\, 2004.09651]\n\nPlease contact the speaker or an organizer to
get Zoom livestream access information.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Roop (Moscow State University)
DTSTART:20200506T093000Z
DTEND:20200506T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/4
DESCRIPTION:Title: Shock waves in Euler flows of gases\nby Mikhail
Roop (Moscow State University) as part of Prague-Hradec Kralove seminar Co
homology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe
study non-stationary 1-dimensional flows of gases described by a quasiline
ar system of differential equations including Euler equation and continuit
y equation. We show that equations in question essentially depend on therm
odynamics of the medium. We represent the system by means of 2-forms on ze
ro-jet space and get some exact solutions by means of such a representatio
n. The solutions obtained are multivalued\, we find caustics and shock wav
e front. The method can be applied to any thermodynamic state of the mediu
m as well as to any thermodynamic process. The talk is based on our joint
paper with Valentin Lychagin\, arXiv:2004.05015.\n\nPlease contact the spe
aker or an organizer to get Zoom livestream access information.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University Hradec Kralove)
DTSTART:20200513T093000Z
DTEND:20200513T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/5
DESCRIPTION:Title: Geometry of gauge PDEs I\nby Alexei Kotov (Unive
rsity Hradec Kralove) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nI will show
how jet spaces and Q-bundles can be incorporated into an invariant mathema
tical description of gauge theories.\n\nPlease contact the speaker or an o
rganizer to get Zoom livestream access information.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Positselski (Institute of Mathematics\, Czech Academy of Sc
iences)
DTSTART:20200401T093000Z
DTEND:20200401T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/6
DESCRIPTION:Title: Koszul algebras and one-dependent random 0-1 sequenc
es\nby Leonid Positselski (Institute of Mathematics\, Czech Academy of
Sciences) as part of Prague-Hradec Kralove seminar Cohomology in algebra\
, geometry\, physics and statistics\n\n\nAbstract\nKoszul algebras are a n
atural class of graded algebras with\nquadratic relations\, defined by a s
eries of homological conditions.\nTo a Koszul algebra over a field with fi
nite-dimensional components\,\none can assign a one-dependent stochastic 0
-1 sequence\, which carries\ninformation about the dimensions of the algeb
ra's grading components.\nThis construction allows to show that the Hilber
t series of a Koszul\nalgebra can be extended meromorphically to the circl
e of double radius.\nConjecturally\, such Hilbert series are meromorphic i
n the whole\ncomplex plane (and consequently\, rational).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University Hradec Kralove)
DTSTART:20200520T093000Z
DTEND:20200520T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/7
DESCRIPTION:Title: Geometry of gauge PDEs II\nby Alexei Kotov (Univ
ersity Hradec Kralove) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nI will show
how jet spaces and Q-bundles can be incorporated into an invariant mathem
atical description of gauge theories.\n\n(This is a continuation of Alex
ei Kotov's seminar from last week.)\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Caputi (Institute of Informatics of the Czech Academy of Sci
ences)
DTSTART:20200610T093000Z
DTEND:20200610T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/8
DESCRIPTION:Title: Cyclic homology for bornological coarse spaces\n
by Luigi Caputi (Institute of Informatics of the Czech Academy of Sciences
) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometr
y\, physics and statistics\n\n\nAbstract\nBornological coarse spaces are "
large scale"\ngeneralizations of metric spaces (up to quasi-isometry). Hom
ological\ninvariants of such spaces are given by coarse homology theories\
, which\nare functors from the category of bornological coarse spaces to a
stable\ncocomplete ∞-category\, satisfying additional axioms. Among the
main\nexamples of coarse homology theories\, there are coarse versions of
\nordinary homology\, of topological\nand algebraic K-theory. In the talk
we define G-equivariant coarse\nversions of the classical Hochschild and c
yclic homologies (of\nalgebras). If k is a field\, the evaluation at the o
ne point space\ninduces equivalences with the classical Hochschild and cyc
lic homology\nof k. In the equivariant setting\, the G-equivariant coarse
Hochschild\n(cyclic) homology of the discrete group G agrees with the clas
sical\nHochschild (cyclic) homology of the associated group algebra k[G].\
n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vojtech Pravda (Institute of Mathematics of the Czech Academy of S
ciences)
DTSTART:20200527T093000Z
DTEND:20200527T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/9
DESCRIPTION:Title: Universal\, almost universal and related spacetimes<
/a>\nby Vojtech Pravda (Institute of Mathematics of the Czech Academy of S
ciences) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nFor universal spacetimes\
, all rank-2 tensors constructed from the metric\, Riemann tensors\, and i
ts covariant derivatives of arbitrary order are proportional to the metric
. Consequently\, all vacuum field equations of generalized theories of gra
vity following from Lagrangian constructed from the Riemann tensors and it
s covariant derivatives of arbitrary order are simultaneously satisfied. W
e will present necessary and sufficient conditions for several classes of
universal spacetimes of Lorentzian signature\, some explicit examples of s
uch spacetimes\, and discuss certain useful generalizations of the univers
al property.\n\nContact an organizer or the speaker for Zoom connection de
tails. Virtual coffee starts already at 11:00 before the seminar.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Somberg (Charles University Prague)
DTSTART:20200603T093000Z
DTEND:20200603T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/10
DESCRIPTION:Title: An approach to the representation theory of symmetr
ic groups\nby Petr Somberg (Charles University Prague) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\n\nAbstract\nWe give an expository account of Vershik-Okounkov
approach to the representation theory of symmetric groups (based on the G
elfand-Tsetlin basis and the Young-Jucys-Murphy elements.) If time permits
\, we explain some geometrical problems which lead to certain conjectural
statements generalizing V-O approach.\n\nContact an organizer or the speak
er for Zoom connection details. Virtual coffee starts already at 11:00 bef
ore the seminar.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART:20200617T093000Z
DTEND:20200617T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/11
DESCRIPTION:Title: Vertex algebra cohomology of foliations on Riemann
surfaces\nby Alexander Zuevsky (Institute of Mathematics of the Czech
Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology i
n algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn the transv
ersal basis formalism\, we construct a vertex algebra cochain complex\, sh
ow its independence on coordinates and choice of basis\, and define the ve
rtex algebra cohomology for a foliation on a smooth complex curve. The fir
st cohomologies are determined in terms of connections and classes of exte
nsions of the vertex algebra. We will introduce the cohomological class\,
consider the main example of $\\operatorname{Re} \\omega=0$ foliation on a
Riemann surface\, and make a connection with considerations of other codi
mension one examples.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen J. Watson (School of Mathematics & Statistics\, University
of Glasgow)
DTSTART:20200624T093000Z
DTEND:20200624T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/12
DESCRIPTION:Title: Lorentzian Symmetry Predicts Universality Beyond Po
wer Laws\nby Stephen J. Watson (School of Mathematics & Statistics\, U
niversity of Glasgow) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nThe statisti
cal physics governing phase-ordering dynamics following a symmetry breakin
g first-order phase transition is an area of active research. The Coarseni
ng/Ageing of the ensemble of phase domains\, wherein irreversible annihil
ation or joining of domains yields a growing characteristic domain length\
, is a omniprescent feature whose universal characteristics one would wish
to understand. Driven kinetic Ising models and growing nano-faceted cryst
als are theoretically important examples of such Coarsening (Ageing) Dynam
ical Systems (CDS)\, since they additionally break thermodynamic fluctuati
on-dissipation relations.\nPower-laws for the growth in time of the charac
teristic size of domains (e.g.\, lengths) of CDS\, and a concomitant {\\e
m scale-invariance} of the associated length distributions\, has so frequ
ently been empirically observed that their presence has acquired the statu
s of a principle\; the so-called Dynamic-Scaling Hypothesis. \nBut the dyn
amical symmetries of a given CDS- its Coarsening Group $G$ - may include m
ore than the global spatio-temporal scalings underlying the {\\em Dynamic
Scaling Hypothesis}. \nIn this talk\, I will present a recently developed
theoretical framework (Ref.[1]) that shows how the symmetry group G of a C
oarsening (ageing) Dynamical System (CDS) necessarily yields G-equivarianc
e (covariance) of the CDS's universal statistical observables. We exhibit
this theory for a variety of model systems\, of both thermodynamic and dr
iven type\, with symmetries that may also be {/em emergent} (Ref. [2\,3])
and/or {\\em hidden}. We will close with a magical theoretical coarsening
law which reflects Lorentzian and parabolic symmetries!\n\n\nReferences:\n
\n[1] Lorentzian symmetry predicts universality beyond scaling laws\,\nSJ
Watson\, EPL 118 (5)\, 56001\, (Aug.2\, 2017)\, Editor's Choice\nhttp://io
pscience.iop.org/article/10.1209/0295-5075/118/56001/meta\n\n[2] Emergent
parabolic scaling of nano-faceting crystal growth\,\nStephen J. Watson\,
Proc. R. Soc. A 471: 20140560 (2015)\nhttp://rspa.royalsocietypublishing.o
rg/content/471/2174/20140560\n\n[3] Scaling Theory and Morphometrics for a
Coarsening Multiscale Surface\, via a Principle of Maximal Dissipation\,\
nStephen J. Watson and Scott A. Norris\, Phys. Rev. Lett. 96\, 176103 (200
6)\nhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.176103\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART:20201007T093000Z
DTEND:20201007T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/13
DESCRIPTION:Title: On the different perspective of the Casals-Murphy c
riterion of looseness\nby Roman Golovko (Charles University) as part o
f Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\n\nAbstract\nWe show that inside a trivial open book $\\
partial (W\\times D^2)$ with page being a Weinstein manifold $(W\, d\\thet
a)$\, any Legendrian which is contained entirely inside a page and which i
ntersects some cocore disc transversely in a single point is loose. This l
eads to the alternative proof of Casals-Murphy criterion of looseness. Thi
s is joint work with Georgios Dimitroglou Rizell.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Cattafi (KU Leuven)
DTSTART:20201014T093000Z
DTEND:20201014T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/14
DESCRIPTION:Title: Formal integrability of geometric structures\nb
y Francesco Cattafi (KU Leuven) as part of Prague-Hradec Kralove seminar C
ohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nA
Γ-structure on a manifold is a maximal atlas whose changes of coordinates
take values in a Lie pseudogroup Γ. Various geometric structures (e.g. s
ymplectic\, complex and contact structures) fit in this framework\, but th
ere is no general definition of almost Γ-structure (e.g. almost symplecti
c\, almost complex and almost contact structures) in terms of Γ. In this
talk we are going to fill this gap by introducing the general definition o
f an almost Γ-structure\, and presenting a characterisation of its formal
integrability. This will be obtained by introducing the concept of princi
pal Pfaffian bundle. We will draw inspiration from the theory of PDEs\, fr
om Poisson geometry\, as well as from similar results in the theory of G-s
tructures\, which we recover as particular cases. This is joint work with
Marius Crainic.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Domenico Fiorenza (Università di Roma “La Sapienza”)
DTSTART:20201021T093000Z
DTEND:20201021T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/15
DESCRIPTION:Title: Formally integrable complex structures on higher di
mensional knot spaces\nby Domenico Fiorenza (Università di Roma “La
Sapienza”) as part of Prague-Hradec Kralove seminar Cohomology in algeb
ra\, geometry\, physics and statistics\n\n\nAbstract\nBy the Brown-Gray’
s classification\, there are four classes of Riemannian manifolds $M$ with
parallel $r$-fold vector cross products: $r = 1$ and $M$ a Kähler manifo
ld\, $r = \\dim M − 1$\, $r = 2$ and $M$ a $G_2$-manifold\, $r = 3$ and
$M$ a $Spin(7)$-manifold. For the first three classes it has been proven b
y Brylinski\, LeBrun\, and Verbitsky\, via ad hoc arguments for each of th
ese classes\, that the higher knot spaces for $M$ carry a natural formally
Kähler structure. More recently\, Henrich provided a new proof for the $
r = \\dim M − 1$ case. In a recent work with Hông Vân Lê (arXiv:1912.
05175)\, we show how a variant of Henrich's construction can be used to pr
ovide a uniform proof for all four classes. In particular\, this provides
a proof for the previously unknown case of $Spin(7)$-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Skoda (University of Zadar and University of Hradec Kralove)
DTSTART:20201104T103000Z
DTEND:20201104T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/17
DESCRIPTION:Title: Gluing bundles over noncommutative flag varieties\nby Zoran Skoda (University of Zadar and University of Hradec Kralove)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\
, physics and statistics\n\n\nAbstract\nLocalization functors may be used
to define local covers in some\nexamples from noncommutative geometry. In
an earlier work\, I have used\nthis technique to treat\ngluing of bundles
over quantum flag varieties with applications to quantum group\ncoherent s
tates and representation theory. A non-flat version of this technique\nis
under development. A basic series of examples is what I call\nuniversal no
ncommutative flag varieties (including Grassmannians)\,\nwhere no "quantum
" relations are imposed.\nVarious classical and quantum flag varieties app
ear as subvarieties. I will\npresent these the rationale behind these exam
ples and of gluing technique\nfor certain special covers. Main aim is to d
erive explicit cocycle describing\ncertain tautological bundle over a univ
ersal noncommutative Grassmannian\nleading to noncommutative double ratios
studied recently\nby Retakh\, Rubtsov and Sharygin.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tat Dat To (UPMC Paris VI)
DTSTART:20201118T103000Z
DTEND:20201118T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/18
DESCRIPTION:Title: Convergence of the Kähler-Ricci flow on varieties
of general type\nby Tat Dat To (UPMC Paris VI) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nWe study the Kähler-Ricci flow on varieties of general t
ype. We show that the normalized Kähler-Ricci flow exists at all times in
the sense of viscosity\, is continuous in an open Zariski set and converg
es to the singular Kähler-Einstein metric. This gives an answer to a ques
tion of Feldman-Ilmanen-Knopf.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfonso Tortorella (KU Leuven)
DTSTART:20210106T103000Z
DTEND:20210106T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/19
DESCRIPTION:Title: Deformations of symplectic foliations\nby Alfon
so Tortorella (KU Leuven) as part of Prague-Hradec Kralove seminar Cohomol
ogy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn this
talk\, based on joint work with Stephane Geudens and Marco Zambon\, I deve
lop the deformation theory of symplectic foliations\, i.e. regular foliati
ons equipped with a leaf-wise symplectic form. The main result is that eac
h symplectic foliation is attached with an $L_\\infty$ algebra controlling
its deformation problem. Indeed\, we establish a one-to-one correspondenc
e between the small deformations of a given symplectic foliation and the M
C elements of the associated $L_\\infty$ algebra. Further\, we prove that\
, under this one-to-one correspondence\, the equivalence by isotopies of s
ymplectic foliations agrees with the gauge equivalence of MC elements. Fin
ally\, we show that the infinitesimal deformations of symplectic foliation
s can be obstructed.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Can (Tulane University)
DTSTART:20201209T104500Z
DTEND:20201209T114500Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/20
DESCRIPTION:Title: Quotients of Classical Symmetric Spaces\nby Mah
ir Can (Tulane University) as part of Prague-Hradec Kralove seminar Cohomo
logy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn this
talk we will discuss some new and old results regarding the wonderful emb
eddings of classical complex symmetric spaces. More precisely\, we will in
troduce certain (non-arithmetic) quotients of classical symmetric spaces.
Then we will describe their combinatorial and geometric properties in rel
ation with their wonderful embeddings. Our running example will be on the
variety of nondegenerate quadrics.\n\nNB: Start time 15 later than usual.
