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BEGIN:VEVENT
SUMMARY:Eckhard Meinrenken (Toronto)
DTSTART:20200416T151500Z
DTEND:20200416T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/1
DESCRIPTION:Title: Van Est differentiation and Van Est integration\nby Eckha
rd Meinrenken (Toronto) as part of Global Poisson webinar\n\nLecture held
in Zoom.\n\nAbstract\nThe classical Van Est theory relates the smooth coho
mology of Lie groups with the cohomology of the associated Lie algebra. So
me aspects of this theory generalize to Lie groupoids and their Lie algebr
oids. In this talk\, we revisit the van Est theory using the Perturbation
Lemma from homological algebra. This leads to precise descriptions of the
van Est differentiation and integration at the level of cochains. The talk
is based on recent work with Maria Amelia Salazar.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Loja Fernandes (Urbana-Champaign)
DTSTART:20200409T151500Z
DTEND:20200409T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/2
DESCRIPTION:Title: Local models around Poisson submanifolds\nby Rui Loja Fer
nandes (Urbana-Champaign) as part of Global Poisson webinar\n\nAbstract: T
BA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20200423T151500Z
DTEND:20200423T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/3
DESCRIPTION:Title: Short star-products for filtered quantizations\nby Pavel
Etingof (MIT) as part of Global Poisson webinar\n\nLecture held in Zoom.\n
\nAbstract\nLet $A$ be a filtered Poisson algebra with Poisson bracket $\\
lbrace{\,\\rbrace}$ of degree $-2$. A {\\it star product} on $A$ is an ass
ociative product $*: A\\otimes A\\to A$ given by $$a*b=ab+\\sum_{i\\ge 1}C
_i(a\,b)\,$$ where $C_i$ has degree $-2i$ and $C_1(a\,b)-C_1(b\,a)=\\lbrac
e{a\,b\\rbrace}$. We call the product * {\\it even} if $C_i(a\,b)=(-1)^i
C_i(b\,a)$ for all $i$\, and call it {\\it short} if $C_i(a\,b)=0$ wheneve
r $i>{\\rm min}({\\rm deg}(a)\, {\\rm deg}(b))$.\n\nMotivated by three-dim
ensional $N=4$ superconformal field theory\, In 2016 Beem\, Peelaers and R
astelli considered short even star-products for homogeneous symplectic sin
gularities (more precisely\, hyperK\\"ahler cones) and conjectured that th
at they exist and depend on finitely many parameters. We prove the depende
nce on finitely many parameters in general and existence for a large class
of examples\, using the connection of this problem with zeroth Hochschild
homology of quantizations suggested by Kontsevich.\n\nBeem\, Peelaers and
Rastelli also computed the first few terms of short quantizations for Kle
inian singularities of type A\, which were later computed to all orders by
Dedushenko\, Pufu and Yacoby. We will discuss some generalizations of the
se results.\n\nThis is joint work with Douglas Stryker.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Weinstein (UC Berkeley and Stanford)
DTSTART:20200430T151500Z
DTEND:20200430T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/4
DESCRIPTION:Title: Failure of Twisted Poisson Property for Monopole Plasma\n
by Alan Weinstein (UC Berkeley and Stanford) as part of Global Poisson web
inar\n\nLecture held in Zoom.\n\nAbstract\nAlthough the dynamical system f
or a charged particle in a continuous background distribution of magnetic
monopoles is given by a twisted Poisson structure\, that for a plasma
of such particles is not. (Joint work with Manuel Lainz and Cristina Sard
ón)\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brent Pym (McGill)
DTSTART:20200507T151500Z
DTEND:20200507T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/5
DESCRIPTION:Title: Holonomic Poisson manifolds\nby Brent Pym (McGill) as par
t of Global Poisson webinar\n\nLecture held in Zoom.\n\nAbstract\nHolonomi
city is a new sort of nondegeneracy condition for\nholomorphic Poisson str
uctures\, closely related to the notion of a log\nsymplectic form\, and in
timately connected with the geometry of\nWeinstein's modular vector field.