Virtual coffee starts on Zoom already at 11:30 before the seminar.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Alexandrov (IBS\, Center for Geometry and Physics\, Poha
ng)
DTSTART:20201202T103000Z
DTEND:20201202T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/21
DESCRIPTION:Title: KP integrability of triple Hodge integrals\nby
Alexander Alexandrov (IBS\, Center for Geometry and Physics\, Pohang) as p
art of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, ph
ysics and statistics\n\n\nAbstract\nIn my talk I will describe a relation
between the Givental group of rank one and Heisenberg-Virasoro symmetry gr
oup of the KP integrable hierarchy. In particular I will show that only a
two-parameter family of the Givental operators can be identified with elem
ents of the Heisenberg-Virasoro symmetry group. This family describes trip
le Hodge integrals satisfying the Calabi-Yau condition. Using identificati
on of the elements of two groups it is possible to prove that the generati
ng function of triple Hodge integrals satisfying the Calabi-Yau condition
and its $\\Theta$-version are tau-functions of the KP hierarchy. This gene
ralizes the result of Kazarian on KP integrability in case of linear Hodge
integrals. I will also describe the relation of this family of tau-functi
ons with the generalized Kontsevich matrix model. My talk is based on two
papers\, arXiv:2009.01615 and arXiv:2009.10961.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Hajek (University Hamburg)
DTSTART:20201216T103000Z
DTEND:20201216T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/22
DESCRIPTION:Title: Chain models of string topology coming from symplec
tic geometry\nby Pavel Hajek (University Hamburg) as part of Prague-Hr
adec Kralove seminar Cohomology in algebra\, geometry\, physics and statis
tics\n\n\nAbstract\nI will recall loop spaces\, natural structures on thei
r homology and the relation to symplectic geometry of the cotangent bundle
(specifically to chain level structures defined by counting holomorphic c
urves). I will then zoom in on the equivariant case and a chain model base
d on de Rham forms and Chern-Simons theory. I will show some computations
and explain how this structure appears in various contexts.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Schenkel (University of Nottingham)
DTSTART:20210113T103000Z
DTEND:20210113T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/23
DESCRIPTION:Title: Boundary conditions and edge modes in gauge theorie
s\nby Alexander Schenkel (University of Nottingham) as part of Prague-
Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and stat
istics\n\n\nAbstract\nThe fields of a classical gauge theory form a smooth
groupoid (aka stack) with morphisms given by gauge transformations. From
this perspective\, the concept of "equality" of two gauge fields $A$ and $
A'$ is not a property but rather additional data given by the choice of a
gauge transformation $A \\to A'$ which witnesses that $A$ and $A'$ are "th
e same". In this talk\, I will explain how this higher-categorical point o
f view is useful to study gauge theories on manifolds with boundaries and
defects. In particular\, I will show that the additional data witnessing b
oundary conditions are precisely the famous edge modes from physics. As ex
amples\, I will discuss 3d Abelian Chern-Simons theory on manifolds with b
oundary\, which is physically describing the quantum Hall system\, and als
o the 4d holomorphic Chern-Simons theory of Costello and Yamazaki where th
e edge modes on surface defects determine 2d integrable field theories.\n\
nThis talk is based on arXiv:19
07.10651 and arXiv:2008.018
29.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilderich Tuschmann (Karlsruhe Institute of Technology)
DTSTART:20210224T103000Z
DTEND:20210224T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/24
DESCRIPTION:Title: (MODULI) SPACES OF RIEMANNIAN METRICS\nby Wilde
rich Tuschmann (Karlsruhe Institute of Technology) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nConsider a smooth manifold with a Riemannian metric satis
fying some sort of curvature constraint like\, for example\, positive scal
ar curvature\, non-negative Ricci or negative sectional curvature\, being
Einstein\, Kähler\, Sasaki\, etc. A natural question to study is then wha
t the space of all such metrics does look like. Moreover\, one can also po
se this question for corresponding moduli spaces of metrics\, i.e.\, quoti
ents of the former by (suitable subgroups of) the diffeomorphism group of
the manifold\, acting by pulling back metrics.\n\nThese spaces are customa
rily equipped with the topology of smooth convergence on compact subsets a
nd the quotient topology\, respectively\, and their topological properties
then provide the right means to measure 'how many' different metrics and
geometries the given manifold actually does exhibit\; but one can topologi
ze and view those also in very different manners.\n\nIn my talk\, I will r
eport on some general results and open questions about spaces and moduli s
paces of metrics with a focus on non-negative Ricci or sectional curvature
as well as other lower curvature bounds on closed and open manifolds\, an
d\, in particular\, also discuss broader non-traditional approaches from m
etric geometry and analysis to these objects and topics.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Gregorovic (University Hradec Kralove)
DTSTART:20210317T103000Z
DTEND:20210317T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/26
DESCRIPTION:Title: First BGG operators on homogeneous parabolic geomet
ries\nby Jan Gregorovic (University Hradec Kralove) as part of Prague-
Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and stat
istics\n\n\nAbstract\nI will briefly review the theory of BGG operators on
parabolic geometries and show\, how to construct and find (normal) soluti
ons of first BGG operators on homogeneous parabolic geometries\, in detail
. In particular\, such a solution can be obtained by purely algebraic comp
utations and using representation theory. This simplifies a construction o
f examples of BGG operators on nonflat homogeneous parabolic geometries ad
mitting nontrivial solutions\, which otherwise appear only rarely in the l
iterature. I will present one of such examples in CR geometry with nontriv
ial solutions for subriemannian metrizability among others.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART:20210324T103000Z
DTEND:20210324T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/27
DESCRIPTION:Title: Reduction cohomology on complex manifolds\nby A
lexander Zuevsky (Institute of Mathematics of the Czech Academy of Science
s) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\n\nAbstract\nDeveloping ideas of classical w
ork of Feigin\, and its development by Wagemann\,\nand proceed with a gene
ralization of ideas of above works. We describe the\nnotion of a cohomolog
y theory of infinite formal series with non-commutative\nmodes and localiz
ation of variables on Riemann surfaces\, constructed via\ncharacteristic f
unctions reduction formulas. We will mention algebraic\nconditions leading
to chain property of complexes for characteristic functions\,\nand repres
ent further restrictions on modular form coefficients in reduction formula
s.\nRelations of reduction cohomologies to analytic continuations of Knizh
nik-Zamolodchikov\nequations as well as an example of application of Bott-
Segal theorem will also be mentioned.\nJacobi forms case example will be c
onsidered.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgy Sharygin (Moscow State University Lomonosov)
DTSTART:20210331T093000Z
DTEND:20210331T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/28
DESCRIPTION:Title: Around the noncommutative cross ratio\nby Georg
y Sharygin (Moscow State University Lomonosov) as part of Prague-Hradec Kr
alove seminar Cohomology in algebra\, geometry\, physics and statistics\n\
n\nAbstract\nThe cross-ratio of four points on a projective line is one of
the most important projective invariants\, which finds most unexpected ap
plications throughout Mathematics from Geometry and Topology to the Integr
able systems theory. I will tell\, how one can widen the domain on which t
his invariant is defined so as to allow one consider "projective lines" ov
er noncommutative field. It turns out that there is an approach\, which al
lows one find such generalization so that most of important properties of
the cross ratio are preserved. Study of this new object is an interesting
new problem. Based on joint work with V.Retakh and V.Rubtsov.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck\, Austria)
DTSTART:20210407T093000Z
DTEND:20210407T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/29
DESCRIPTION:Title: The de Finetti theorem in categorical probability\nby Tobias Fritz (University of Innsbruck\, Austria) as part of Prague-
Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and stat
istics\n\n\nAbstract\nWhile probability theory is traditionally based on m
easure theory and Kolmogorov's axioms as a foundation\, the recently prop
osed formalism of Markov categories constitutes a potential alternative ap
proach in which a (modest) number of classical theorems of probability and
statistics have already been reproduced and generalized. In this talk\, I
will introduce this approach and illustrate its utility by providing a st
atement and proof of the classical de Finetti theorem in entirely abstract
categorical terms without measure theory. Based on joint work with Tomá
š Gonda\, Paolo Perrone and Eigil Rischel.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/2
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Benini (University of Genoa)
DTSTART:20210414T093000Z
DTEND:20210414T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/30
DESCRIPTION:Title: Smooth 1-dimensional algebraic quantum field theori
es\nby Marco Benini (University of Genoa) as part of Prague-Hradec Kra
love seminar Cohomology in algebra\, geometry\, physics and statistics\n\n
\nAbstract\nAlgebraic quantum field theory (AQFT) axiomatizes quantum fiel
d theories (QFTs) as functors A assigning to each spacetime M an algebra A
(M)\, interpreted as the algebra of observables of a QFT over the spacetim
e M. To support this physical interpretation\, certain physical axioms are
imposed on the functors A. None of these axioms\, however\, addresses the
following physically desirable feature: given a "smooth" family M_s of sp
acetimes\, the family of algebras of observables A(M_s) should depend "smo
othly" on the parameter s in an appropriate sense. (Speaking even more loo
sely\, a "mild variation" of the geometry of spacetime should determine a
"mild variation" of the algebra of observables.) The purpose of this talk
is to present a framework\, based on stacks of categories\, that allows fo
r the smooth refinement of AQFTs mentioned above. To illustrate this frame
work\, we will explore in detail the case of smooth 1-dimensional AQFTs. (
Based on arXiv:2010.13808 [math-ph].)\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Reiterer (Berner Fachhochschule\, Switzerland)
DTSTART:20210421T093000Z
DTEND:20210421T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/31
DESCRIPTION:Title: Filtered expansions in general relativity\nby M
ichael Reiterer (Berner Fachhochschule\, Switzerland) as part of Prague-Hr
adec Kralove seminar Cohomology in algebra\, geometry\, physics and statis
tics\n\n\nAbstract\nI will review the BKL (Belinskii-Khalatnikov-Lifshitz)
proposal for singularities in general relativity\, for spatially homogene
ous and spatially inhomogeneous spacetimes. Then I will discuss a construc
tion of formal power series solutions\, for one BKL bounce\, which is a bu
ilding block for the BKL proposal. I will in particular highlight the alge
braic tools that we use\, namely Maurer-Cartan perturbation theory and a f
iltration that organizes the calculations. Joint with Eugene Trubowitz\, s
ee arXiv:1905.09026 and arXiv:2005.03390.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémie Joudioux (Albert Einstein Institute\, Golm)
DTSTART:20210428T093000Z
DTEND:20210428T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/32
DESCRIPTION:Title: Hertz potentials and the decay of higher-spin field
s\nby Jérémie Joudioux (Albert Einstein Institute\, Golm) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\n\nAbstract\nThe purpose of the talk is to illustrate how
differential complexes can be used in relativity. Electromagnetism and li
nearized gravity (more generally higher-spin fields) are governed by hyper
bolic systems of partial differential equations. Solutions to these system
s can be generated by the mean of potentials (here\, Hertz potentials) sat
isfying a wave equation. It is possible to recast the problem of represent
ing a solution to these higher-spin fields by Hertz potentials in the cont
ext of the initial value problem. Initial data for higher-spin fields sati
sfy constraint equations\, and cannot be chosen freely. The integrability
conditions for these constraints are described by elliptic complexes. Thes
e elliptic complexes also happen to be those describing the relation betwe
en initial data for higher-spin fields and those for their Hertz potential
s. The problem of describing the asymptotic behavior of generic solutions
to higher-spin fields can then be completely deduced from the asymptotic b
ehavior of solutions to the scalar wave equations on flat spacetime.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART:20210310T103000Z
DTEND:20210310T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/33
DESCRIPTION:Title: Diffeological statistical models and diffeological
Hausdorff measures\nby Hong Van Le (Institute of Mathematics of the Cz
ech Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn my ta
lk I shall first explain the concept of diffeological spaces intr
oduced by Souriau. Then I shall explain how to use this concept
to endow natural smooth structures on subsets of probability measures
on an arbitrary measurable space. I shall discuss the concept o
f the diffeological Fisher metric and the resulting notion of the diffe
ological Hausdorff measure that are categorically natural\, and mea
ningful for statistical estimations used in statistical physics and dat
a analysis.\n \n My talk is based on my paper and my joint paper with Alexei Tuzhilin.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Francoise (Sorbonne Université\, Paris)
DTSTART:20210505T093000Z
DTEND:20210505T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/34
DESCRIPTION:Title: Information Geometry and Hamiltonian Systems on Lie
Groups\nby Jean-Pierre Francoise (Sorbonne Université\, Paris) as pa
rt of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phy
sics and statistics\n\n\nAbstract\nThe link between Hamiltonian Integrable
Systems and Information Geometry was discovered by Amari\, Fujiwara and N
akamura (90s). In particular\, Nakamura succeeded to define the tau-functi
on for the open Toda Lattice by using Information Geometry .\n\nWe propose
a more general study of Hamiltonian Systems related with the Information
Geometry on Lie groups.\n\nFisher-Rao semi-definite metric is naturally in
duced as a left-invariant semi-definite metric on the Lie group\, which is
regarded as the parameter space of the family of probability density func
tions. For a specific choice of family of probability density functions on
compact semi-simple Lie group\, the equation for the geodesic flow is der
ived through the Euler-Poincaré reduction. Certain perspectives are menti
oned about the geodesics equation on the basis of its similarity with the
Bloch-Brockett –Ratiu double bracket equation and with the Euler-Arnol'd
equation for a generalized free rigid body dynamics.\n\nThis is a joint w
ork with Daisuke Tarama (Ritsumeikan University).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Santi (UiT The Artic University of Norway)
DTSTART:20210512T093000Z
DTEND:20210512T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/35
DESCRIPTION:Title: $G(3)$ supergeometry and a supersymmetric extension
of the Hilbert-Cartan equation\nby Andrea Santi (UiT The Artic Univer
sity of Norway) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\n\nAbstract\nI will report on t
he realization of the simple Lie superalgebra $G(3)$ as supersymmetry of v
arious geometric structures – most importantly super-versions of the Hil
bert–Cartan equation and Cartan’s involutive PDE system that exhibit $
G(2)$ symmetry – and compute\, via Spencer cohomology groups\, the Tanak
a-Weisfeiler prolongation of the negatively graded Lie superalgebras assoc
iated with two particular choices of parabolics. I will then discuss non-h
olonomic superdistributions with growth vector $(2|4\, 1|2\, 2|0)$ obtaine
d as super-deformations of rank 2 distributions in a 5-dimensional space\,
and show that the second Spencer cohomology group gives a binary quadric\
, thereby providing a “square-root” of Cartan’s classical binary qua
rtic invariant for $(2\, 3\, 5)$-distributions. If time allows\, I will ou
tline an extension of Tanaka’s geometric prolongation scheme to the case
of supermanifolds. This is a joint work with B. Kruglikov and D. The.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kotaro Kawai (Gakushuin University\, Tokyo)
DTSTART:20210519T093000Z
DTEND:20210519T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/36
DESCRIPTION:Title: Deformed Donaldson-Thomas connections\nby Kotar
o Kawai (Gakushuin University\, Tokyo) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstr
act\nThe deformed Donaldson-Thomas (dDT) connection is a Hermitian connect
ion of a Hermitian line bundle over a $G_2$-manifold satisfying certain no
nlinear PDEs. This is considered to be the mirror of a calibrated (associa
tive) submanifold via mirror symmetry. As the name indicates\, the dDT con
nection can also be considered as an analogue of the Donaldson-Thomas conn
ection ($G_2$-instanton).\n\nIn this talk\, after reviewing these backgrou
nds\, I will show that dDT connections indeed have properties similar to a
ssociative submanifolds and $G_2$-instantons. I would also like to present
some related problems. This is joint work with Hikaru Yamamoto.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Zima (Charles University)
DTSTART:20210526T093000Z
DTEND:20210526T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/37
DESCRIPTION:Title: Symmetry\, holonomy and special geometries\nby
Petr Zima (Charles University) as part of Prague-Hradec Kralove seminar Co
homology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nVar
ious types of geometrical structures can be described via their so called
structure group. This becomes especially apparent when studying homogeneou
s spaces. Those spaces are of the form G/H where G is a transitive symmetr
y group and H is the isotropy subgroup which plays the role of structure g
roup. A natural question is to ask whether we can enlarge or reduce the st
ructure group while preserving the geometrical structure. Particular answe
r is given by the notion of holonomy that provides the smallest possible s
tructure group H. We will review these notions and demonstrate them by exa
mples of special Riemannian geometries.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Martel-Tordjman (University of Burgundy)
DTSTART:20211006T093000Z
DTEND:20211006T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/38
DESCRIPTION:Title: Modules of quantized Lie algebras and their braidin
g from homology of configuration spaces\nby Jules Martel-Tordjman (Uni
versity of Burgundy) as part of Prague-Hradec Kralove seminar Cohomology i
n algebra\, geometry\, physics and statistics\n\n\nAbstract\nFrom any semi
-simple Lie algebra\, Drinfel'd has defined an associated quantized versio
n called a quantum group. The theory of modules over quantum groups has be
en widely used to produce topological invariants in low dimension such as:
braid groups representations\, the famous Jones polynomial for knots or t
opological quantum field theories à la Witten--Reshetikhin--Turaev (provi
ding representations of mapping class groups of surfaces expected to have
rich properties and 3-manifold invariants).\nAll these constructions rely
on the algebraic background surrounding quantum groups so that their topol
ogical content is often mysterious in the end\, and finally the subject of
many conjectures in this field called quantum topology.\nWe are able to r
ecover quantum groups modules from homology of configuration spaces\, and
it gives a homological model for quantum braid group representations and k
not invariants such as the ones arising from the Jones family.\n\nIn this
talk I'll present in details how to recover the sl_2 case: quantum Verma m
odules and their braiding\, from homology of configuration spaces.\nIf I h
ave time I'll say a few words on how to generalize this to every semi-simp
le Lie algebra (which is a joint work in progress with S. Bigelow)\, and h
ow it sheds light on the topological content of Jones invariants of knots.
\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Borovoi (Tel Aviv University)
DTSTART:20211013T093000Z
DTEND:20211013T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/39
DESCRIPTION:Title: Using second Galois cohomology to search for a real
point in a real homogeneous space\nby Mikhail Borovoi (Tel Aviv Unive
rsity) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, ge
ometry\, physics and statistics\n\n\nAbstract\nLet G be a real algebraic g
roup and Y be its real homogeneous space\, say an orbit of the complex gro
up G(C)\, stable under the complex conjugation\, in a linear representatio
n of G. We wish to find a real point in Y or to prove that Y contains no r
eal points. We arrived at this problem when classifying trivectors on R^9.
I will explain a method of solving it using second (nonabelian) Galois co
homology.\n\nNo preliminary knowledge of Galois cohomology (first or secon
d\, abelian or nonabelian) is assumed.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/3
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaoru Ono (RIMS\, Kyoto)
DTSTART:20211020T093000Z
DTEND:20211020T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/40
DESCRIPTION:Title: An approach to the construction of virtual fundamen
tal cycle/chain with integer coefficients\nby Kaoru Ono (RIMS\, Kyoto)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry
\, physics and statistics\n\n\nAbstract\nAround 2000\, Kenji Fukaya and I
proposed the construction of \nvirtual fundamental cycle/chais with intege
r coeffients under the condition that \nthe moduli spaces carry consistent
(relative) stable complex structures. Starting with\nthe construction o
f virtual fundamental cycle/chains with rational coefficents\, \nI will ex
plain our ideas for the construction with integer coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Magnot (University d'Angers\, France)
DTSTART:20211027T093000Z
DTEND:20211027T103000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/41
DESCRIPTION:Title: On the differential geometry of groups of diffeomor
phisms and of non-formal pseudo-differential operators\nby Jean-Pierre
Magnot (University d'Angers\, France) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstr
act\nAfter reviewing a class of infinite dimensional groups based on the c
entral extension of a group of diffeomorphisms by a group of pseudo-differ
ential operators (PDOs)\, I will explain:\n\n1) how the action of the grou
p of diffeomorphisms generates the dressing operator of a KP hierarchy\, w
hich is shown to be well-posed in a class of NON FORMAL PDOs\n\n2) How ren
ormalized traces enables to define pseudo-Riemannian metrics on some of th
ese groups of PDOs\, different from the classical sobolev metrics present
in the literature\n\n3) how the geodesic equation of one of these metrics
admit an infinite number of independent integrals of the motion\n\nPart o
f the results of this talk are obtained from works in collaboration with E
nrique G. Reyes. Arxiv identifiers of related publications/preprints are:
2104.08159 \; 2007.00387 \; 1808.03791 and 1407.1427\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur J. Parzygnat (IHES\, Paris)
DTSTART:20211103T103000Z
DTEND:20211103T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/42
DESCRIPTION:Title: A categorical approach to quantum probability\n
by Arthur J. Parzygnat (IHES\, Paris) as part of Prague-Hradec Kralove sem
inar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstra
ct\nRecent advances in categorical probability theory suggest ideas on how
to make inference in quantum mechanics. I will focus on two cases\, which
are Bayesian updating and disintegrations. Bayesian updating can be viewe
d as an algorithm for making decisions or guesses based on evidence. Disin
tegrations are special cases and are closely related to conditional expect
ations and error correction in classical and quantum computation. This wil
l be an introduction to the subject\, and I will give many examples.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Alekseevsky (Institute for Information Transmission Problem
s\, Moscow)
DTSTART:20211110T103000Z
DTEND:20211110T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/43
DESCRIPTION:Title: Shortest and straightest geodesics in sub-Riemannia
n geometry\nby Dmitri Alekseevsky (Institute for Information Transmiss
ion Problems\, Moscow) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe present
a short introduction to sub-Riemannian geometry\, concentrating\non the va
rious definitions of sub-Riemannian geodesics and their relationships.\nE.
Herz remark that there are two main characterisations of geodesics in\nRi
emannian geometry: geodesics as shortest curves\, based on the Mopertrui's
\nprinciple of least action ( variational approach ) and\ngeodesics as str
aightest curves based on d'Alembert's principle of virtual\nwork.\n\nThese
lead to different\, but equivalent definitions of geodesics in Riemannian
\ngeometry. These definitions can be generalized to sub-Riemannian geometr
y\,\nbut they become non equivalent. We consider 3 definitions of sub-Riem
annian\ngeodesics as shortest curves (Euler-Lagrange\, Hamilton and Pontry
agin)\,\nwhich mostly used in control theory and 3 definitions of geodesic
s as straightest\ncurves (d'Alembert \, Levi-Civita-Schouten and Cartan-Ta
naka-Morimoto )\,\nused in nonholonomic mechanics. We discuss relationship
between geodesicsof different types.\nGeneralising R. Montgomery result\,
we consider a class of sub-Riemannian\nmetrics on the total space P of th
e principal bundle π : P → M = P/G\nover a Riemannian manifold M with a
principal connection ( the Chaplygin\nsystems)\, where shortest geodesics
consistent with straightest geodesics. This\nis an extension of the first
example by L. D. Faddeev and A.M. Vershik.\nIt gives a partial answer on
their question about characterization of\nsub-Riemannian manifolds with th
is property.\n\nUsing the geometry of flag manifolds\, we describe some cl
asses of compact\nhomogeneous sub-Riemannian manifolds ( including contact
sub-Riemannian\nmanifolds and symmetric sub-Riemannian manifolds ) where
straightest geodesics\ncoincides with shortest geodesics. Construction of
geodesics in these cases\nreduces to description of Riemannian geodesics o
f the Riemannian homogeneous\nmanifold.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ha Quang Minh (RIKEN Institute\, Tokyo)
DTSTART:20211124T103000Z
DTEND:20211124T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/44
DESCRIPTION:Title: Regularized information geometric and optimal trans
port distances between covariance operators and Gaussian processes\nby
Ha Quang Minh (RIKEN Institute\, Tokyo) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbs
tract\nInformation geometry (IG) and Optimal transport (OT) have been attr
acting much research attention in various fields\, in particular machine l
earning and statistics. In this talk\, we present results on the generaliz
ation of IG and OT distances for finite-dimensional Gaussian measures to t
he setting of infinite-dimensional Gaussian measures and Gaussian processe
s. Our focus is on the Entropic Regularization of the 2-Wasserstein distan
ce and the generalization of the Fisher-Rao distance and related quantitie
s. In both settings\, regularization leads to many desirable theoretical p
roperties\, including in particular dimension-independent convergence and
sample complexity. All of the presented formulations admit closed form exp
ressions that can be efficiently computed and applied practically.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Kruglikov (University of Tromsø)
DTSTART:20211201T103000Z
DTEND:20211201T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/45
DESCRIPTION:Title: Relative Differential Invariants\nby Boris Krug
likov (University of Tromsø) as part of Prague-Hradec Kralove seminar Coh
omology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nRela
tive invariants help to understand singularities of group actions on manif
olds. Their weights are cocycles modulo coboundaries and thus correspond t
o the first Gelfand-Fuks cohomology. Relative differential invariants corr
espond to prolongation of the action to jet-spaces\, and are important in
the equivalence problem. I will discuss the weight lattice and the finiten
ess theorem for relative differential invariants.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Strobl (University of Lyon)
DTSTART:20211208T103000Z
DTEND:20211208T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/46
DESCRIPTION:Title: Morita equivalence of singular Riemannian foliation
s and I-Poisson geometry\nby Thomas Strobl (University of Lyon) as par
t of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phys
ics and statistics\n\n\nAbstract\nWe recall the notion of singular foliati
ons and show how to extend it in a compatible way to the presence of a Rie
mannian metric. Morita equivalence of such structures provides an equivale
nce relation on the geometry transverse to the leaves. Finally we extend
"coisotropic submanifolds of a Poisson manifold" to potentially singular s
ubspaces\, yielding what we call an I-Poisson structure\, and use this not
ion to construct an invariant of singular Riemannian foliations under the
above-mentioned Morita equivalence. \nThis is joint work in progress with
Hadi Nahari.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov (Dartmouth College)
DTSTART:20211215T103000Z
DTEND:20211215T113000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/47
DESCRIPTION:Title: Linking: causality and black holes\; and cosmic cen
sorship of smooth structures\nby Vladimir Chernov (Dartmouth College)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\
, physics and statistics\n\n\nAbstract\nTwo events in a spacetime are call
ed causally related if the information can get from one event point to the
other.\n \nIn the joint works with Stefan Nemirovski we established that
Legendrian linking of the spheres of light rays passing through the two po
ints completely determines causality for spacetimes of dimensions greater
or equal than 4. For the spaces times of dimension 3 causal structure is c
ompletely determined by topological linking.\n \nThese results settle the
conjectures of Robert Low and of Jose Natario and Paul Todd. They also giv
e an answer to the problem on the Vladimir Arnold problem list communicate
d by Roger Penrose.\n \nWe will discuss these results and some ideas about
how to apply the link theory to the study of black holes.\n \nIf time per
mits we will explain why exotic smooth structures are likely not useful in
general relativity\, since the natural physical assumption impose strong
censorship on the class of possible smooth structures on a spacetime and s
uch a structure is unique and natural.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pasha Zusmanovich (University Ostrava)
DTSTART:20220302T123000Z
DTEND:20220302T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/49
DESCRIPTION:Title: On Lie algebras in characteristic 2\nby Pasha Z
usmanovich (University Ostrava) as part of Prague-Hradec Kralove seminar C
ohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nI
will report on a small progress in ongoing classification efforts of simpl
e Lie algebras in characteristic 2. The main character is a certain 15-dim
ensional simple Lie algebra which appears as a deformation of a certain se
misimple Lie algebra with peculiar cohomological properties.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/4
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zuevsky (Institute of Mathematics of the Czech Academy o
f Sciences)
DTSTART:20220309T123000Z
DTEND:20220309T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/50
DESCRIPTION:Title: Lie algebra of operators on moduli space of Riemann
surfaces\nby Alexander Zuevsky (Institute of Mathematics of the Czech
Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe recall va
riational formulas for holomorphic elements on Riemann surfaces\nwith resp
ect to arbitrary local coordinates on the moduli space of complex structur
es.\nThese formulas are written in terms of a canonical element on the mo
duli space\nwhich corresponds to the pairing between the space of quadrati
c differentials and\nthe tangent space to the moduli space. Next\, we rec
all the notion of continual\nLie algebras introduced by Saveliev and Versh
ik and provide several classical examples.\nWe show that canonical differe
ntial operators on moduli space $\\mathcal M_{n\, 3g-3}$\nof Riemann surfa
ces form a continual Lie algebra with the base field given by domains\nof
points on $\\mathcal M_{n\, 3g-3}$\, where $n$ is the number of punctured
points.\nGeneral formulation of exactly solvable models associated to cont
inual Lie algebras\nwill be given. As an application\, we provide explicit
formulas for solutions to solvable equations.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART:20220316T123000Z
DTEND:20220316T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/51
DESCRIPTION:Title: CR-twistor spaces over manifolds with $G_2$ -and $S
pin(7)$-structures\nby Hong Van Le (Institute of Mathematics of the Cz
ech Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn 1984
LeBrun constructed a CR-twistor space over an arbitrary conformal Rie
mannian 3-manifold and proved that the CR-structure is formally integr
able. This twistor construction has been generalized by Rossi in
1985 for $m$-dimensional Riemannian manifolds endowed with a $(m-1)$-fo
ld vector cross product (VCP). In 2011 Verbitsky generalized LeBrun
's construction of twistor-spaces to $7$-manifolds endowed wit
h a $G$-structure. In my talk I shall explain how to unify and gene
ralize LeBrun's\, Rossi's and Verbitsky's construction of a CR-twi
stor space to the case where a Riemannian manifold $(M\, g)$
has a VCP structure. Then I shall show that the formal integrabili
ty of the CR-structure is expressed in terms of a torsion tensor on
the twistor space\, which is a Grassmanian bundle over $(M\, g)$. If
the VCP structure on $(M\,g)$ is generated by a $G_2$- or $Spin(7)$-struc
ture\, the "vertical" component of the torsion tensor vanishes\, if a
nd only if $(M\, g)$ has constant curvature\, and the "horizontal" compo
nent vanishes\, if $(M\,g)$ is a torsion-free $G_2$ or $Spin(7)$
-manifold. Finally I shall discuss related open problems. This is a joint
work with Domenico Fiorenza.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andras Stipsicz (Alfréd Rényi Institute of Mathematics\, Hungari
an Academy of Sciences)
DTSTART:20220323T123000Z
DTEND:20220323T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/52
DESCRIPTION:Title: Four-manifolds and knots\nby Andras Stipsicz (A
lfréd Rényi Institute of Mathematics\, Hungarian Academy of Sciences) as
part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\,
physics and statistics\n\n\nAbstract\nSlice knots (which bound a disk in t
he four-space) play important role both\nin knot theory and in smooth four
-dimensional topology. I will explain some of these\ncommon points\, recal
l a simple way to construct slice knots and focus on obstructions\nof slic
eness provided by knot Floer homology.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Krutov (Institute of Mathematics of the Czech Academy of Sc
iences)
DTSTART:20220330T113000Z
DTEND:20220330T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/53
DESCRIPTION:Title: Nondegenerate invariant symmetric bilinear forms on
simple Lie superalgebras in characteristic 2\nby Andrey Krutov (Insti
tute of Mathematics of the Czech Academy of Sciences) as part of Prague-Hr
adec Kralove seminar Cohomology in algebra\, geometry\, physics and statis
tics\n\n\nAbstract\nAs is well-known\, the dimension of the space spanned
by the non-degenerate invariant symmetric bilinear forms (NISes) on any si
mple finite-dimensional Lie algebra or Lie superalgebra is equal to at mos
t 1 if the characteristic of the algebraically closed ground field is not
2.\n\nWe prove that in characteristic 2\, the superdimension of the space
spanned by NISes can be equal to 0\, or 1\, or 0|1\, or 1|1\; it is equal
to 1|1 if and only if the Lie superalgebra is a queerification (defined in
arXiv:1407.1695) of a simple classically restricted Lie algebra with a NI
S (for examples\, mainly in characteristic distinct from 2\, see arXiv:180
6.05505).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stepan Hudecek (Charles University)
DTSTART:20220406T113000Z
DTEND:20220406T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/54
DESCRIPTION:Title: Symmetry and Separation of variables\nby Stepan
Hudecek (Charles University) as part of Prague-Hradec Kralove seminar Coh
omology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe p
resent a condition under which a differential operator on a two dimensiona
l manifold admits a so-called separated solution and the separation is non
-trivial in a sense\, that we explain. Along the way we "develop" definiti
ons in order to make these propositions precise\, such as of a symmetry ge
nerating an operator and of a function that does not depend on a set of va
riables with respect to a coordinate chart.\n\nWe are motivated by problem
s in Physics\, where the separation of variables is often used\, e.g.\, in
specific problems of electromagnetic waves\, quantum mechanics (hydrogen
atom)\, or in general relativity. In mathematical Physics the notion of s
eparation was studied in many works\, including the works of Kalnins\, Win
ternitz\, Miller and Koornwinder. In a part of the Physics literature\, th
e notion of the separation is studied without giving a definition of a sep
arated solution.\n\nIn mathematics\, more abstract versions of the separat
ion occurred in the works of Stackel\, Kostant\, and M. Eastwood. However\
, as far as we know\, no sufficient condition on the non-triviality of a s
eparated solution occurs in any of these works.\n\nThe talk is based on a
bachelor thesis of the speaker. Joint work with S. Krysl (Math. Inst.\, Ch
arles University).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Markl (Institute of Mathematics of the Czech Academy of Sci
ences)
DTSTART:20220413T113000Z
DTEND:20220413T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/55
DESCRIPTION:Title: Combinatorics of multilinear differential operators
\, or still another explanation of the ubiquity of Lie and strongly homoto
py Lie algebras\nby Martin Markl (Institute of Mathematics of the Czec
h Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nAs a motiva
tion\, we start with an analysis of the interplay between the classical Ja
cobi identity and differential operators\, and\ncompare it with the effect
of the associator. Moving to the `quantized' level\, we compare the natu
re of the big bracket and\nIBL(=infinitesimal Lie bialgebras)-infinity alg
ebras with Terilla's quantization of associative algebras.\nIn the second
part\, we introduce a filtration mimicking combinatorial properties of mul
tidifferential operators\, and\nthe associated notion of tight operads. W
e then come back to Lie algebras and give another reason why they deserve\
nto be\, along with commutative and associative algebras\, recognized as o
ne of the Three Graces.\n\nThe talk will be based on the paper "Calculus
of multilinear differential operators\, operator $L_\\infty$-algebras and
$IBL_\\infty$-algebras"\n of Denis Bashkirov and mine. Its preprint is av
ailable at\nhttps://arxiv.org/abs/2108.12158\, published version at https
://users.math.cas.cz/~markl/.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Leites (NYUAD and Stockholm U.)
DTSTART:20220420T113000Z
DTEND:20220420T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/56
DESCRIPTION:Title: Structures of G(2) type in super setting and in pos
itive characteristic\, and related curvature tensors\nby Dimitri Leite
s (NYUAD and Stockholm U.) as part of Prague-Hradec Kralove seminar Cohomo
logy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nCartan
and Killing described finite-dimensional simple Lie algebras (over fields
of real or complex numbers) in terms of the distributions they preserve. T
he technique of root system and Dynkin (Coxeter) graphs was discovered sev
eral decades later. Two o the four series of simple infinite-dimensional L
ie algebras of vector fields are Cartan prolongations of non-positive part
s of simple finite-dimensional Lie algebras. For any $\\mathbb{Z}$-grading
of any simple finite-dimensional Lie algebra $\\mathfrak{g}$ (bar the two
series of examples)\, the Cartan prolongation of the non-positive part of
$\\mathfrak{g}$ returns $\\mathfrak{g}$. This is not so for the exception
al Lie algebra $\\mathfrak{g}_2$ in characteristic 5\, whose Cartan prolon
gation is called Melikyan algebra. Recall that the Lie superalgebras appea
red not in high energy physics in 1970s\, but in topology\, and either ove
r $\\mathbb{Z}$ as super Lie rings\, or over finite fields. Lately\, modul
ar Lie (super)algebras became of interest due to their relation to quantum
groups. I intend to tell you about two modular Lie superalgebras construc
ted (together with S.Bouarroudj and P.Grozman) a la the Melikyan algebra.
I hope to have time to say how to compute the analogs of the curvature ten
sors in presence of non-integrable distribution these algebras preserve.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enxin Wu (Shantou University\, China)
DTSTART:20220427T113000Z
DTEND:20220427T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/57
DESCRIPTION:Title: Smooth vector spaces\nby Enxin Wu (Shantou Univ
ersity\, China) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\n\nAbstract\nVector spaces are
fundamental objects in mathematics. In practice\, \nvector spaces from fun
ctional analysis and vector bundle theory carry smooth \ninformation. In t
his talk\, I will present a general homology theory of such vector \nspace
s in the setting of diffeology. The connection to topological vector space
s \nand vector bundle theory will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem\, Isr
ael)
DTSTART:20220504T113000Z
DTEND:20220504T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/58
DESCRIPTION:Title: Every symplectic manifold is a (linear) coadjoint o
rbit\nby Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem\
, Israel) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nI will show that every s
ymplectic manifold is a (linear) coadjoint orbit of the group of automorph
isms of the integration bundle\, independently of the group of periods of
the symplectic form. This result generalizes the Kirilov-Kostant-Souriau t
heorem when the symplectic manifold is homogeneous under the action of a L
ie group and the symplectic form is integral.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willem de Graaf (University of Trento)
DTSTART:20220511T113000Z
DTEND:20220511T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/59
DESCRIPTION:Title: Classification of four qubit and rebit states\n
by Willem de Graaf (University of Trento) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAb
stract\nWe consider the problem of classifying the orbits of $SL(2\, \\mat
hbb{C})^4$ on the space\n$\\mathbb{C}^2 \\otimes \\mathbb{C}^2 \\otimes \\
mathbb{C}^2 \\otimes \\mathbb{C}^2$. In quantum information theory this is
known as the\nclassification of four qubit states under SLOCC operations.