It encompasses many natural Poisson\nstructures arising in gauge theory
\, representation theory\, and algebraic\ngeometry. The motivation for t
he definition comes from deformation\ntheory: a Poisson manifold is holono
mic when its space of deformations\nis "as finite-dimensional as possible"
\, in a sense I will make precise\nduring the talk (via D-modules). I wi
ll describe the basic theory and\nexamples of holonomic Poisson manifolds\
, along with some concrete\nclassification results\, including the discove
ry of many new irreducible\ncomponents of the moduli space of Poisson four
folds. This talk is based\non joint works with Schedler\, and Matviichuk
--Schedler.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (UPC)
DTSTART:20200514T151500Z
DTEND:20200514T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/6
DESCRIPTION:Title: From b-Poisson manifolds to singular contact structures\n
by Eva Miranda (UPC) as part of Global Poisson webinar\n\nLecture held in
Zoom.\n\nAbstract\nTaking as starting point motivating examples from celes
tial mechanics and fluid dynamics\, we introduce the odd-dimensional count
erpart of b-Poisson/log-symplectic structures as Jacobi structures with tr
ansversality conditions.\nWe discuss the basic theory and some constructio
ns. In particular\, we prove that a connected component of a convex hy
persurface of a contact manifold can be realized as a connected component
of the critical set of a $b^m$-contact structure. In dimension 3\, this co
nstruction yields the existence of a generic set of surfaces $Z$ such that
the pair $(M\,Z)$ is a $b^{2k}$-contact manifold and $Z$ is its critical
hypersurface.\n\n We also consider classical problems in Hamiltonian/Ree
b dynamics and address the Weinstein conjecture on the existence of period
ic orbits of the Reeb vector field in this singular set-up. We end up this
talk with some applications of this singular Weinstein conjecture to the
motivating examples discussed at the beginning.\n\nThis is joint work with
Cédric Oms.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (UC Berkeley)
DTSTART:20200521T151500Z
DTEND:20200521T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/7
DESCRIPTION:Title: Integrable systems of Calogero-Moser type and moduli spaces o
f flat connections\nby Nicolai Reshetikhin (UC Berkeley) as part of Gl
obal Poisson webinar\n\nLecture held in Zoom.\n\nAbstract\nThe talk will b
e focused on spin Calogero-Moser systems related to symmetric spaces. They
have natural generalizations related to moduli spaces of flat connections
.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Ratiu (EPFL and Shanghai)
DTSTART:20200528T151500Z
DTEND:20200528T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/8
DESCRIPTION:Title: Differential character valued momentum maps and the Teichmül
ler space\nby Tudor Ratiu (EPFL and Shanghai) as part of Global Poisso
n webinar\n\n\nAbstract\nIt is well-known that the actions of several diff
eomorphism groups of geometric interest do not admit momentum maps. The de
finition of the Teichmüller space via Riemannian geometry strongly sugges
t that it is a symplectic reduced space. I will present an extension of th
e classical momentum map which always exists for actions of diffeomorphism
groups possessing the crucial Noether property. This extended momentum ma
p has no longer values in (pre)duals of Lie algebras\; its values are in d
ifferential character groups. This extended momentum map encodes discrete
topological information\, something the classical momentum map cannot do.
In order to focus the presentation\, the Teichmüller space will serve as
the example of this theory. The talk is based on joint work with Tobias Di
ez from TU Delft.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Kontsevich (IHÉS)
DTSTART:20200604T151500Z
DTEND:20200604T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/9
DESCRIPTION:Title: Quantum minimal surface and noncommutative Kaehler geometry\nby Maxim Kontsevich (IHÉS) as part of Global Poisson webinar\n\n\nAbs
tract\nI will talk about several interrelated topics\, based on works 1903
.10792 and 2003.03171. Minimal surfaces in Euclidean space can be approxim
ated (in sense of Berezin-Toeplitz quantization) by representations of Yan
g-Mills algebra given by relations $\\forall i\\\,\\sum_j[X_j\,[X_j\,X_i]]
=0$ where $X_i$ are self-adjoint operators. Similarly\, complex affine cur
ves are approximated by representations of hermitian Yang-Mills algebra $\
\sum_k [Z_k^\\dagger\,Z_k]=\\hbar\\cdot id$ where $Z_i$ are commuting oper
ators (but not self-adjoint in general). I will explain how the latter equ
ation appears in the context of a version of Kaehler geometry for noncommu
tative algebras.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khesin (Toronto)
DTSTART:20200611T151500Z
DTEND:20200611T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/10
DESCRIPTION:Title: Hamiltonian geometry of compressible fluids\nby Boris Kh
esin (Toronto) as part of Global Poisson webinar\n\n\nAbstract\nWe describ
e a geometric framework to study Newton's equations on infinite-dimensiona