We approach\nthe problem by constructing the representation via a symmetr
ic pair of max-\nimal rank. This makes it possible to apply the theory of
θ-representations\ndeveloped by Vinberg in the 70’s. The orbits are dev
ided into three types:\nnilpotent\, semisimple and mixed. The orbits of ea
ch type are classified sep-\narately. We also obtain the stabilizers of re
presentatives of the orbits. The\ntalk will end with some comments on the
same problem over R\, known as\nthe classification of four rebit states. T
his is joint work with Heiko Dietrich\,\nAlessio Marrani and Marcos Origli
a.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/5
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART:20221012T113000Z
DTEND:20221012T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/60
DESCRIPTION:Title: On non-geometric augmentations in high dimensions a
nd torsion of Legendrian contact homology\nby Roman Golovko (Charles U
niversity) as part of Prague-Hradec Kralove seminar Cohomology in algebra\
, geometry\, physics and statistics\n\n\nAbstract\nWe construct the augmen
tations of high dimensional Legendrian submanifolds of the contact Euclide
an vector space which are not induced by exact Lagrangian fillings. Beside
s that\, for an arbitrary finitely generated abelian group G\, we construc
t the examples of Legendrian submanifolds whose integral linearized Legend
rian contact (co)homology realizes G.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of the Czech Academy of Scie
nces)
DTSTART:20221019T113000Z
DTEND:20221019T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/61
DESCRIPTION:Title: Floer-Novikov (co)homology associated with non-abel
ian coverings and symplectic fixed points\nby Hong Van Le (Institute o
f Mathematics of the Czech Academy of Sciences) as part of Prague-Hradec K
ralove seminar Cohomology in algebra\, geometry\, physics and statistics\n
\n\nAbstract\nIn my talk I shall explain our with Kaoru Ono const
ruction of Floer-Novikov cohomology groups $HFN^* (M^{\\Gamma_\\xi \\
times H}\,\\xi\, Q)$ defined on a regular covering $M^{\\Gamma_\\xi \\time
s H}$ of a compact symplectic manifold $(M\, \\omega)$ with transfo
rmation group $\\Gamma_\\xi \\times H$ and associated to a locally
symplectic isotopy ${\\{\\varphi_t\\}}$ of $(M\, \\omega)$ with flux $\\
xi \\in H ^1 (M\, R)$. Then $H$ acts naturally on $HFN^* (M^{\\Gamma_\\xi
\\times H}\,\\xi\, Q)$. For a subgroup $G \\subset H$ denote by $(HFN^
* (M^{\\Gamma_\\xi \\times H}\,\\xi\, Q))^G$ the subgroup of $HFN^* (M
^{\\Gamma_\\xi \\times H}\, \\xi\, Q)$ consisting of the fixed points
of the $G$-action. We prove that the rank of $(HFN^* (M ^{\\Gamma_
\\xi \\times H}\,\\xi\, Q))^G$ equals the rank of the subgroup
$(HN^* (M^{\\Gamma_\\xi \\times H}\, Q))^G$ of the fixed points of the
$G$-action in the Novikov cohomology group $HN^* (M^{\\Gamma_\\xi \\ti
mes H}\, \\Q)$. If $H$ is trivial\, this implies our previous resul
t asserting that the sum of the Betti numbers of $HFN^* (M ^{\\Gamm
a_\\xi}\, \\xi\, Q)$ equals the sum of the Betti numbers of the Noviko
v cohomology group $HN_* (M\, \\xi\, Q)$. This equality leads to th
e classical cohomological estimate of the numbers of the fixed poin
ts of a nondegenerate locally Hamiltonian symplectomorphism. If $H$
is nontrivial\, we obtain a new lower bound for the number of the
fixed points of non-degenerate locally Hamiltonian symplectomorphis
ms of $(M\, \\omega)$.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Magnot (University d'Angers\, France)
DTSTART:20221026T113000Z
DTEND:20221026T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/62
DESCRIPTION:Title: On some diffeologies on spaces of probabilities\, s
paces of measures\, and spaces of means\nby Jean-Pierre Magnot (Univer
sity d'Angers\, France) as part of Prague-Hradec Kralove seminar Cohomolog
y in algebra\, geometry\, physics and statistics\n\n\nAbstract\nPassing fr
om probabilities to finite measures\, from finite measures to measures\, a
nd from measures to infinite dimensional integrals\,we develop examples of
diffeologies on each of these classes of spaces\, partially from works of
the author\, and partially from other approaches in the existing literatu
re. The highlighted spaces include finite and infinite configurations\, Mo
nte-carlo sequences\, Radon measures\, Haar and Lebesgue integrals in the
space of connections\, and an infinite dimensional Lebesgue mean. The high
lighted diffeologies include functional diffeology\, vague diffeology\, th
e Cauchy diffeology and pro-finite diffeologies. The exposition intends to
give a rigorous differential geometric setting for some actual different
ial geometry related to probability and integration theory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foling Zou (University of Michigan)
DTSTART:20221102T123000Z
DTEND:20221102T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/63
DESCRIPTION:Title: Steenrod Algebra and Equivariant Algebraic Topology
\nby Foling Zou (University of Michigan) as part of Prague-Hradec Kral
ove seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\
nAbstract\nSteenrod algebra give stable cohomology operations.\nNon-equiva
riantly\, the dual Steenrod algebra spectrum is a wedge of\nsuspensions of
HZ/p. It is explicitly computed and fundamental in a lot of\ncomputations
in algebraic topology. Consider the equivariant\nEilenberg–Maclane spec
tra H = HZ/p for the cyclic group of order p. I will\ntalk about the compu
tation of the dual Steenrod algebra of H. It turns out\nthat when p is odd
\, H ∧ H is a wedge of suspensions of H and another\nspectrum\, which we
call HM. This is joint work with Po Hu\, Igor Kriz\, and\nPetr Somberg\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Landi (Pennsylvania State University)
DTSTART:20221109T123000Z
DTEND:20221109T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/64
DESCRIPTION:Title: The Topological Half of the Grothendieck-Hirzebruch
-Riemann-Roch Theorem\nby Eugenio Landi (Pennsylvania State University
) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometr
y\, physics and statistics\n\n\nAbstract\nThe HRR theorem famously states
that the holomorphic Euler characteristic of $X$ with coefficients in a ho
lomorphic vector bundle $V$ equals $\\int_X ch(V)td(X)$. This can be rewri
tten as two theorems: the first one\, analytical\, identifying $\\chi(X\,V
)$ with the K-theoretic pushforward of $V$ to the point\, while the second
\, purely topological\, identifying the pushforward with the integral. The
same can be said for the GHRR theorem and pushforwards along proper holom
orphic maps between holomorphic manifolds. I will focus on the second half
\, introducing orientations and pushforwards in cohomology and explaining
how the presence of the Todd class is natural and expected.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lambie-Hanson (Institute of Mathematics of the Czech Academy
of Sciences)
DTSTART:20221116T123000Z
DTEND:20221116T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/65
DESCRIPTION:Title: Condensed mathematics and set theory\nby Chris
Lambie-Hanson (Institute of Mathematics of the Czech Academy of Sciences)
as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\
, physics and statistics\n\n\nAbstract\nRecently\, Clausen and Scholze ini
tiated the study of condensed mathematics\, providing a framework in which
to do algebra in situations in which the algebraic structures under consi
deration also carry topological information. The fundamental idea is to re
place the categories of topological spaces or topological abelian groups\,
which are poorly behaved algebraically\, with the more algebraically robu
st categories of condensed sets or condensed abelian groups. In this talk\
, we will give a very brief introduction to condensed mathematics and sket
ch a couple of very basic applications of set theoretic techniques to foun
dational questions therein. Time permitting\, we will also briefly touch o
n related applications of these set theoretic ideas to other topics in hom
ological algebra.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Pacini (University of Torino\, Italy)
DTSTART:20221130T123000Z
DTEND:20221130T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/67
DESCRIPTION:Title: G2 vs. Kähler\nby Tommaso Pacini (University o
f Torino\, Italy) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\n\nAbstract\nWe shall compare
two categories of manifolds\, known as G2 and Kahler\, focusing on (i) th
eir submanifold geometry\, (ii) their function theory. We shall also discu
ss interactions between these topics. The talk is intended for a general a
udience.\nIn particular\, we shall survey results in the preprints arXiv:2107.14117\, arXiv:2207.13956\, arXiv:2208.12535\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florio Ciaglia (Universidad Carlos III de Madrid)
DTSTART:20221214T123000Z
DTEND:20221214T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/68
DESCRIPTION:Title: Jordan algebras\, coadjoint orbits\, and informatio
n geometry\nby Florio Ciaglia (Universidad Carlos III de Madrid) as pa
rt of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phy
sics and statistics\n\n\nAbstract\nThe purpose of this talk is to present
a connection between the mathematical entities mentioned in the title. It
will be argued that Jordan algebras provide a suitable playground in which
parametric models of classical and quantum information geometry can joyfu
lly play (and hopefully thrive). In order to recover the Riemannian geomet
ry of parametric models extensively used in classical and quantum informat
ion geometry\, the method of coadjoint orbits will be adapted to Jordan al
gebras. Indeed\, given the symmetric nature of the Jordan product\, the an
alogue of the Konstant-Kirillov-Souriau symplectic form becomes a symmetri
c covariant tensor field. When suitable choices of Jordan algebras are mad
e\, it is possible to recover the Fisher-Rao metric tensor characteristic
of classical information geometry or the Bures-Helstrom metric tensor appe
aring in quantum information geometry. This instance tells us that geometr
ical structures in information geometry can be found looking at algebraic
structures associated with Jordan algebras. The discussion will focus only
on the finite-dimensional case\, but questions and comments on the possib
ility of extending the results in infinite dimensions are welcome.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hoang Duc Luu (Max-Planck-Institute for Mathematics in Sciences\,
Leipzig)
DTSTART:20230104T123000Z
DTEND:20230104T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/69
DESCRIPTION:Title: Ergodicity of dynamical systems under stochastic no
ises\nby Hoang Duc Luu (Max-Planck-Institute for Mathematics in Scienc
es\, Leipzig) as part of Prague-Hradec Kralove seminar Cohomology in algeb
ra\, geometry\, physics and statistics\n\n\nAbstract\nIn this talk i am go
ing to present how to construct and prove the ergodicity of a metric dynam
ical system\, from which one can generate a stochastic flow such as a rand
om dynamical system. Such topic appears when one attempts to study the lon
g term behavior of a dynamical system under stochastic noises\, for instan
ce stochastic differential equations. We would like to consider the proble
m w.r.t different types of calculus used to solve the equations\, like Ito
or rough path theory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/6
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Salnikov (La Rochelle University\, France)
DTSTART:20221207T123000Z
DTEND:20221207T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/70
DESCRIPTION:Title: Some constructions from graded geometry\nby Vla
dimir Salnikov (La Rochelle University\, France) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\
n\n\nAbstract\nIn this talk I introduce some natural constructions from th
e "graded world"\, paying particular attention to the differences between
N- and Z- graded manifolds. I will start by the construction of the sheaf
of functions on graded manifolds and describe its structure. The intrinsic
properties of this functional space are conveniently given using the lang
uage of filtrations\, allowing to formulate the analog of Batchelor’s th
eorem. Afterwards I will briefly introduce graded Hopf algebras and Harish
-Chandra pairs\, which in turn provide the result of equivalence of catego
ries between graded Lie groups and algebras. These constructions are then
used to solve the integration problem of differential graded Lie algebras
to differential graded Lie groups. Time permitting\, I will also say a few
words on canonical forms of differential graded manifolds.\n\nThis talk i
s based on: \n\n[1] B. Jubin\, A. Kotov\, N. Poncin\, V. Salnikov\, Diffe
rential graded Lie groups and their differential graded Lie algebras\, Transformation Groups\,
27\, 2022\n\n[2] A. Kotov\, V. Salnikov\, The category of Z-graded man
ifolds: what happens if you do not stay positive\, Preprint: arXiv:2108.13496\n\n[3] A. Kotov\, V. Sa
lnikov\, Various instances of Harish-Chandra pairs\, Preprint: arXiv:2207.07083\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Temkin (Dartmouth College)
DTSTART:20230111T123000Z
DTEND:20230111T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/72
DESCRIPTION:Title: On numbers associated with a strong Morse function<
/a>\nby Misha Temkin (Dartmouth College) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbs
tract\nMorse function on a manifold $M$ is called strong if all its critic
al points have different critical values. Given a strong Morse function $f
$ and a field $F$ we construct a bunch of elements of $F$\, which we call
Bruhat numbers (they're defined up to sign). More concretely\, Bruhat numb
er is written on each bar in the barcode of $f$ (a.k.a. Barannikov decompo
sition). It turns out that if homology of $M$ over $F$ is that of a sphere
\, then the product of all the numbers is independent of $f$. We then cons
truct the barcode and Bruhat numbers with twisted (a.k.a. local) coefficie
nts and prove that the mentioned product equals the Reidemeister torsion o
f $M$. In particular\, it's again independent of $f$. This way we link Mor
se theory to the Reidemeister torsion via barcodes. Time permitting\, we w
ill also discuss how parametric Morse theory comes into play. Based on a j
oint work with Petya Pushkar\, https://arxiv.org/abs/2012.05307\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arman Taghavi-Chabert (Warsaw University)
DTSTART:20230222T123000Z
DTEND:20230222T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/73
DESCRIPTION:Title: Perturbations of Fefferman’s conformal structures
\nby Arman Taghavi-Chabert (Warsaw University) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nIn 1976\, Charles Fefferman constructed\, in a canonical
way\, a conformal structure of Lorentzian\nsignature on a circle bundle ov
er any given strictly pseudo-convex Cauchy-Riemann (CR) manifolds\nof hype
rsurface type.\n\nIt is also known\, notably through the work of Roger Pen
rose and his associates\, and of the Warsaw\ngroup led by Andrzej Trautman
\, that CR three-folds underlie four-dimensional Einstein Lorentzian\nmetr
ics whose Weyl tensors are said to be algebraically special.\n\nIn this ta
lk\, I will show how these algebraically special Einstein metrics find a n
atural formulation as exact perturbations of Fefferman’s original constr
uction. The additional CR data required turns out to be constrained by a n
on-linear\, or gauged\, analogue of a second-order (BGG) differential oper
ator\, and is related to the existence of CR functions.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hông Vân Lê (Institute of Mathematics of the Czech Academy of S
ciences)
DTSTART:20230301T123000Z
DTEND:20230301T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/74
DESCRIPTION:Title: Complex reflection groups and classification of $3$
-forms in $R^9$ and of $4$-forms in $R^8$\nby Hông Vân Lê (Institut
e of Mathematics of the Czech Academy of Sciences) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nIn my talk I shall discuss the role of complex ref
lection groups in Vinberg-Elashvili's classification of 3-forms in $C^
9$\,\n Antonyan's classification of 4-forms in $C^8$ and Borovoi-De Gr
aaf-Lê's classification of 3-forms in $R^9$. \nI shall also explai
n the role of complex reflection groups in classification of 4-f
orms in $R^8$.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Pushkar (Higher School of Economics\, Moscow)
DTSTART:20230315T123000Z
DTEND:20230315T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/75
DESCRIPTION:Title: One parameter Morse theory and Morse theory for man
ifolds with boundaries\nby Petr Pushkar (Higher School of Economics\,
Moscow) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, g
eometry\, physics and statistics\n\n\nAbstract\nLet M be a compact manifol
d with boundary N and g be a generic germ of a function along N. I will e
xplain how one can estimate from below a number of critical points of Mors
e extension of g to a function on M. Construction lies in one parameter M
orse theory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Strakoš (Uppsala University)
DTSTART:20230329T113000Z
DTEND:20230329T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/76
DESCRIPTION:Title: Augmentations of Chekanov-Eliashberg Algebra and Ge
ography of Bilinearized Legendrian Contact Homology\nby Filip Strakoš
(Uppsala University) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe will star
t with a brief introduction to a relative version of symplectic field theo
ry (SFT) for Legendrian submanifolds in a particular class of contact mani
folds. This will provide us with Chekanov-Eliashberg differential graded a
lgebra (DGA)\, whose homology is an invariant of Legendrian isotopy. This
algebraic structure is difficult to compute and so we will simplify the di
fferential using (bi)linearization. Then we will sketch the proof of DGA-h
omotopy criterion for augmentations using a duality long exact sequence\,
which may be seen as a version of Poincare duality for this relative SFT.
We will mention the geometric origin of those augmentations coming from ex
act Lagrangian fillings of our Legendrian submanifold. If time permits\, w
e will show the application of the mentioned results to the question of ge
ography for bilinearized Legendrian contact homology of disconnected Legen
drian submanifolds in a one jet space\, which is a generalization of work
of Bourgeois and Galant for the connected case.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svatopluk Krysl (Charles University)
DTSTART:20230405T113000Z
DTEND:20230405T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/77
DESCRIPTION:Title: Twistor complexes in symplectic geometry\nby Sv
atopluk Krysl (Charles University) as part of Prague-Hradec Kralove semina
r Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract\
nFor a manifold with a vanishing second Stiefel--Whitney class and equippe
d with a symplectic form\, it is possible to define the so-called symplect
ic spinor bundle (B. Kostant) that is a parallel notion to the spinor bund
le on a Riemannian manifold. The fibre of the bundle is an infinite dimens
ional complex vector space which is called the space of symplectic spinors
. It is a direct sum of two irreducible representations of the connected d
ouble cover of the symplectic group.\n\n The tensor product of exterior fo
rms on the manifold with the symplectic spinor bundle ("twisted" deRham co
mplex) splits into subbundles and the symplectic twistor operators are def
ined with help of them. We describe their construction. Computing a repres
entation-theoretic characteristic (Schur--Weyl--Howe type duality)\, we ca
n determine the symbols of the symplectic twistor operators and prove the
ellipticity of the cohomological complexes formed by these operators.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Skoda (University of Zadar and University of Hradec Kralove)
DTSTART:20230419T113000Z
DTEND:20230419T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/78
DESCRIPTION:Title: Nonabelian Čech cocycles in noncommutative geometr
y\nby Zoran Skoda (University of Zadar and University of Hradec Kralov
e) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\n\nAbstract\nGluing of sheaves\, bundles and
similar objects is the subject of descent theory. In this talk we shall f
ocus on a kind of\nnoncommutative geometry where spaces are represented by
Abelian categories which locally look like (= are glued from)\nfull categ
ories of one sided modules over noncommutative "coordinate" rings. Localit
y may be in the sense\nof localizations\, but also more generally in the s
ense of faithfully flat covers presented by corings.\nPrincipal bundles wi
ll have such global spaces with categorified action analogous to a princip
al action of a structure\ngroup and the cover of the total space will have
to be in an appropriate category respecting the action.\nA very general (
nonaffine) principality or Galois kind of condition will be formulated in
terms of categorical adjunctions.\nThen the cocycles will be introduced in
several levels of generality\; in the main special case related to struct
ure groups\ncoming from Hopf algebras\, and locally cleft extensions\, we
use comonads in a pair of new auxiliary bicategories found in 2019.\nCompa
ring different cocycles is first done for the case involving the same cove
r of the base.\nComparison for different base covers\, studied in a projec
t with M. Stojić\, uses refinements which involve additional\ndata in gen
eral. Passing to the colimit defining cohomology classes requires some set
-theoretical care\nregarding that a priori such refinements form a proper
class.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Nariman (Purdue University)
DTSTART:20230426T133000Z
DTEND:20230426T143000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/79
DESCRIPTION:Title: On local and global invariants of flat bundles\
nby Sam Nariman (Purdue University) as part of Prague-Hradec Kralove semin
ar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract
\nCharacteristic classes of flat bundles are related to the group cohomolo
gy of diffeomorphism groups. But computing the group cohomology of these l
arge groups as discrete groups is too complicated. Even calculating the se
cond cohomology of these groups will resolve deep problems in foliation th
eory. However\, it is easier to define certain natural cohomology classes
(characteristic classes) in group cohomology of diffeomorphism groups. We
will discuss that they are rarely bounded classes but some of them (e.g. G
odbillon-Vey classes) are continuous cocycles. We will discuss some ways t
o detect their nontriviality inspired by the work of Thurston and Bott-Seg
al.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/7
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Nordstroem (University of Bath)
DTSTART:20230503T113000Z
DTEND:20230503T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/80
DESCRIPTION:Title: Massey tensors and the rational homotopy type of 7-
and 8-manifolds\nby Johannes Nordstroem (University of Bath) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physic
s and statistics\n\n\nAbstract\nDefining tensors on the cohomology of a di
fferential graded algebra by multiplying Massey products by a further elem
ent gives an object that has less dependence on choices than the Massey pr
oducts\, making them easier to work with. On the other hand\, all Massey p
roducts can be recovered from these tensors when the cohomology algebra sa
tisfies Poincare duality\, like for the de Rham complex of a closed manifo
ld. Moreover\, suitable interpretations of these tensors can capture infor
mation about the rational homotopy type even when the Massey products are
undefined. For closed simply-connected 7-manifolds these tensors (along wi
th the cohomology algebra itself) suffice to determine the rational homoto
py type. Conjecturally the same is true for closed 8-manifolds\, but at le
ast the vanishing of the tensors is equivalent to formality in that case.
This is based on joint work with Diarmuid Crowley and Csaba Nagy.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Slovak (Masaryk University)
DTSTART:20230517T113000Z
DTEND:20230517T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/81
DESCRIPTION:Title: Almost invariant differential calculus\nby Jan
Slovak (Masaryk University) as part of Prague-Hradec Kralove seminar Cohom
ology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nFor mo
re than hundred years\, various concepts were developed to understand the
\nfields of geometric objects and invariant \ndifferential operators betwe
en them for conformal Riemannian and projective geometries. More recently\
, several general tools were presented for the entire class of parabolic g
eometries\, i.e.\, the Cartan geometries modelled on homogeneous spaces G/
P with P a parabolic subgroup in a semi-simple Lie group G. Similarly to c
onformal Riemannian and projective structures\, all these geometries deter
mine a class of distinguished affine connections\, which carry an affine s
tructure modelled on differential 1-forms . They correspond to reductions
of P to its reductive Levi factor\, and they are called the Weyl structur
es similarly to the conformal case. The standard definition of differentia
l invariants in this setting is as affine invariants of these connections\
, which do not depend on the choice within the class. In this talk\, we de
scribe a universal calculus which provides an important first step to dete
rmine such invariants. I shall present a natural procedure how to construc
t all affine invariants of Weyl connections\, which depend only tensoriall
y on the deformations. This is a joint work with Andreas Cap.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Santi (University of Rome "Tor Vergata")
DTSTART:20230510T113000Z
DTEND:20230510T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/82
DESCRIPTION:Title: On 3-nondegenerate CR manifolds in dimension 7\
nby Andrea Santi (University of Rome "Tor Vergata") as part of Prague-Hrad
ec Kralove seminar Cohomology in algebra\, geometry\, physics and statisti
cs\n\n\nAbstract\nI will report on joint works with B. Kruglikov on CR hyp
ersurfaces in C 4 with a degenerate Levi form. I will discuss the symmetry
dimension bound 8 for all the 3-nondegenerate 7-dimensional CR real-analy
tic structures and present the classification of the locally homogeneous o
nes. The bound 8 is achieved on the homogeneous model\, which is locally t
he only homogeneous 3-nondegenerate 7-dimensional CR manifold.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guchuan Li (Michigan University)
DTSTART:20230524T113000Z
DTEND:20230524T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/83
DESCRIPTION:Title: From the real cobordism theory to the Kervaire inva
riant one problem\nby Guchuan Li (Michigan University) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\n\nAbstract\nI will review how the real cobordism theory plays
an important role in Hill—Hopkins—Ravenel’s solution to the Kervai
re invariant one problem and leads to new computations in chromatic homoto
py theory at the prime 2. Then I will report about my joint work with Po H
u\, Igor Kriz\, Petr Somberg\, and Foling Zou on the construction of odd p
rime analogues of real cobordism theory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem)
DTSTART:20230531T113000Z
DTEND:20230531T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/84
DESCRIPTION:Title: Generalized Prequantum Bundle in Diffeology\nby
Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics a
nd statistics\n\n\nAbstract\nI will show how we can extend the classical c
ircle-prequantum bundle in the case of integral symplectic manifold to any
closed 2-form on any diffeological space and for any group of periods eve
n when the torus of period is not a circle but an irrational torus. I will
discuss the definition of the periods of the 2-form and the construction
of the generalized prequantum bundle as a quotient of the space of paths o
nly\, without the help of an extra structure. I may give on or two singula
r examples.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck)
DTSTART:20231004T113000Z
DTEND:20231004T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/85
DESCRIPTION:Title: An approach to homological algebra up to $\\epsilon
$\nby Tobias Fritz (University of Innsbruck) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\
n\n\nAbstract\nA theorem of Kazhdan on approximate representations of grou
ps is based on a proof which seems to use cohomological methods "up to $\\
epsilon$". This means that being a cocycle or a coboundary is not a yes/no
-property of a cochain $C$\, but rather a quantitative statement where one
measures how strongly $C$ deviates from being either. Based on Grandis's
framework for nonabelian homological algebra\, I will present a framework
for such quantitative homological algebra and sketch the intuition behind
the resulting definitions of kernel and cokernel. Unfortunately\, the resu
lting category does not satisfy the axioms required of homological categor
ies in Grandis's sense. Our main result solves this problem by showing tha
t an arrow category is a homological category already under very weak assu
mptions. It follows that derived functors and long exact sequences can be
constructed for arrow categories quite generally\, and for quantitative ho
mological algebra in particular.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiy Maksymenko (Institute of Mathematics NAS of Ukraine)
DTSTART:20231011T113000Z
DTEND:20231011T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/86
DESCRIPTION:Title: Homotopy types of diffeomorphism groups of polar Mo
rse-Bott foliations on lens spaces\nby Sergiy Maksymenko (Institute of
Mathematics NAS of Ukraine) as part of Prague-Hradec Kralove seminar Coho
mology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nLet D
2 = {|z| ≤ 1} be the closed unit 2-disk in the complex plane\, and S 1 =
∂D2 be its boundary. Consider the partition F on the solid torus T = S
1 × D2 into 2-tori S 1 × {|z| = r}\, r ∈ [0\; 1]\, parallel to its bou
ndary and one singular circle S 1 × 0. A diffeomorphism h : T → T is ca
lled foliated (resp. leaf preserving) if for each leaf ω ∈ F its image
h(ω) is also leaf of F (resp. h(ω) = ω). Gluing two copies of T by some
diffeomorphism between their boundaries\, one gets a lens space Lp\,q wit
h a Morse-Bott foliation Fp\,q obtained from F on each copy of T. Denote b
y Df ol(F\, ∂T) and Dlp(F\, ∂T) respectively the groups of foliated an
d leaf preserving diffeomorphisms of T fixed on the boundary ∂T. Similar
ly\, let Df ol(Fp\,q) and Dlp(Fp\,q) be respectively the groups of foliate
d and leaf preserving diffeomorphisms of Fp\,q. Endow all those groups wit
h the corresponding C ∞ Whitney topologies. The aim of the talk is to gi
ve a complete description the homotopy types of the above groups Df ol(F\,
∂T)\, Dlp(F\, ∂T)\, Df ol(Fp\,q)\, Dlp(Fp\,q) for all p\, q. In parti
cular\, we will show that Dlp(Fp\,q) is a strong deformation retract of Df
ol(Fp\,q). Moreover\, let D(Lp\,q) be the group of all diffeomorphisms of
Lp\,q. Then for q 6≡ 1(modp) the inclusions Isom(Lp\,q) ⊂ Dlp(Fp\,q)
⊂ Df ol(Fp\,q) ⊂ D(Lp\,q) are weak homotopy equivalences\, where Isom(
Lp\,q) is the isometry group of Lp\,q of the canonical elliptic metric on
Lp\,q.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Part (Institute of Mathematics\, Czech Academy of Sciences)
DTSTART:20231025T113000Z
DTEND:20231025T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/87
DESCRIPTION:Title: Geometric complexity theory program and lower bound
s for restricted models\nby Fedor Part (Institute of Mathematics\, Cze
ch Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomolog
y in algebra\, geometry\, physics and statistics\n\n\nAbstract\nGeometric
complexity theory (GCT) suggests to look on the closure of a complexity cl
ass C of polynomials as the closure of the orbit of a polynomial Qc under
the action of GL where Qc depends on C. For example\, polynomials that can
be approximated by those computable by formulas of size S correspond to t
he variety which is the orbit closure of the determinant of S^a x S^a matr
ix of variables for some constant a. In the core of many complexity lower
bounds lie variations of the partial derivatives method which implicitly c
onstruct a polynomial F on the space of polynomials (also known as catalec
ticant) such that F does not vanish on some explicit P but vanishes on all
polynomials in a complexity class C. GCT provides a systematic program fo
r finding such separating F by studying vanishing ideals and algebras of r
egular functions of orbit closure varieties using algebraic geometry and r
epresentation theory. However it is not easy to implement\, despite a vast
amount of beautiful results no complexity lower bound has been proven thi
s way so far. In the talk I will give an overview of the recent work relev
ant for GCT approach to proving complexity lower bounds in the regime of d
epth 3 formulas\, which correspond to secant varieties of Chow variety\, a
nd other restricted models.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Caputi (University of Turin)
DTSTART:20231101T123000Z
DTEND:20231101T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/88
DESCRIPTION:Title: From the Mayer-Vietoris spectral sequence to überh
omology\nby Luigi Caputi (University of Turin) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nÜberhomology is a recently defined triply-graded homolog
y theory for simplicial complexes\, which yields both topological and comb
inatorial information. When restricted to (simple) graphs\, a certain spec
ialization of überhomology yields a categorification of the connected dom
ination polynomial at -1\; which shows that überhomology of graphs is als
o related to connected dominating sets. In this talk\, after introducing t
he notion of überhomology\, and showing its relation to connected dominat
ion\, we shall see a further property: überhomology of simplicial complex
es can be identified with the second page of the Mayer-Vietoris spectral s
equence\, with respect to anti-star covers.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kotrbary (Institute of Mathematics\, Charles University)
DTSTART:20231108T123000Z
DTEND:20231108T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/89
DESCRIPTION:Title: Towards Hodge theory for smooth translation-invaria
nt valuations\nby Jan Kotrbary (Institute of Mathematics\, Charles Uni
versity) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nIt follows from seminal w
ork of Semyon Alesker that the space of \nsmooth\, translation-invariant v
aluations (finitely additive measures) \non convex bodies carries a natura
l structure of a graded algebra \nsatisfying Poincaré duality. It is conj
ectured that the Alesker \nalgebra further satisfies versions of (mixed) h
ard Lefschetz theorem \nand (mixed) Hodge-Riemann relations\, i.e.\, prope
rties formally analogous \nto those of cohomology of compact Kähler manif
olds. \nIn this talk\, we will report on recent progress towards \nthis co
njecture and explain its relevance in convex geometry\, \nin particular fo
r geometric inequalities of convex bodies.\nBased on joint work with Andre
as Bernig and Thomas Wannerer.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/8
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tornike Kadeishvili (A. Razmadze Mathematical Institute of Tbilisi
State University)
DTSTART:20231122T123000Z
DTEND:20231122T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/90
DESCRIPTION:Title: Homotopy algebras A(∞)\, C(∞)\, B(∞)\, hGa<
/a>\nby Tornike Kadeishvili (A. Razmadze Mathematical Institute of Tbilisi
State University) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nTo construct ef
fective modern algebraic models now are used so called\nstrong homotopy al
gebras where the classical defining identities like\n associativity\, com
mutativity\, Jakobi\, Leibniz\, … [1] hold only up\nto coherent homotopi
es. We are going to present the notions of\nhomotopy A(∞)\, C(∞)\, B
(∞)\, hGa algebras as the structures\nobtained by changing or adding som
e structures to standard bar\nconstruction. We are going to also present s
ome models and their\napplications.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Suhr (University of Bochum)
DTSTART:20231129T123000Z
DTEND:20231129T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/91
DESCRIPTION:Title: The theorem of Lusternik and Schnirelmann for rever
sible Finsler metrics\nby Stefan Suhr (University of Bochum) as part o
f Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\n\nAbstract\nThe theorem on the existence of three simpl
e closed geodesics on every Riemannian 2-sphere has a "colorful" history a
nd many applications on closed geodesics. I will give an introduction to t
he problem and outline a proof for the reversible Finsler case. Finally I
will comment on some applications for closed geodesics. The talk is based
on a collaboration with De Philippis\, Marini\, and Mazzucchelli.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfonso García-Parrado (University of Cordoba\, Spain)
DTSTART:20231213T130000Z
DTEND:20231213T140000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/92
DESCRIPTION:Title: An IDEAL covariant characterization of the Kerr con
formal structure\nby Alfonso García-Parrado (University of Cordoba\,
Spain) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, ge
ometry\, physics and statistics\n\n\nAbstract\nWe present an IDEAL char
acterization of the family of four dimensional Lorentzian spacetimes t
hat are conformally related to the Kerr vacuum solution.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Druzhkov (Russian-Armenian University\, Yerevan)
DTSTART:20231115T123000Z
DTEND:20231115T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/93
DESCRIPTION:Title: Internal Lagrangians of PDEs\nby Konstantin Dru
zhkov (Russian-Armenian University\, Yerevan) as part of Prague-Hradec Kra
love seminar Cohomology in algebra\, geometry\, physics and statistics\n\n
\nAbstract\nIt is known that differential equations arising from the princ
iple of stationary action encode the variational nature in terms of their
intrinsic geometry. Three reasonable questions come up:\n\n1. Where exactl
y does a variational equation contain information about its variational na
ture?\n\n2. What is the meaning of cohomology that encodes the variational
nature of an equation?\n\n3. What details about the variational nature of
a differential equation are known to its intrinsic geometry?\n\nWe propos
e (partial) answers to these questions:\n\n1. There is a natural complex o
n a differential equation: quotient of the de Rham complex by the complex
of twice Cartan forms. One of its cohomology groups encodes the variationa
l nature. We call elements of this group internal Lagrangians.\n\n2. Inter
nal Lagrangians are related to integral functionals defined on a certain c
lass of submanifolds of a differential equation. Such submanifolds can be
treated as almost solutions since (informally speaking) they are composed
of initial-boundary conditions lifted to infinitely prolonged equations.\n
\nSo\, we can introduce the notion of stationary points of an internal Lag
rangian.\n\n3. The non-degeneracy of a variational principle is inherited
by the corresponding internal Lagrangian. The case of degenerate Lagrangia
ns requires a separate study.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Van Le (Institute of Mathematics of ASCR)
DTSTART:20231206T123000Z
DTEND:20231206T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/94
DESCRIPTION:Title: Unital $C_\\infty$-algebras and the real homotopy t
ype of simply connected compact 8-manifolds\nby Hong Van Le (Institute
of Mathematics of ASCR) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\n\nAbstract\nIn 1979 M
iller showed that any (r-1)-connected compact manifold of dimension less t
han or equal to (4r-2)\, r ≥ 2\, is formal. In 2020 Crowley-Nordström
showed that the rational homotopy type of a (r-1)-connected compact manifo
ld $M$ of dimension less than or equal (5r-3)\, r ≥ 2\, is determined by
its cohomology algebra H*(M\, Q) and by the Bianchi-Massey tensor introdu
ced by them. In my talk I shall explain how to encode the real homotopy ty
pe of a (r-1)-connected compact manifold of dimension n ≤ 6r-4\, r ≥ 2
\, in terms of a minimal unital C_∞-algebra whose higher multiplications
μ_k vanish for k ≥ 5. I shall discuss consequences and the relatio
nship between our results and several previous results on formality and
homotopy type of manifolds of low dimensions. My talk shall be based on my
joint work with Domenico Fiorenza arXiv:2310.19506.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Pulemotov (University of Queensland)
DTSTART:20240214T123000Z
DTEND:20240214T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/95
DESCRIPTION:Title: Palais--Smale sequences for the prescribed Ricci cu
rvature functional\nby Artem Pulemotov (University of Queensland) as p
art of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, ph
ysics and statistics\n\n\nAbstract\nOn homogeneous spaces\, solutions to t
he prescribed Ricci curvature equation coincide with the critical points o
f the scalar curvature functional subject to a constraint. We provide a co
mplete description of Palais--Smale sequences for this functional. As an a
pplication\, we obtain new existence results for the prescribed Ricci curv
ature equation\, which enables us to observe previously unseen phenomena.
Joint work with Wolfgang Ziller (University of Pennsylvania).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (Hradec-Kralove University)
DTSTART:20240221T123000Z
DTEND:20240221T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/96
DESCRIPTION:Title: Z-graded Q-manifolds\nby Alexei Kotov (Hradec-K
ralove University) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nThe main object
is a Z-graded (super)manifold supplied with a homological degree 1 vector
field. We explain the difference between non-negative\, non-positive and
general cases. A classification in the general case is given. The talk is
based upon a joint article with Camille Laurent-Gengoux and Vladimir Salni
kov.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva (Institute of Mathematics of ASCR)
DTSTART:20240228T123000Z
DTEND:20240228T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/97
DESCRIPTION:Title: Functorial approach to rank functions\nby Alexa
ndra Zvonareva (Institute of Mathematics of ASCR) as part of Prague-Hradec
Kralove seminar Cohomology in algebra\, geometry\, physics and statistics
\n\n\nAbstract\nFor a skeletally small triangulated category C Chuang and
Lazarev recently introduced the notion of a rank function on C. For simpli
city\, by a rank function on C we will mean an assignment to each object o
f C of a non-negative real number such that certain natural conditions hol
d. Such functions are closely related to functors into simple triangulated
categories. On the other hand\, to each skeletally small additive categor
y C one can associate its abelianisation mod-C. I will discuss the connect
ion between rank functions on C and translation-invariant additive functio
ns on mod-C. This connection allows to use the machinery of additive funct
ions on abelian categories to study rank functions on triangulated categor
ies\, to classify integer rank functions in terms of certain objects and t
o obtain nice decompositions. This is based on a joint work with Teresa Co
nde\, Mikhail Gorsky\, and Frederik Marks.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov (Dartmouth College)
DTSTART:20240313T140000Z
DTEND:20240313T150000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/98
DESCRIPTION:Title: Virtual Legendrian knots and possible relations to
causality in Borde–Sorkin spacetimes\nby Vladimir Chernov (Dartmouth
College) as part of Prague-Hradec Kralove seminar Cohomology in algebra\,
geometry\, physics and statistics\n\n\nAbstract\nWe review our results wi
th Stefan Nemirovski on the relation\nof Legendrian linking and causal str
ucture in globally hyperbolic\nspacetimes. After that we discuss virtual L
egendrian knots defined as\nLegendrian knots in $ST^∗M$ studied up to is
otopy and modification of\n$ST^∗M$ induced by surgery on M that were int
roduced by Patricia Cahn\nand Asa Levi. We formulate a few conjectures abo
ut them and\nconjecturally relate them to causality in Borde–Sorkin spac
etimes that\nare manifolds with a Lorentz metric that is degenerate at cri
tical\npoints of a Morse "timelike" function and that consist of globally\
nhyperbolic pieces between critical levels. We prove these conjectures\nfo
r 2+1 dimensional Borde–Sorkin spacetimes.\nThe talk is based on the joi
nt work with Rustam Sadykov.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K V Subrahmanyam (Chennai Mathematical Institute)
DTSTART:20240320T123000Z
DTEND:20240320T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/99
DESCRIPTION:Title: Stabilizer limits and Orbit closures with applicati
ons to Geometric Complexity Theory\nby K V Subrahmanyam (Chennai Mathe
matical Institute) as part of Prague-Hradec Kralove seminar Cohomology in
algebra\, geometry\, physics and statistics\n\n\nAbstract\nLet $G\\subsete
q GL(X)$ be a reductive group acting on a finite dimensional vector space
$V$ over $\\C$. A central problem in Geometric Complexity Theory is the st
udy points $y\,z\\in V$ where (i) $z$ is obtained as the leading term of t
he action of a 1-parameter subgroup $\\lambda (t)\\subseteq G$ on $y$\, an
d (ii) $y$ and $z$ have large distinctive stabilizers $K\,H \\subseteq G$.