l configuration spaces of diffeomorphisms and smooth probability densities
. It turns out that several important PDEs of hydrodynamical origin can be
described in this framework in a natural way. In particular\, the so-call
ed Madelung transform between the Schrödinger-type equations on wave func
tions and Newton's equations on densities turns out to be a Kähler map be
tween the corresponding phase spaces\, equipped with the Fubini-Study and
Fisher-Rao information metrics. This is a joint work with G.Misiolek and K
.Modin.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Sklyanin (York)
DTSTART:20200528T080000Z
DTEND:20200528T100000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/12
DESCRIPTION:Title: Groupes de Lie et espaces des modules\nby Evgeny Sklyani
n (York) as part of Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Mazzocco (University of Birmingham)
DTSTART:20200716T151500Z
DTEND:20200716T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/13
DESCRIPTION:Title: Quantum uniformisation and CY algebras\nby Marta Mazzocc
o (University of Birmingham) as part of Global Poisson webinar\n\n\nAbstra
ct\nIn this talk\, I will discuss a special class of quantum del Pezzo sur
faces. In particular I will introduce the generalised Sklyanin-Painlevé a
lgebra and characterise its PBW/PHS/Koszul properties. This algebra contai
ns as limiting cases the generalised Sklyanin algebra\, Etingof-Ginzburg a
nd Etingof-Oblomkov-Rains quantum del Pezzo and the quantum monodromy mani
folds of the Painlevé equations.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reyer Sjamaar (Cornell University)
DTSTART:20200723T151500Z
DTEND:20200723T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/14
DESCRIPTION:Title: Reduction and quantization for log symplectic manifolds\
nby Reyer Sjamaar (Cornell University) as part of Global Poisson webinar\n
\n\nAbstract\nKirillov's orbit method suggests that the classical analogue
of a representation of a Lie group G is a Hamiltonian G-action on a sympl
ectic manifold M. The classical analogue of isotypical subspaces should th
en be the symplectic quotients of M. This "quantization commutes with redu
ction" problem was articulated in the 80's by Guillemin and Sternberg and
solved by them in the context of Kaehler quantization and homogeneous quan
tization. In the 90's Meinrenken solved an index-theoretic version of the
problem. Yi Lin\, Yiannis Loizides\, Yanli Song\, and I have been trying t
o extend Meinrenken’s theorem to log symplectic manifolds\, and this tal
k will be a progress report on our work.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Gualtieri (University of Toronto)
DTSTART:20200730T151500Z
DTEND:20200730T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/15
DESCRIPTION:Title: Branes in symplectic groupoids\nby Marco Gualtieri (Univ
ersity of Toronto) as part of Global Poisson webinar\n\n\nAbstract\nAfter
an introduction to coisotropic A-branes in symplectic manifolds and their
role in mirror symmetry\, I will explain how the problem of holomorphic qu
antization of Poisson brackets may be recast\, and in some cases solved\,
as a problem of computing morphisms between coisotropic branes in symplect
ic groupoids. This is joint work with Francis Bischoff and Joshua Lack
man\n\nPlease register to obtain the password. Use your full name and inst
itutional email address.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrique Bursztyn (IMPA)
DTSTART:20200806T151500Z
DTEND:20200806T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/16
DESCRIPTION:Title: Morita equivalence of formal Poisson structures and links wi
th deformation quantization\nby Henrique Bursztyn (IMPA) as part of Gl
obal Poisson webinar\n\n\nAbstract\nThe classical notion of Morita equival
ence of algebras has a geometric version for Poisson manifolds (due to Xu)
\, defined in terms of Weinstein's dual pairs. A natural question is whet
her these two parallel Morita theories could be related by quantization. M
otivated by this question\, this talk will discuss an extension of Morita
equivalence of Poisson manifolds to the setting of {\\em formal} Poisson s
tructures\, and present a result characterizing Morita equivalent formal P
oisson structures vanishing in zeroth order in terms of ``B-field transfor
mations'' (joint work with I. Ortiz and S. Waldmann). Using the correspond
ence between formal Poisson structures and star products (due to Kontsevic
h)\, this result leads to a concrete link between Morita equivalence in Po
isson geometry and noncommutative algebra via deformation quantization.\n\
nPlease register to obtain the password. Use your full name and institutio
nal email address.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (Universität Zürich)
DTSTART:20200813T151500Z
DTEND:20200813T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/17
DESCRIPTION:Title: Complexified Floer homology and skein modules\nby Pavel
Safronov (Universität Zürich) as part of Global Poisson webinar\n\nAbstr
act: TBA\n\nPlease register to obtain the password. Use your full name and
institutional email address.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Sabatini (Universität zu Köln)
DTSTART:20200917T151500Z
DTEND:20200917T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/18
DESCRIPTION:Title: Some topological properties of monotone complexity one spa
ces\nby Silvia Sabatini (Universität zu Köln) as part of Global Pois
son webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nigel Hitchin (University of Oxford)
DTSTART:20201008T151500Z
DTEND:20201008T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/19
DESCRIPTION:Title: Teichmueller spaces and the geometry of geodesics\nby Ni
gel Hitchin (University of Oxford) as part of Global Poisson webinar\n\n\n
Abstract\nThe talk concerns a moduli space of representations of the funda
mental group of a compact surface into the group of Hamiltonian diffeomorp
hisms of $\\mathbb{S}^1 \\times \\mathbb{R}$. The motivation comes from ap
plying the ideas of Higgs bundles for $\\mathrm{SL}(N\,\\mathbb{R})$ with
$N$ equal to infinity.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alajandro Cabrera (UFRJ)
DTSTART:20201015T151500Z
DTEND:20201015T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/20
DESCRIPTION:Title: Semiclassical aspects of quantization: Local symplectic grou
poids\, generating functions and the Poisson sigma model\nby Alajandro
Cabrera (UFRJ) as part of Global Poisson webinar\n\n\nAbstract\nThe aim o
f this talk is to present three results related to local symplectic group
oids in connection to quantization of the underlying Poisson manifold. We
first review the notion of a generating function $S$ for such local symple
ctic groupoids and outline the first result stating that such $S$ always e
xist and how to construct them. When the Poisson manifold is a coordinate
space\, we provide an explicit (integral) formula for $S$. The second resu
lt makes reference to quantization: we show that the formal Taylor expansi
on $S_K$ of the coordinate $S$ yields the tree-level part of Kontsevich's
quantization formula\, as first studied by Cattaneo-Dherin-Felder. We also
sketch how the (non-formal) analytic formula for $S$ actually "explains"
the graph structure of $S_K$\, using Butcher series techniques. Finally\,
the third result relates $S$ to the functional perspective underlying the
Poisson Sigma Model: we can recover $S$ by evaluating a functional on a s
et of solutions ("semiclassical fields") for a system of PDEs on a disk\,
which we also show how to solve (non-perturbatively). We comment on conclu
sions and further directions at the end.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavol Ševera (University of Geneva)
DTSTART:20201022T151500Z
DTEND:20201022T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/21
DESCRIPTION:Title: Quantization of Poisson Hopf algebras and moduli of flat con
nections\nby Pavol Ševera (University of Geneva) as part of Global Po
isson webinar\n\n\nAbstract\nI will describe a universal quantization of P
oisson Hopf algebras using simplicial methods\, i.e. nerves of Hopf algebr
as (a joint work with Jan Pulmann). The motivation for this method comes f
rom moduli spaces of flat connections on surfaces with decorated boundarie
s (an older joint work with David Li-Bland).\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Cattaneo (Universität Zürich)
DTSTART:20201029T161500Z
DTEND:20201029T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/22
DESCRIPTION:Title: Hamilton-Jacobi and Quantum Chern-Simons on Cylinders\nb
y Alberto Cattaneo (Universität Zürich) as part of Global Poisson webin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezra Getzler (University of Northwestern)
DTSTART:20201119T161500Z
DTEND:20201119T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/23
DESCRIPTION:Title: Classical field theory\, variational calculus\, and the Bata
lin-Vilkovisky formalism\nby Ezra Getzler (University of Northwestern
) as part of Global Poisson webinar\n\n\nAbstract\n"The Batalin-Vilkovisky
formalism extends Noether's approach to classical field theories\, which
is restricted to the Euler-Lagrange locus (or ""on-shell""\, as physicists
say)\, off-shell. This is of course important in the study of quantizatio
n of field theories\, since the quantized theory is not restricted to the
Euler-Lagrange locus.\n
\nIn the variational calculus\, the action
functional is the integral of a local expression in the fields and their d
erivatives. The symmetries of the action may be expressed by the classical
Batalin-Vilkovisky master equation\, which is a Maurer-Cartan equation fo
r functionals of the classical fields\, ghost fields expressing the symmet
ries of the theory\, and certain auxilliary fields known as antifields.\n<
br>
\nThe Batalin-Vilkovisky formalism has a natural extension in funct
ionals are lifted to densities. In the first part of today's talk\, I expl
ain this extension. which relies on the Soloviev bracket in the variationa
l calculus\, originally introduced in the study of general relativity.\n
\nSymmetries of a field theory involving diffeomorphisms of the worl
d sheet do not really fit into the formalism of the variational calculus.