\n\nWe address the question: under what conditions can (i) and (ii) be sim
ultaneously satisfied\, i.e\, there exists a 1-PS $\\lambda \\subseteq G$
for which $z$ is observed as a limit of $y$.\n\n\nUsing $\\lambda$\, we de
velop a leading term analysis which applies to $V$ as well as to ${\\mathc
al G}= Lie(G)$ the Lie algebra of $G$ and its subalgebras ${\\cal K}$ and
${\\cal H}$\, the Lie algebras of $K$ and $H$ respectively.\n\nThrough thi
s we construct the Lie algebra $\\hat{\\mathcal K} \\subseteq {\\mathcal H
}$ which connects $y$ and $z$ through their Lie algebras. Here $\\hat{\\ma
thcal K}$ is the leading term Lie algebra obtained from ${\\mathcal K}$ by
the adjoint action of $\\lambda(t)$. We develop the properties of $\\hat{
\\mathcal K}$ and relate it to the action of ${\\mathcal H}$ on $\\overlin
e{N}=V/T_z O(z)$\, the normal slice to the orbit $O(z)$.\n\n\nWe examine t
he case when a semisimple element belongs to both ${\\mathcal H}$ and ${\\
mathcal K}$. We call this a alignment. We describe some consequen
ces of alignment and relate it to existing work on lower bounds in the cas
e of the determinant and permanent.\n\nWe also connect alignment to in
termediate $G$-varieties $W$ which lie between the orbit closures of
$z$ and $y$\, i.e. $\\overline{O(z)} \\subsetneq W \\subsetneq O(y)$. Thes
e have a direct bearing on representation theoretic as well as geometric p
roperties which connect $z$ and $y$.\n\n\nThis is joint work with Bharat A
dsul and Milind Sohoni.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/9
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (v. Javakhishvili Tbilisi State University\, Geo
rgia)
DTSTART:20240410T113000Z
DTEND:20240410T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/101
DESCRIPTION:Title: Morava K-theory rings of p-groups in transferred C
hern characteristic chasses I\nby Malkhaz Bakuradze (v. Javakhishvili
Tbilisi State University\, Georgia) as part of Prague-Hradec Kralove semin
ar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstract
\nThis talk provides the explicit calculations by the author and his co-au
thors on the Honda formal group law and Morava K-theory of finite groups.
Much attention is paid to the multiplicative structure and presentation of
the generators in terms of Chern classes and their transfers. This is mot
ivated by the still open question whether the mod -2 Morava K-theory of an
y finite group is evenly generated by the Chen classes and their transfers
. This conjecture by Hopkins-Kuhn-Ravenel was rejected by a counterexample
for p>2 case.\n\n\nIn the first lecture we present some points character
istic of Morava's K-theory and formal properties of the transfer map. \n\n
In the second lecture we will look in detail at some specific examples.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
01/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (v. Javakhishvili Tbilisi State University\, Geo
rgia)
DTSTART:20240417T113000Z
DTEND:20240417T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/102
DESCRIPTION:Title: Morava K-theory rings of p-groups in transferred C
hern characteristic classes II\nby Malkhaz Bakuradze (v. Javakhishvili
Tbilisi State University\, Georgia) as part of Prague-Hradec Kralove semi
nar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstrac
t\nThis talk provides the explicit calculations by the author and his co-a
uthors on the Honda formal group law and Morava K-theory of finite groups.
Much attention is paid to the multiplicative structure and presentation o
f the generators in terms of Chern classes and their transfers. This is mo
tivated by the still open question whether the mod -2 Morava K-theory of a
ny finite group is evenly generated by the Chen classes and their transfer
s. This conjecture by Hopkins-Kuhn-Ravenel was rejected by a counterexampl
e for p>2 case.\n\n\nIn the first lecture we present some points characte
ristic of Morava's K-theory and formal properties of the transfer map. \n\
nIn the second lecture we will look in detail at some specific examples.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
02/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aliaksandr Hancharuk (Jilin University (China))
DTSTART:20240306T123000Z
DTEND:20240306T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/103
DESCRIPTION:Title: Koszul-Tate resolutions and trees\nby Aliaksan
dr Hancharuk (Jilin University (China)) as part of Prague-Hradec Kralove s
eminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbst
ract\nGiven a commutative algebra O\, a proper ideal I\, and a resolution
of O/I by projective O-modules\, we construct an explicit Koszul-Tate reso
lution. We call it the arborescent Koszul-Tate resolution since it is inde
xed by decorated trees. When the O-module resolution has finite length\, o
nly finitely many operations are needed to construct the arborescent Koszu
l-Tate resolution---this is compared with the classical Tate algorithm\, w
hich may require infinitely many such computations. Examples and applicati
ons are discussed. This is based on a joint work with Camille Laurent-Geng
oux and Thomas Strobl.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
03/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksy Tralle (University of Warmia and Mazury)
DTSTART:20240522T113000Z
DTEND:20240522T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/104
DESCRIPTION:Title: Orbifold constructions of Sasakian structures on S
male-Barden manifolds\nby Aleksy Tralle (University of Warmia and Mazu
ry) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geome
try\, physics and statistics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
04/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kovalev (Cambridge University)
DTSTART:20240529T113000Z
DTEND:20240529T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/105
DESCRIPTION:Title: On nearly parallel $G_2$-manifolds\nby Alexei
Kovalev (Cambridge University) as part of Prague-Hradec Kralove seminar Co
homology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nA n
early parallel $G_2$-structure on a 7-manifold can be given by a 3-form\n$
\\phi$ of special algebraic type satisfying a differential equation\n$d\\p
hi = \\tau^* \\phi$ for a non-zero constant $\\tau$. We consider\nnearly p
arallel $G_2$-structures on the Aloff--Wallach spaces and\non regular Sasa
ki--Einstein 7-manifolds. We give a construction and\nexplicit examples of
associative 3-folds (a particular type of minimal\nsubmanifolds) in these
spaces.\n\nJoint work with M. Fernández\, A. Fino\, and V. Muñoz.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
05/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Čoupek (Department of Probability and Mathematical Statistic
s\, Charles University)
DTSTART:20240514T113000Z
DTEND:20240514T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/106
DESCRIPTION:Title: Iterated integrals and controlled ODEs\nby Pet
r Čoupek (Department of Probability and Mathematical Statistics\, Charles
University) as part of Prague-Hradec Kralove seminar Cohomology in algebr
a\, geometry\, physics and statistics\n\n\nAbstract\nThe purpose of this n
on-technical talk is to discuss the role that\niterated integrals (an inst
ance of the so-called mapping space signature)\nplay in the theory of ordi
nary differential equations (ODEs) of the form\n\n \\[ \\dot{Y}(t) = f(
Y(t))\\dot{X}(t)\\]\n\nwhere the path $X$ models the input and the path $Y
$ models the output\nof a physical system whose dynamics is governed by a
(non-linear function)\n$f$. When $X$ is sufficiently regular (e.g.\\ Lipsc
hitz) function\, the\nsolution to the ODE can be\, roughly speaking\, foun
d as a limit of its\niterated integrals. Such regularity is\, however\, ty
pically not obtained\nif $X$ is a sample path of a stochastic process (e.g
.\\ the Wiener process)\nand $\\dot X$ models the random noise (e.g.\\ the
white noise). In the talk\,\nwe will discuss why low regularity is a prob
lem\, what can be done\, and why\nit is important to understand the algebr
aical and analytical properties of\nthe iterated integrals (and\, more gen
erally\, the mapping space signature).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
06/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camille Laurent-Gengoux (Université de Lorraine\, IECL)
DTSTART:20240403T113000Z
DTEND:20240403T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/107
DESCRIPTION:Title: The neighborhood of a leaf of a singular foliation
\nby Camille Laurent-Gengoux (Université de Lorraine\, IECL) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physic
s and statistics\n\n\nAbstract\nNear a leaf\, regular foliations are class
ified by their monodromies. What about the singular leaves of singular fol
iations? The first point is that for a singular leaf\, there is a transver
se singular foliation\, which is constant all along the leaf. In a previou
s work\, Leonid Ryvkin and I have proven that for simply connected singula
r leaves with a certain type of transverse singular foliations\, there is
only one possiblity: the direct product. Here\, we present a complete clas
sification at the formal level\, which is composed of two parts: a sort of
monodromy and a finite dimensional principal bundle. We use a presentatio
n where Yang-Mills bundles (as introduced by Kotov and Strobl) play a cent
ral role. Joint work with Simon Raphael Fischer (Taipei).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
07/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Strung (Institute of Mathematics of ASCR)
DTSTART:20240424T113000Z
DTEND:20240424T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/108
DESCRIPTION:Title: An introduction to the classification of C*-algebr
as\nby Karen Strung (Institute of Mathematics of ASCR) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\n\nAbstract\nI will give an expository talk about the C*-algeb
ra classification program. In recent years\, the following classification
theorem was established after years of work by many authors:\n\n\nTheorem:
Let A and B be simple\, separable\, nuclear C*-algebras which tracially a
bsorb the Jiang-Su algebra and satisfy the UCT. Then an isomorphism of the
Elliott Invariants of A and B can be lifted to a *-isoomorphism of A and
B.\n\n\nI will explain the terms in the theorem\, and discuss how everythi
ng fits together.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
08/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University of Hradec Kralove)
DTSTART:20241002T113000Z
DTEND:20241002T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/109
DESCRIPTION:Title: Graded super Hopf algebroids\nby Alexei Kotov
(University of Hradec Kralove) as part of Prague-Hradec Kralove seminar Co
homology in algebra\, geometry\, physics and statistics\n\nLecture held in
blue lecture room\, rear building\, ground floor.\n\nAbstract\nThe talk w
ill be focused on Hopf algebras and algebroids in the category of Z-graded
varieties. The theory of Harish-Chandra pairs will be briefly discussed a
nd their generalization to action algebroids will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
09/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Grigoriev (Moscow State University and Mons University)
DTSTART:20241009T113000Z
DTEND:20241009T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/110
DESCRIPTION:Title: Graded geometry of local gauge theories\nby Ma
xim Grigoriev (Moscow State University and Mons University) as part of Pra
gue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and
statistics\n\n\nAbstract\nGauge PDEs generalize AKSZ sigma models to the c
ase of general local gauge theories. Despite being very flexible and invar
iant these geometrical objects are usually infinite-dimensional and are di
fficult to define explicitly\, just like standard infinitely-prolonged PDE
s. We propose a notion of a weak gauge PDE where the nilpotency of the BRS
T differential is relaxed in a controllable way. In this approach a nontop
ological local gauge theory can be described in terms of a finite-dimensio
nal geometrical object. Moreover\, among such objects one can find a minim
al one which is unique in a certain sense. In the case of a Lagrangian sys
tem\, the respective weak gauge PDE naturally arises from the presymplecti
c structure. We prove that any weak gauge PDE determines the standard jet-
bundle BV formulation of the underlying gauge theory\, giving an unambiguo
us field-theoretical interpretation of these objects. The relation to the
covariant phase space and the multisymplectic approaches is also discussed
. The formalism is illustrated by a variety of models including (super) gr
avity\, (chiral) Yang-Mills\, and a non-Lagrangian self-dual Yang-Mills th
eory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Doucha (Institute of Mathematics of ASCR)
DTSTART:20241016T113000Z
DTEND:20241016T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/111
DESCRIPTION:Title: Shadowing of actions of hyperbolic groups on their
boundaries\nby Michal Doucha (Institute of Mathematics of ASCR) as pa
rt of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, phy
sics and statistics\n\nLecture held in Konírna\, front building\, ground
floor.\n\nAbstract\nI will give a quick introduction to general Gromov hyp
erbolic metric spaces\, in particular hyperbolic groups\, and their bounda
ries. A very useful way of studying hyperbolic groups is via their canonic
al actions on their boundaries. I will discuss a very recent result of K.
Mann et al that such actions are topologically stable (although this was a
pparently hinted by Gromov in his paper on hyperbolic groups from 1987) an
d present my result that these actions in fact have the so-called shadowin
g (a.k.a. pseudo-orbit tracing) property\, which implies the topological s
tablity as a corollary.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Štěpán Holub (Charles University)
DTSTART:20241030T123000Z
DTEND:20241030T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/112
DESCRIPTION:Title: Combinatorics on Words in Isabelle/HOL\nby Št
ěpán Holub (Charles University) as part of Prague-Hradec Kralove seminar
Cohomology in algebra\, geometry\, physics and statistics\n\nLecture held
in blue lecture room\, rear building\, ground floor.\n\nAbstract\nThe tal
k will present the ongoing project of formalization of combinatorics on wo
rds in the computer proof assistant Isabelle/HOL. Independently of the par
ticular formalized topic\, the talk will attempt to serve as an introducti
on to Isabelle/HOL for beginners.\n\n(Demonstration file: PresentationWeb.thy)
\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoran Skoda (University of Zadar)
DTSTART:20241106T123000Z
DTEND:20241106T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/113
DESCRIPTION:Title: Braiding phenomena in cyclic homology\nby Zora
n Skoda (University of Zadar) as part of Prague-Hradec Kralove seminar Coh
omology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nUnli
ke the case of Hochschild (co)homology and most other cohomology theories\
, the original constructions of cyclic (co)homology in 1980s did not have
coefficients. In a variant\, Hopf cyclic homology\, the coefficients were
discovered around 2000 as stable anti-Yetter--Drinfeld modules\, reminding
of Yetter--Drinfeld (YD) modules familiar from the center construction. B
ressler observed that cyclic nerve of a groupoid is determined by the ordi
nary nerve of its inertia groupoid. Thus I conjectured in late 2002 that p
assing to the appropriate monoidal category of sheaves one could replace t
he (sheaves over) inertia by taking the monoidal center of the (sheaves ov
er) original groupoid. This has been proved in 2004 in two variants\, well
known by Hinich on orbifold case and another by me. As monoidal center in
volves braiding\, it pointed that requiring or adding braidings can provid
e examples of cyclic homology with coefficients\; I constructed some toy e
xamples using standard resolutions and Bohm\, Stefan and others independen
tly much more realistic examples using distributive laws. It fits also wit
h work of Kaledin who introduced new kind of traces to treat coefficients.
Kowalzig has recently also explained anti- for YD modules in the case of
centers of certain bimodule categories. This talk is to outline motivation
s and my present picture of these braiding (or Yang--Baxter) phenomena in
cyclic homology.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaroslav Bazaikin (Jan Evangelista Purkyně University in Ústí n
ad Labem)
DTSTART:20241113T123000Z
DTEND:20241113T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/114
DESCRIPTION:Title: On Chern-Losik class for codimension two foliation
s\nby Yaroslav Bazaikin (Jan Evangelista Purkyně University in Ústí
nad Labem) as part of Prague-Hradec Kralove seminar Cohomology in algebra
\, geometry\, physics and statistics\n\n\nAbstract\nLosik classes generali
ze characteristic classes of foliations using Gelfand-Fuchs cohomology app
roach. The Chern-Losik class for foliations of codimension one was constru
cted by Losik\, and he also showed the non-triviality of this class for a
foliation with two leaves with a hyperbolic holonomy group. In the talk th
e construction of the Chern-Losik class to foliations of arbitrary codimen
sion is done. The non-triviality of the Chern-Losik class of codimension t
wo foliations is investigated. Examples of codimension two foliations with
nontrivial Chern-Losik class are constructed.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Galaev (University of Hradec Kralove)
DTSTART:20241120T123000Z
DTEND:20241120T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/115
DESCRIPTION:Title: Conformally homogeneous Lorentzian spaces\nby
Anton Galaev (University of Hradec Kralove) as part of Prague-Hradec Kralo
ve seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\n
Abstract\nThis is a joint work with Dmitri Alekseevsky. We prove that if a
simply connected non-conformally flat conformal Lorentzian manifold $(M\,
c)$ admits an essential transitive group of conformal transformations\, th
en there exists a metric $g\\in c$ such that $(M\,g)$ is a complete homoge
neous plane wave. We also prove that the group of conformal transformation
s of a non-conformally flat simply connected homogeneous plane wave $(M\,g
)$ consists of homotheties\, hence it is a 1-dimensional extension of the
group of isometries.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro H. Carvalho (University of Hradec Kralove)
DTSTART:20241127T123000Z
DTEND:20241127T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/116
DESCRIPTION:Title: Homological reduction of Poisson structures\nb
y Pedro H. Carvalho (University of Hradec Kralove) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\n\nAbstract\nFrom Roytenberg-Ševera\, we know that Poisson manifolds
are in one-to-one correspondence with symplectic NQ-manifolds of degree on
e. Cattaneo-Zambon further extended this relation to the level of reductio
n with their graded geometric approach to Poisson reduction. Based on thes
e ideas\, we explain how homotopy Poisson structures may arise as homologi
cal models for Poisson reduced spaces obtained from more general reduction
setups. Our results extend the classical homological formulation of hamil
tonian reduction of symplectic and Poisson manifolds due to Kostant-Sternb
erg and Stasheff.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART:20241204T123000Z
DTEND:20241204T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/117
DESCRIPTION:Title: Lagrangian concordance is not a partial order\
nby Roman Golovko (Charles University) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbstr
act\nWe will show that Lagrangian concordance between Legendrian submanifo
lds is not anti-symmetric\, and hence does not define a partial order. Par
tially it is based on joint work with Georgios Dimitroglou Rizell.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willi Kepplinger (University of Vienna)
DTSTART:20241211T123000Z
DTEND:20241211T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/118
DESCRIPTION:Title: Interactions between contact topology\, Riemannian
geometry\, and spectral theory\nby Willi Kepplinger (University of Vi
enna) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geo
metry\, physics and statistics\n\n\nAbstract\nIt has long been recognized
that there should be ''good ways'' of using Riemannian geometry in order t
o make progress in contact topology. In the first place\, Riemannian geome
try in general and geometric analysis in particular have had an incredible
impact on the development of the field of low dimensional topology\, and
many people have hoped that the same would be true for contact topology as
well. Various attempts have been made over the years to realize this hope
but\, except for a couple of notable results\, strong connections have re
mained elusive. Nevertheless these few exceptions do show the promise of t
his approach\, and the goal of my talk is to highlight some of these succe
sses (some of which are quite recent) and to sketch some possible paths fo
r future developments.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Knesel (Charles University)
DTSTART:20241218T123000Z
DTEND:20241218T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/119
DESCRIPTION:Title: Representation theory\, Schubert calculus and alge
braic topology of some embedded flag submanifolds\nby Jakub Knesel (Ch
arles University) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\nLecture held in Konirna semi
nar room in the front building.\n\nAbstract\nIn this talk we provide a rep
resentation-theoretical approach to computing characteristic classes of no
rmal bundles of embeddings of real\, complex and quaternionic Grassmannian
s\, with the use of Schubert calculus\, namely the Pieri formula. A conseq
uence of these calculations is an alternative recursive way of computing c
haracteristic classes of tangent bundles of Grassmannians.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Beltita (Institute of Mathematics "Simion Stoilow" of the R
omanian Academy of Sciences)
DTSTART:20250219T123000Z
DTEND:20250219T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/120
DESCRIPTION:Title: On the integrability of transitive Lie algebroids<
/a>\nby Daniel Beltita (Institute of Mathematics "Simion Stoilow" of the R
omanian Academy of Sciences) as part of Prague-Hradec Kralove seminar Coho
mology in algebra\, geometry\, physics and statistics\n\n\nAbstract\nWe di
scuss an approach to the integration problem for general transitive Lie al
gebroids using two basic ingredients: the Čech cohomology and the general
ization of smooth manifolds that was proposed by Raymond Barre under the n
ame of Q-manifolds. To this end we study the notion of Q-principal bundle\
, i.e.\, a natural version of principal fibre bundles in the theory of Q-m
anifolds. We then prove that every transitive Lie algebroid arises from th
e Atiyah sequence of a Q-principal bundle and we give the interpretation o
f that result in terms of groupoids. The presentation is based on joint wo
rk with Fernand Pelletier.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University of Hradec Kralove)
DTSTART:20250212T123000Z
DTEND:20250212T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/121
DESCRIPTION:Title: Invariants of piecewise linear curves (joint with
Yaroslav Bazaikin)\nby Alexei Kotov (University of Hradec Kralove) as
part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, p
hysics and statistics\n\nLecture held in blue lecture room\, rear building
\, ground floor.\n\nAbstract\nThe problem of classification of geometric o
bjects under the action of a group or a pseudogroup of transformations has
a long history and dates back to the Erlangen program of Felix Klein. We
propose a "discrete" version of this theory\, in which\, instead of smooth
structures\, we consider their piecewise smooth approximations\, consisti
ng of "simple" blocks. In this talk\, we will focus on the classification
of the piecewise linear curves in an affine space under the action of the
affine transformation group. The obtained "discrete" invariants in the lim
it give known differential invariants for a similar problem in a smooth ca
se.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vsevolod Shevchishin (University of Warmia and Mazury at Olsztyn)
DTSTART:20250226T123000Z
DTEND:20250226T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/122
DESCRIPTION:Title: Laemotentoma: Treating of symplectic neck stretchi
ng in symplectic 4-manifolds across Lagrangian surfaces\nby Vsevolod S
hevchishin (University of Warmia and Mazury at Olsztyn) as part of Prague-
Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and stat
istics\n\nLecture held in blue lecture room\, rear building\, ground floor
.\n\nAbstract\nRecently Borman-Li-Wu found an example of two Lagrangian em
beddings\nof the real projective plane RP^2 in a symplectic 4-manifold\nwh
ich are Z_2-homologous but not isotopic\, even smoothly.\n\nIn my talk I m
ake a short introduction to the technique\nof the symplectic neck stretchi
ng ("Laemotentoma")\nand show how it can be used to classify Lagrangian em
beddings\nof RP^2 in symplectic 4-manifolds. In particular\, I show that\n
for any given number N there exist a rational symplectic 4-manifold\nX and
Lagrangian embeddings P_1\, ...\, P_N of RP^2 in X\nin the same Z_2-homol
ogy class which are pairwisely not isotopic\, even smoothly.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Vysoký (Czech Technical University)
DTSTART:20250305T123000Z
DTEND:20250305T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/123
DESCRIPTION:Title: Graded Lie groups with Examples\nby Jan Vysok
ý (Czech Technical University) as part of Prague-Hradec Kralove seminar C
ohomology in algebra\, geometry\, physics and statistics\n\nLecture held i
n blue lecture room\, rear building\, ground floor.\n\nAbstract\nLie group
s and their algebras are fundamental mathematical objects of differential
geometry. We show how their analogue is brought into the realm of graded m
anifolds. Standard aspects of graded Lie theory are discussed. We focus on
examples\, namely of graded versions of general\, orthogonal and symplect
ic Lie groups.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Zuevsky (Institute of Mathematics of ASCR)
DTSTART:20250312T123000Z
DTEND:20250312T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/124
DESCRIPTION:Title: CFT correlation determinants with elliptic functio
ns\nby Sasha Zuevsky (Institute of Mathematics of ASCR) as part of Pra
gue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and
statistics\n\nLecture held in blue lecture room\, rear building\, ground f
loor.\n\nAbstract\nIn this talk we show how to use the determinantal repre
sentations for correlation functions in CFT to derive new determinant form
ulas for powers of the modular discriminant expressed via deformed ellipti
c functions with parameters in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Chekeres (University of l'Aquila\, Italy)
DTSTART:20250319T123000Z
DTEND:20250319T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/125
DESCRIPTION:Title: Odd and generalized Wilson surfaces\nby Olga C
hekeres (University of l'Aquila\, Italy) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\n\nAbs
tract\nIn this talk I discuss various extensions and generalizations of Wi
lson surface observables in gauge theories. Previously\, Wilson surface ob
servables were interpreted as a class of Poisson sigma models. We profit f
rom this construction to define and study the super version of Wilson surf
aces. We provide some 'proof of concept' examples to illustrate modificati
ons resulting from appearance of odd degrees of freedom in the target. We
also explain some natural directions for defining the analogues of Wilson
surface observables in higher dimensions.\n\nThe talk is mostly based on h
ttps://arxiv.org/abs/2403.09820. This is a joint work with Vladimir Salnik
ov.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaoru Ono (Kyoto University)
DTSTART:20250326T140000Z
DTEND:20250326T153000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/126
DESCRIPTION:Title: 21st Eduard Čech Lecture: Some Developments in La
grangian Floer Theory\nby Kaoru Ono (Kyoto University) as part of Pra
gue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and
statistics\n\nLecture held in blue lecture room\, rear building\, ground f
loor.\n\nAbstract\nAndreas Floer initiated what is now called Floer theory
in the middle of 1980’s. I start with some background such as the Arnol
d conjecture for fixed points of Hamiltonian diffeomorphisms\, which motiv
ates him to build Floer (co)homology. After mentioning his construction\,
I will sketch a general story of Floer theory for Lagrangian submanifolds
and explain some applications based on my joint work with Kenji Fukaya\, Y
ong-Geun Oh and Hiroshi Ohta. I would also like to speak on a recent joint
work with Bohui Chen and Bai-Ling Wang on Lagrangian Floer theory on symp
lectic orbifolds. In particular\, we introduced the notion of dihedral twi
sted sectors\, which is a counterpart of the twisted sector (inertia orbif
old) in orbifold Gromov-Witten theory due to Weimin Chen and Yongbin Ruan.
\n\nOfficial announcement: https://www.math.cas.cz/index.php/news/item/265
\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaoru Ono (RIMS\, Kyoto University)
DTSTART:20250402T113000Z
DTEND:20250402T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/127
DESCRIPTION:Title: Lagrangian Floer theory on symplectic orbifolds\nby Kaoru Ono (RIMS\, Kyoto University) as part of Prague-Hradec Kralove
seminar Cohomology in algebra\, geometry\, physics and statistics\n\nLect
ure held in blue lecture room\, rear building\, ground floor.\n\nAbstract\
nW. Chen and Y. Ruan developed Gromov-Witten theory on symplectic orbifold
s\, where an imporatn notion\, the inertia orbifold (twisted sector) plays
an important role. When a Lagrangian is contained in the regular part\, L
agrangian Floer theory was studied by C.-H. Cho and M. Poddar. In joint wo
rks with B. Chen and B.-L. Wang\, we introduce the notion of dihedral twis
ted sector associated with a Lagrangian in a symplectic orbifold. After re
viewing some preliminaries on orbifolds such as orbifold morphisms\, I wil
l present the notion of dihedral twisted sector associated with a Lagrangi
an in a symplectic orbifold and explain how to construct Lagrangian Floer
theory in symplectic orbifolds. This talk is based on a joint work with B.
Chen and B.-L. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaoru Ono (RIMS\, Kyoto University)
DTSTART:20250409T113000Z
DTEND:20250409T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/128
DESCRIPTION:Title: Some applications of Lagrangian Floer theory\n
by Kaoru Ono (RIMS\, Kyoto University) as part of Prague-Hradec Kralove se
minar Cohomology in algebra\, geometry\, physics and statistics\n\nLecture
held in blue lecture room\, rear building\, ground floor.\n\nAbstract\nI
will explain a bit more on general story of Lagrangian Floer theory\, whic
h I touch in Eduard Cech Lecture. Firstly\, we will presentLagrangian Floe
r theory such as the construction of the filtered $A_{\\infty}$-structure\
, (weak) Mauer-Cartan equation\, bulk deformation\, etc. Then we explain i
ts efficiency through some application such as the case of Lagrangian toru
s fibers in compact Kähler toric manifolds\, This is mainly based on join
t works with K. Fukaya.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (Iv. Javakhishvili Tbilisi State University)
DTSTART:20250416T113000Z
DTEND:20250416T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/129
DESCRIPTION:Title: The transfer and Symplectic Cobordism I\nby Ma
lkhaz Bakuradze (Iv. Javakhishvili Tbilisi State University) as part of Pr
ague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and
statistics\n\nLecture held in blue lecture room\, rear building\, ground
floor.\n\nAbstract\nWe use the Connerf-Floyd- Pontrjagin characteristic cl
asses and stable transfer map to derive some generating relations in sympl
ectic cobordism ring.\n\nFor instance it is proved that all four-fol
d products of Ray classes are zero. Similar results are provided in the se
lf conjugate cobordism ring.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (University of Bonn)
DTSTART:20250423T113000Z
DTEND:20250423T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/130
DESCRIPTION:Title: The Kaplansky conjectures\nby Giles Gardam (Un
iversity of Bonn) as part of Prague-Hradec Kralove seminar Cohomology in a
lgebra\, geometry\, physics and statistics\n\n\nAbstract\nThere is a serie
s of four long-standing conjectures on group rings that are attributed to
Kaplansky. For example\, the zero divisor conjecture states that the group
ring of a torsion-free group over a field has no zero divisors. I will di
scuss what is known about these conjectures and my disproof of the unit co
njecture.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malkhaz Bakuradze (Iv. Javakhishvili Tbilisi State University)
DTSTART:20250430T113000Z
DTEND:20250430T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/131
DESCRIPTION:Title: The transfer and Symplectic Cobordism II\nby M
alkhaz Bakuradze (Iv. Javakhishvili Tbilisi State University) as part of P
rague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics an
d statistics\n\nLecture held in blue lecture room\, rear building\, ground
floor.\n\nAbstract\nThis lecture is a continuation of the lecture on Wedn
esday April 16\n\nWe use the Connerf-Floyd- Pontrjagin characteristic clas
ses and stable transfer map to derive some generating relations in symplec
tic cobordism ring.\n\nFor instance it is proved that all four-fold pro
ducts of Ray classes are zero. Similar results are provided in the self co
njugate cobordism ring.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Ryvkin (Université Claude Bernard Lyon 1)
DTSTART:20250507T113000Z
DTEND:20250507T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/132
DESCRIPTION:Title: Vector bundles over unordered configuration spaces
\nby Leonid Ryvkin (Université Claude Bernard Lyon 1) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\nLecture held in the blue lecture room + ZOOM meeting.\n\nAbst
ract\nI will describe a recent construction of a symmetrized external tens
or product of vector bundles of unordered configuration spaces (over some
fixed manifold M). Together with the usual tensor product this constructio
n induces a 2-monoidal structure on these vector bundles and naturally app
ears when trying to construct a geometric model for the multilocal observa
bles in field theory. I will also discuss how equipping the configuration
with a certain natural bornology can compensate the fact that they are non
-compact\, even when the initial manifold M is.\n\nbased on joint work wit
h Alessandra Frabetti and Olga Kravchenko.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martha Valentina Guarin Escudero (Charles University)
DTSTART:20250521T113000Z
DTEND:20250521T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/133
DESCRIPTION:Title: Globalizations of L-infinity algebras associated t
o dg-manifolds\nby Martha Valentina Guarin Escudero (Charles Universit
y) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\nLecture held in blue lecture room + ZOOM me
eting.\n\nAbstract\nIn this talk\, we discuss how to use a version of Fedo
sov's construction to define an L-infinity structure on the space of vecto
r fields on a dg-manifold. Additionally\, we compare such construction wit
h an approach exposed by Stienon\, Xu and Seoul which is related to formal
exponential maps and Kapranov L-infinity algebras.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Bonavolontа (European Investment Bank\, Luxembourg)
DTSTART:20250514T113000Z
DTEND:20250514T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/134
DESCRIPTION:Title: Information Geometry and Quantitative Finance: som
e applications\nby Giuseppe Bonavolontа (European Investment Bank\, L
uxembourg) as part of Prague-Hradec Kralove seminar Cohomology in algebra\
, geometry\, physics and statistics\n\nLecture held in ZOOM meeting.\n\nAb
stract\nThis presentation explores some applications and implementations o
f information geometry within the field of quantitative finance\, highligh
ting its relevance especially for model risk.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slaven Kozic (University of Zagreb\, Croatia)
DTSTART:20250528T113000Z
DTEND:20250528T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/135
DESCRIPTION:Title: On some new constructions in quantum vertex algebr
a theory\nby Slaven Kozic (University of Zagreb\, Croatia) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics a
nd statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nOne important
problem in the vertex algebra theory is to associate certain vertex algebr
a-like objects\, the quantum vertex algebras\, to various classes of quant
um groups\, such as quantum affine algebras or double Yangians. In this ta
lk\, after giving a brief introduction to the main concepts of quantum ver
tex algebra theory\, I will discuss the aforementioned problem in the sett
ing of the Etingof-Kazhdan quantum affine vertex algebra associated with t
he trigonometric R-matrix of type A. The main focus will be on its connect
ion with the representation theory of the quantum affine algebra of type A
\, the explicit description of its center at the critical level and some f
urther applications to the construction of certain commutative subalgebras
. The talk is in part based on the joint works with Lucia Bagnoli and Alex
ander Molev.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marijana Butorac (Rijka University Croatia)
DTSTART:20251008T113000Z
DTEND:20251008T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/136
DESCRIPTION:Title: Combinatorial bases of standard modules for affine
Lie algebras\nby Marijana Butorac (Rijka University Croatia) as part
of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physic
s and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nWe consider
standard modules of affine Lie algebras. In this talk I will present cons
truction of combinatorial bases of standard modules with rectangular highe
st weights\, which relies on the the construction of quasi-particle bases
of the Feigin-Stoyanovsky principal subspaces. This talk is based on joint
works with Slaven Kožić and Mirko Primc.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M.A. Zubkov (Ariel University\, Physics Department\, Ariel\, 40700
00\, Israel)
DTSTART:20251119T123000Z
DTEND:20251119T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/137
DESCRIPTION:Title: Wigner - Weyl calculus and the theory of topologic
al response\nby M.A. Zubkov (Ariel University\, Physics Department\, A
riel\, 4070000\, Israel) as part of Prague-Hradec Kralove seminar Cohomolo
gy in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM
meeting.\n\nAbstract\nI review the theory of topological response in moder
n materials (including the three - dimensional topological semimetals and
the two - dimensional systems with quantum Hall effect) as well as in the
elementary particle physics. The proposed theory is based on the specific
version of Wigner - Weyl calculus developed for the quantum field theory d
uring the recent years by the group working in Ariel University\, Israel.\
n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel (VUB))
DTSTART:20251022T113000Z
DTEND:20251022T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/138
DESCRIPTION:Title: An introduction to Nichols algebras\nby Leandr
o Vendramin (Vrije Universiteit Brussel (VUB)) as part of Prague-Hradec Kr
alove seminar Cohomology in algebra\, geometry\, physics and statistics\n\
nLecture held in ZOOM meeting.\n\nAbstract\nNichols algebras appear in var
ious areas of mathematics\, ranging from \nHopf algebras and quantum group
s to Schubert calculus and conformal \nfield theory. Originally introduced
in the 1970s through the work of \nNichols\, they have been rediscovered
multiple times\, maybe because \nthey appear in several different contexts
. In this introductory talk\, \nI will review the basic concepts and outli
ne the main challenges \ninvolved in classifying Nichols algebras over gro
ups. In particular\, I \nwill discuss some recent classification theorems\
, highlighting a \nresult obtained in collaboration with Andruskiewitsch a
nd Heckenberger \nconcerning finite-dimension.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Galaev (Hradec-Králové University)
DTSTART:20251029T123000Z
DTEND:20251029T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/139
DESCRIPTION:Title: Holonomy of K-contact sub-Riemannian manifolds
\nby Anton Galaev (Hradec-Králové University) as part of Prague-Hradec K
ralove seminar Cohomology in algebra\, geometry\, physics and statistics\n
\nLecture held in ZOOM meeting.\n\nAbstract\nGiven a contact sub-Riemannia
n manifold (M\, θ\, g)\, where θ is a contact form on M\, and g is a met
ric on the contact distribution D = ker θ\, there is the Schouten connect
ion\, which defines parallel transport of vectors tangent to D along curve
s tangent to D. The holonomy group of this connection is called the horizo
ntal holonomy group. The adapted connection is an extension of the horizon
tal connection to a connection on the vector bundle D over M. I will show
that in the K-contact case (which means that the Reeb vector field is a Ki
lling one)\, the holonomy of the adapted connection is the holonomy of som
e Riemannian manifold\, and the horizontal holonomy either coincides with
the holonomy of the adapted connection\, or it is a codimension-one normal
subgroup of the later group. I will discuss the question of existence
of parallel horizontal spinors\, examples\, and consequences.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaroslav Bazaikin (The Jan Evangelista Purkyně University in Úst
í nad Labem)
DTSTART:20251112T123000Z
DTEND:20251112T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/141
DESCRIPTION:Title: On Losik characteristic classes of quotient of $S^
1$ by special linear transformations\nby Yaroslav Bazaikin (The Jan Ev
angelista Purkyně University in Ústí nad Labem) as part of Prague-Hrade
c Kralove seminar Cohomology in algebra\, geometry\, physics and statistic
s\n\nLecture held in the blue lecture room +ZOOM meeting.\n\nAbstract\nWe
study Chern-Losik and Godbillon-Vey-Losik classes of quotient $S^1/\\varph
i$\, where $\\varphi \\in SL(2\,\\mathbb{R})$. These classes arise geometr
ically as invariants of foliated suspensions over action $\\varphi$ on $S^
1$. This is joint work with Anton Galaev and Yury Efremenko.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Golovko (Charles University)
DTSTART:20251126T123000Z
DTEND:20251126T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/142
DESCRIPTION:Title: Non-regular Lagrangian concordances between Legend
rain knots\nby Roman Golovko (Charles University) as part of Prague-Hr
adec Kralove seminar Cohomology in algebra\, geometry\, physics and statis
tics\n\nLecture held in the blue lecture room + ZOOM meeting.\n\nAbstract\
nFor a while\, it was an open question whether a Lagrangian cobordism with
a non-empty positive end can be decomposed into a concatenation of elemen
tary pieces: traces of Legendrian isotopies\, isolated standard-unknot bir
ths inducing Lagrangian 0-handle attachments\, and Legendrian surgeries in
ducing Lagrangian 1-handle attachments. We answer this question negatively
. This is joint work with Georgios Dimitroglou Rizell.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukihiro Okamoto (Tokyo Metropolitan University)
DTSTART:20251203T123000Z
DTEND:20251203T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/143
DESCRIPTION:Title: Legendrian non-isotopic unit conormal bundles in h
igh dimensions\nby Yukihiro Okamoto (Tokyo Metropolitan University) as
part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\,
physics and statistics\n\n\nAbstract\nFor any compact submanifold of $\\ma
thbb{R}^n$\, its unit conormal bundle is a compact Legendrian submanifold
of the unit cotangent bundle of $\\mathbb{R}^n$. In this talk\, I will giv
e examples of pairs of compact connected submanifolds of $\\mathbb{R}^n$ o
f codimension greater than 3 such that their unit conormal bundles are not
Legendrian isotopic\, although these two Legendrian submanifolds cannot b
e distinguished by classical invariants. The main tools to distinguish the
m are the strip Legendrian contact homology and a coproduct on it. I will
explain that\, in a special case including the main examples\, the coprodu
ct can be computed by using the idea of string topology.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teimuraz Pirashvili (University of Georgia)
DTSTART:20251210T123000Z
DTEND:20251210T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/144
DESCRIPTION:Title: The category of finite sets and cohomology theorie
s of commutative algebras\nby Teimuraz Pirashvili (University of Georg
ia) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geome
try\, physics and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\
nIt is well-known that the category of exponential functors F → V from t
he category of finite sets to the category of vector spaces is equivalent
to the category of commutative algebras. Hence functors F → V can be con
sidered as generalized algebras and one can ask what constructions and not
ions of commutative algebras have extensions to functors F → V and if su
ch extension exists what for it is good? We will see that several homology
theories have such extensions and give some applications.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hông Vân Lê (Institute of Mathematics of ASCR)
DTSTART:20251217T123000Z
DTEND:20251217T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/145
DESCRIPTION:Title: Probabilistic morphisms\, stochastic processes\, a
nd Bayesian supervised learning\nby Hông Vân Lê (Institute of Mathe
matics of ASCR) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\nLecture held in the blue lectu
re room + ZOOM meeting.\n\nAbstract\nUsing a categorical approach to Marko
v kernels\, and stochastic processes taking values in the space of probabi
lity measures on a label space\, I propose a unifying model for Bayesian s
upervised learning. I show that batch learning equals online learning i
n Bayesian supervised learning. As a result\, I derive a recursive formula
for predictive distributions which reduces to the Kalman filter in Gaussi
an process regression. Finally\, I shall discuss some related problems in
mathematical machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Fritz (University of Innsbruck\, Austria)
DTSTART:20260211T123000Z
DTEND:20260211T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/146
DESCRIPTION:Title: Optimizing over iid distributions and the Beat the
Average game\nby Tobias Fritz (University of Innsbruck\, Austria) as
part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, p
hysics and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nA casi
no offers the following game. There are three cups each containing a die.