In my article ""Covariance in the Batalin-Vilkovisky formalism""\, I exp
lain how to take into account such symmetries of the world sheet by incorp
orating a curvature term into the Batalin-Vilkovisky master equation\, ass
ociated to a differential graded Lie algebra with curvature. This construc
tion is the subject of the second part of the talk.\n
\nI will fini
sh with a few words on the work of Bonechi\, Cattaneo\, Qiu and Zabzine\,
who studied the extension of our formalism to quantum field theory."\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Jeffrey (University of Toronto)
DTSTART:20201210T161500Z
DTEND:20201210T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/24
DESCRIPTION:Title: Flat connections and the $SU(2)$ commutator map\nby Lisa
Jeffrey (University of Toronto) as part of Global Poisson webinar\n\n\nA
bstract\nThis talk is joint work with Nan-Kuo Ho\, Paul Selick and Eugene
Xia. We describe the space of conjugacy classes of representations of the
fundamental group of a genus 2 oriented 2-manifold into $G:=SU(2)$. \n\n1.
We identify the cohomology ring and a cell decomposition of a space homot
opy equivalent to the space of commuting pairs in $SU(2)$. \n2. We compute
the cohomology of the space $M:=\\mu^{-1}(-I)$ where $\\mu: G^4 \\to G$ i
s the product of commutators. \n3. We give a new proof of the cohomology o
f $A:=M/G$\, both as a group and as a ring. The group structure is due to
Atiyah and Bott in their landmark 1983 paper. The ring structure is due to
Michael Thaddeus 1992. \n4. We compute the cohomology of the total space
of the prequantum line bundle over $A$. \n5. We identify the transition fu
nctions of the induced SO(3) bundle $M\\to A$. \n\nTo appear in QJM (Atiya
h memorial special issue). arXiv:2005.07390\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Polterovich (Tel Aviv University)
DTSTART:20201105T161500Z
DTEND:20201105T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/25
DESCRIPTION:Title: Approximate representations and quantization\nby Leonid
Polterovich (Tel Aviv University) as part of Global Poisson webinar\n\n\
nAbstract\nWe discuss some links between Ulam-type stability for algebra
s and groups ("approximate representations are close to genuine representa
tions") and quantization\, with applications to classification of quanti
zations and Hamiltonian actions of finitely presented groups. (with L.Char
les\, L.Ioos\, D.Kazhdan).\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Vitagliano (University of Salerno)
DTSTART:20201112T161500Z
DTEND:20201112T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/26
DESCRIPTION:Title: Calculus up to Homotopy on the Space of Solutions of a PDE\nby Luca Vitagliano (University of Salerno) as part of Global Poisson w
ebinar\n\n\nAbstract\nEvery partial differential equation (PDE) can be enc
oded in a geometric object\, what is sometimes called a diffiety\, which i
s a submanifold of an appropriate type in an infinite jet space. There is
a Lie algebroid naturally attached to a diffiety\, and the associated Lie
algebroid cohomology contains important coordinate independent information
on the PDE: variational principles\, symmetries\, conservation laws\, rec
ursion operators\, etc. To some extent these cohomologies can also be inte
rpreted as vector fields\, differential forms\, tensors\, etc. on the spac
e of solutions. This interpretation is supported by the fact that we find
the appropriate algebraic structures in cohomology. I will review this the
ory and show that those algebraic structures do actually come from homotop
y algebras at the level of cochains\, confirming an old conjecture of A. M
. Vinogradov that “the calculus on the space of solutions of a PDE is a
calculus up to homotopy”.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megumi Harada (McMaster University)
DTSTART:20201126T161500Z
DTEND:20201126T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/27
DESCRIPTION:Title: Newton-Okounkov bodies\, integrable systems\, and convergenc
e of polarizations\nby Megumi Harada (McMaster University) as part of
Global Poisson webinar\n\n\nAbstract\nLet $X$ be a smooth irreducible comp
lex algebraic variety of dimension $n$ and $L$ a very ample Hermitian line
bundle. In this talk I will recount\, in very broad strokes\, two interco
nnected stories related to the symplectic geometry of $X$. The first story
is that the theory of Newton-Okounkov bodies\, and the toric degeneratio
ns to which they give rise\, can provide -- in rather general situations -
- constructions of integrable systems on $X$. The main tool in the first s
tory is the gradient-Hamiltonian vector field. The second story concerns t
he ``independence of polarization'' issue which arises in the theory of ge
ometric quantization. Specifically\, given a toric degeneration of $(X\,L)
$ satisfying some technical hypotheses\, we construct a deformation $\\{J_
s\\}$ of the complex structure on $X$ and bases $B_s$ of $H^0(X\, L\, J_s
)$ so that $J_0$ is the standard complex structure and\, in the limit as $
s \\to \\infty$\, the basis elements approach dirac-delta distributions ce
ntered at Bohr-Sommerfeld fibers of the moment map associated to the integ
rable system on $X$ (constructed using the first story). This significant
ly generalizes previous results in geometric quantization proving independ
ence of polarization between Kahler quantizations and real polarizations.\
n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioan Marcut (Radboud Universiteit Nijmegen)
DTSTART:20201203T161500Z
DTEND:20201203T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/28
DESCRIPTION:Title: Poisson non-degeneracy of the Lie algebra $\\mathfrak{sl}(2\
,\\mathbb{C})=\\mathfrak{so}(3\,1)$\nby Ioan Marcut (Radboud Universit
eit Nijmegen) as part of Global Poisson webinar\n\n\nAbstract\n"In this ta
lk\, I will revisit the classical problem of linearizing Poisson structure
s around fixed points\, introduced by Alan Weinstein. If\nthe isotropy Lie
algebra at the fixed point is semi-simple\, the problem has been settled
in most cases\, through the works of Conn\, Weinstein\, Monnier and Zung.
The lowest dimensional semi-simple Lie algebra for which the problem was s
till open is $\\mathfrak{sl}(2\,\\mathbb{C})=\\mathfrak{so}(3\,1)$. Togeth
er with my PhD student Florian Zeiser we have shown that $\\mathfrak{sl}(2
\,\\mathbb{C})$ is the first non-compact semi-simple Lie algebra that is P
oisson non-degenerate""\, in the sense that a version of Conn's theorem ho
lds for this Lie algebra. I will explain the main ingredients of the proof
."""\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marius Crainic (Utrecht University)
DTSTART:20201217T161500Z
DTEND:20201217T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/29
DESCRIPTION:Title: From Poisson Geometry to (almost) geometric structures\n
by Marius Crainic (Utrecht University) as part of Global Poisson webinar\n
\n\nAbstract\nI will report on an approach to general geometric structures
(with an eye on integrability) based on groupoids endowed with multiplica
tive structures\; Poisson geometry (with its symplectic groupoids\, Hamilt
onian theories and Morita equivalences) will provide us with some guiding
principles. This allows one to discuss general "almost structures" and an
integrability theorem based on Nash-Moser techniques (and this also opens
up the way for a general "smooth Cartan-Kahler theorem"). This report is b
ased on collaborations/discussions with Francesco Cataffi (almost structur
es)\, Ioan Marcut (Nash-Moser techniques)\, Maria Amelia Salzar (Pfaffian
groupoids).\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Melrose (MIT)
DTSTART:20210114T161500Z
DTEND:20210114T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/30
DESCRIPTION:Title: Resolution of Lie algebroids and quantization\nby Richar
d Melrose (MIT) as part of Global Poisson webinar\n\n\nAbstract\nI will gi
ve an overview of what is known about the resolution of Lie algebroids --
limited for the most part to the `geometric case' of a subalgebra of the L
ie algebra of vector fields on a manifold. This gives a direct quantizatio
n with corresponding algebras (and modules) of pseudodifferential operator
s. In particular I will make the case that the notion of a groupoid is ina
dequate here even though there is as yet no precise replacement for it.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Tabachnikov (Penn State)
DTSTART:20210121T161500Z