You are being told that the dice in the cups are all the same\, but possib
ly nonstandard. For a bet of \\$1\, the game master shakes all three cups
and lets you choose one of them. You win \\$2 if the die in your cup displ
ays at least the average of the other two\, and you lose otherwise. Is thi
s game fair? If not\, how should the casino design the dice to maximize th
eir profit?\n\nIn this talk\, I will answer this question\, explain what i
t is an example of\, and outline our partial results on a more difficult q
uestion of the same type: how likely can we make the event $X_1 + X_2 + X_
3 < 2 X_4$\, given the constraint that the random variables $X_1\, ...\, X
_4$ must be iid? Surprisingly\, obtaining good bounds involves solving cha
llenging combinatorial optimization problems.\n\nBased on joint work with
Pierre C Bellec (arXiv:2412.15179)\, which has recently been featured as a
test case for the AI tool AlphaEvolve (arXiv:2511.02864).\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Fioresi (University of Bologna)
DTSTART:20260218T123000Z
DTEND:20260218T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/147
DESCRIPTION:Title: Geometric Deep Learning meets Quantum Groups\n
by Rita Fioresi (University of Bologna) as part of Prague-Hradec Kralove s
eminar Cohomology in algebra\, geometry\, physics and statistics\n\nLectur
e held in ZOOM meeting.\n\nAbstract\nWe show how the noncommutative langua
ge of quantum differential calculi can help with a natural description of
differential operators in graph neural networks (message passing mechanism
). Joint work with F. Zanchetta\, A. Simonetti.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ida Zadeh (University of Southampton\, UK)
DTSTART:20260225T111500Z
DTEND:20260225T121500Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/148
DESCRIPTION:Title: Tracking the symmetries of Z3-orbifold K3s within
the Mathieu groups\nby Ida Zadeh (University of Southampton\, UK) as p
art of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, ph
ysics and statistics\n\nLecture held in ZOOM meeting.\n\nAbstract\nThis se
minar starts EARLIER than the usual schedule.\n\nWe shall open t
he seminar room + ZOOM meeting at 12.00 for (virtual) coffee and close
ZOOM at 13.30\n\nThe goal of this talk is to determine the group of holom
orphic symplectic automorphisms of Z3-orbifold limits of K3 surfaces\, and
to track this group within two of the sporadic groups Mathieu 12 and Math
ieu 24. To do so\, I will provide a counterpart to the extensive studies b
y Nikulin and others of the geometry and symmetries of classical Kummer su
rfaces\, which involves a variation of Kondo's lattice techniques that Tao
rmina and Wendland introduced earlier in the genesis of their symmetry sur
fing programme. I will realise the finite group of symplectic automorphism
s of this class of K3 surfaces as a subgroup of Mathieu 12 and Mathieu 24
in terms of permutations of respectively 12 and 24 elements. The talk is b
ased on a joint work with Kasia Budzik\, Anne Taormina\, Mara Ungureanu an
d Katrin Wendland.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Krutov (Charles University)
DTSTART:20260304T123000Z
DTEND:20260304T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/149
DESCRIPTION:Title: Non-integrable distributions with simple infinite-
dimensional Lie superalgebra of symmetries\nby Andrey Krutov (Charles
University) as part of Prague-Hradec Kralove seminar Cohomology in algebra
\, geometry\, physics and statistics\n\nLecture held in the blue lecture r
oom +ZOOM meeting.\n\nAbstract\nThe only simple infinite-dimensional Lie a
lgebras preserving a non-integrable distribution are the algebras of conta
ct vector fields in odd dimensions. We formulate analogs of the above stat
ement and prove them for (super)varieties over algebraically closed fields
of any characteristic $p\\geq0$.\n\nOver fields $\\mathbb{K}$ of characte
ristic $p>0$\, we classify the Weisfeiler gradings (briefly: W-gradings)\,
those corresponding to a maximal subalgebra of finite codimension\, of th
e known simple vectorial Lie (super)algebras with unconstrained shearing v
ector of heights of the indeterminates\, distinguish W-gradings of (super)
algebras preserving non-integrable distributions.\n\nJoin work with D. Lei
tes and I. Shchepochkina (arXiv:2309.16370)\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russell Avdek (Institut de Mathématiques de Jussieu\, Sorbonne Un
iversité)
DTSTART:20260311T123000Z
DTEND:20260311T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/150
DESCRIPTION:Title: Numerical invariants of contact manifolds and thei
r divisors\nby Russell Avdek (Institut de Mathématiques de Jussieu\,
Sorbonne Université) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM mee
ting.\n\nAbstract\nI will introduce an invariant E(K) of codim=2 contact s
ubmanifolds K of a contact manifold (of any dimension)\, generalizing the
self-linking number SL(K) of transverse links in the contact 3-sphere. Ext
ending the observation that SL(L)=1 mod 2 for knots\, modular properties E
(K) are intimately related to the divisibilities of certain Chern numbers.
A generalization of Gompf's d3 invariant of contact 3-manifolds is also d
efined and used to uncover surprising properties of E(K). These tools prov
ide novel information about Milnor numbers of complex hypersurface singula
rities.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hông Vân Lê (Institute of Mathematics of ASCR)
DTSTART:20260318T123000Z
DTEND:20260318T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/151
DESCRIPTION:Title: Minimal Unital Cyclic C∞-Algebras and the Real a
nd Rational Homotopy Type of Closed Manifolds\nby Hông Vân Lê (Inst
itute of Mathematics of ASCR) as part of Prague-Hradec Kralove seminar Coh
omology in algebra\, geometry\, physics and statistics\n\nLecture held in
blue lecture room + ZOOM meeting.\n\nAbstract\nUsing the notion of isotopy
modulo $k$\, with $k \\in \\mathbb{N}^+$\, we introduce a stratification
on the set of all minimal $C_\\infty$-algebra enhancements of a finite-typ
e graded commutative algebra $H^*$. We determine obstruction classes defin
ing the extendability of isotopy modulo $k$ to isotopy modulo $(k+1)$ for
minimal $C_\\infty$-algebra enhancements of $H^*$ and demonstrate their ge
neralized additivity. As a result\, we define a complete set of invariants
of the rational homotopy type of closed simply connected manifolds M . We
prove that if M is a closed (r − 1)-connected manifold of dimension n
≤ l(r − 1) + 2 (where r ≥ 2\, l ≥ 4)\, the real and rational homot
opy type of M is defined uniquely by the cohomology algebra H*(M\, F) and
the isotopy modulo (l − 2) of the corresponding minimal unital cyclic C
∞ -algebra enhancements of H*(M\, F) for F = R\, Q\, respectively. Combi
ning this with the Hodge homotopy introduced by Fiorenza-Kawai-Lê-Schwach
höfer\, we provide a new proof of a theorem by Crowley-Nordström: a (r
−1)-connected closed manifold M of dimension 4r − 1 with b_r (M) ≤ 3
is intrinsically formal if there exists a φ ∈ H^(2r−1) (M\, R) such
that the map H^r (M\, R) → H^(3r−1) (M\, R)\, x → φ ∪ x is an iso
morphism. Furthermore\, we provide a new proof and extension of Cavalcanti
’s result\, showing that a (r − 1)-connected closed manifold M of dime
nsion 4r with b_r (M) ≤ 2 is intrinsically formal under similar conditio
ns. This talk is based on \nhttps://arxiv.org/abs/2603.01219\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizaveta Vishnyakova (Department of Math. UFMG\, Belo Horizonte\,
Brazil)
DTSTART:20260401T110000Z
DTEND:20260401T120000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/152
DESCRIPTION:Title: About Graded coverings of supermanifolds and their
applications\nby Elizaveta Vishnyakova (Department of Math. UFMG\, Be
lo Horizonte\, Brazil) as part of Prague-Hradec Kralove seminar Cohomology
in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM me
eting.\n\nAbstract\nIn geometry\, the concept of a covering space is class
ical and well established. A familiar example is the universal covering \\
( p: \\mathbb{R} \\to S^1 \\)\, given by \\( t \\mapsto \\exp(it) \\). Ana
logous constructions appear in algebra as well—for instance\, in the the
ory of modules over rings\, where one encounters flat or torsion-free cove
rings. Although they arise in different contexts\, these notions share a c
ommon underlying idea: an object from a given category is covered by an ob
ject belonging to a smaller (or different) category in such a way that cer
tain universal properties are satisfied.\n\n\n\nIn their paper "Super Atiy
ah classes and obstructions to splitting of supermoduli space\," Donagi an
d Witten introduced a construction of the first obstruction class to the s
plitting of a supermanifold. Later\, we observed that the infinite prolong
ation of their construction satisfies universal properties analogous to th
ose found in other covering theories. In other words\, this construction y
ields a covering of a supermanifold in the category of graded manifolds as
sociated with the nontrivial homomorphism \\( \\mathbb{Z} \\to \\mathbb{Z}
_2 \\). Moreover\, the space of infinite jets can also be viewed as a cove
ring of a (super)manifold in the category of graded manifolds correspondin
g to the homomorphism \\( \\mathbb{Z} \\times \\mathbb{Z}_2 \\to \\mathbb{
Z}_2 \\)\, given by \\( (m\, \\bar{n}) \\mapsto \\bar{n} \\). (For ordinar
y manifolds\, this homomorphism reduces to the trivial map \\( \\mathbb{Z}
\\to 0 \\).)\n\nOur talk is devoted to the current state of the theory of
graded coverings\, including the general framework\, key examples\, and a
presentation of our recent results.\n\nThe seminar starts **30 minutes ea
rlier than usual**.\n\nWe shall open ZOOM meeting at 12.45 for virtual cof
fee and close ZOOM at 14.30\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov (University of Hradec Kralove)
DTSTART:20260415T113000Z
DTEND:20260415T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/153
DESCRIPTION:by Alexei Kotov (University of Hradec Kralove) as part of Prag
ue-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and s
tatistics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Bieliavsky (UCLouvain)
DTSTART:20260422T113000Z
DTEND:20260422T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/154
DESCRIPTION:by Pierre Bieliavsky (UCLouvain) as part of Prague-Hradec Kral
ove seminar Cohomology in algebra\, geometry\, physics and statistics\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svatopluk Kryls (Mathematical Institute\, Charles University)
DTSTART:20260506T113000Z
DTEND:20260506T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/155
DESCRIPTION:by Svatopluk Kryls (Mathematical Institute\, Charles Universit
y) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geomet
ry\, physics and statistics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Hajek (Wolfram Insitute for Computational Foundation of Scie
nces)
DTSTART:20260527T113000Z
DTEND:20260527T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/156
DESCRIPTION:by Pavel Hajek (Wolfram Insitute for Computational Foundation
of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in algebr
a\, geometry\, physics and statistics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Khavkine (Institute of Mathematics of ASCR)
DTSTART:20260429T113000Z
DTEND:20260429T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/157
DESCRIPTION:by Igor Khavkine (Institute of Mathematics of ASCR) as part of
Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics
and statistics\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruben Louis (University of Illinos Urbana-Champaign Urbana)
DTSTART:20260408T113000Z
DTEND:20260408T123000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/158
DESCRIPTION:Title: On construction of differential Z-graded varieties
(Joint work with A. Hancharuk)\nby Ruben Louis (University of Illinos
Urbana-Champaign Urbana) as part of Prague-Hradec Kralove seminar Cohomol
ogy in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM
meeting.\n\nAbstract\nGiven a commutative unital algebra O\, a proper ide
al I⊂O\, and a positively graded differential variety over O/I\, we cons
truct a Z-graded extension whose negative part is an arborescent Koszul–
Tate resolution of O/I. This extension is obtained by means of an explicit
algorithm that exploits the homotopy retract data of the arborescent Kosz
ul–Tate resolution\, thereby significantly reducing the number of homolo
gical computations required in the construction.\n\nWhen the positively gr
aded differential variety is defined over O and preserves the ideal I\, th
e extension admits a canonical and explicit description in terms of decora
ted trees together with the associated computed data.\n\nAs a by-product\,
to every Lie–Rinehart algebra over the coordinate ring of an affine var
iety W\, we associate an explicit differential Z-graded variety. Its negat
ive component is the arborescent Koszul–Tate resolution of the coordinat
e ring of W\, while its positive component is the universal dg-variety
of the given Lie–Rinehart algebra.\n\nThese constructions also yield app
lications to singular foliation theory\, extending results of C. Laurent-G
engoux\, S. Lavau\, and T. Strobl. Explicit examples are provided.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Kettner (Mathematical Institute\, Charles University)
DTSTART:20260325T123000Z
DTEND:20260325T133000Z
DTSTAMP:20260404T095038Z
UID:PHK-cohomology-seminar/159
DESCRIPTION:Title: $K$-theory for the $C^*$-algebra of a homeomorphis
m and a vector bundle\nby Aaron Kettner (Mathematical Institute\, Char
les University) as part of Prague-Hradec Kralove seminar Cohomology in alg
ebra\, geometry\, physics and statistics\n\nLecture held in blue lecture r
oom + ZOOM meeting.\n\nAbstract\nWe outline how to construct a C*-algebra
from a homeomorphism on a compact Hausdorff space $X$\, together with a ve
ctor bundle over $X$. This generalizes crossed products of the form $C(X)\
\rtimes_\\alpha\\mathbb{Z}$. Under reasonable assumptions these $C^*$-alge
bras turn out to be classifiable in the sense of the Elliott program. We s
ketch K-theory calculations which are work in progress with Karen Strung a
nd Sven Raum.\n
LOCATION:https://stable.researchseminars.org/talk/PHK-cohomology-seminar/1
59/
END:VEVENT
END:VCALENDAR