DTEND:20210121T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/31
DESCRIPTION:Title: Cross-ratio dynamics on ideal polygons\nby Sergei Tabach
nikov (Penn State) as part of Global Poisson webinar\n\n\nAbstract\nDefine
a relation between labeled ideal polygons in the hyperbolic space by requ
iring that the complex distances (a combination of the distance and the an
gle) between their respective sides equal c\; the complex number c is a pa
rameter of the relation. This defines a 1-parameter family of maps on the
moduli space of ideal polygons in the hyperbolic space (or\, in its real v
ersion\, in the hyperbolic plane). I shall discuss complete integrability
of this family of maps and related topics\, including its connection with
the Korteweg-de Vries equation.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaomeng Xu (Peking University)
DTSTART:20210128T130000Z
DTEND:20210128T140000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/33
DESCRIPTION:Title: Stokes phenomenon and quantum Ginzburg-Weinstein isomorphism
s\nby Xiaomeng Xu (Peking University) as part of Global Poisson webin
ar\n\n\nAbstract\nThis talk first gives an introduction to the Stokes matr
ices of meromorphic linear systems of ordinary differential equations. It
then uses the quantum Stokes matrices to construct the quantization of a f
amily of Ginzburg-Weinstein isomorphisms from ${\\frak g \\frak l}_n^*$ to
the dual Poisson Lie group ${\\rm GL}_n^*$ found by Boalch. In the end\,
it gives explicit formula for the quantization\, as special Drinfeld isomo
rphisms from the quantum group $U_\\hbar({\\frak g \\frak l}_n)$ to the cl
assical $U({\\frak g \\frak l}_n)$\, and briefly discusses the relation wi
th representation theory of quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Witten (Institute for Advanced Study)
DTSTART:20210211T161500Z
DTEND:20210211T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/34
DESCRIPTION:Title: Quantization by Branes and Geometric Langlands\nby Edwar
d Witten (Institute for Advanced Study) as part of Global Poisson webinar\
n\n\nAbstract\nIn this talk\, which is based on work with D. Gaiotto\, I w
ill explain a quantum field theory perspective on recent developments in t
he geometric Langlands program by P. Etinghof\, E. Frenkel\, and D. Kazhda
n (see their paper https://arxiv.org/abs/1908.09677).\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenchang Zhu (Göttingen)
DTSTART:20210218T161500Z
DTEND:20210218T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/35
DESCRIPTION:Title: Classifying space $BG$ as a symplectic stack\nby Chencha
ng Zhu (Göttingen) as part of Global Poisson webinar\n\n\nAbstract\nIt i
s probably well known to people who know it well that $BG$ carries a sort
of symplectic structure\, if the Lie algebra of $G$ is quadratic Lie alge
bra. In this talk\, we explore various differential-geometric (1-group\,
2-group\, double-group) models to realise this (2-shift) symplectic struc
ture in concrete formulas and show the equivalences between them.\n\nIn th
e infinite dimensional models (2-group\, double-group)\, Segal's symplecti
c form on based loop groups turns out to be additionally multiplicative or
almost so. These models are equivalent to a finite dimensional model wit
h Cartan 3-form and Karshon-Weinstein 2-form via Morita Equivalence. All t
hese forms give rise to the first Pontryagin class on $BG$. Moreover\, the
y are related to the original invariant pairing on the Lie algebra through
an explicit integration and Van Est procedure. Finally\, as you might hav
e guessed\, the associated String group $BString(G)$ may be seen as a preq
uantization of this symplectic structure. From the math-physics point of v
iew\, what is behind is the Chern-Simons sigma model.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Martínez Torres (PUC-Rio)
DTSTART:20210225T161500Z
DTEND:20210225T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/36
DESCRIPTION:Title: Coregular submanifolds and Poisson submersions\nby David
Martínez Torres (PUC-Rio) as part of Global Poisson webinar\n\n\nAbstrac
t\nThis talk discusses aspects of the theory of submanifolds and submersio
ns in Poisson geometry. In the first part we present the general picture c
oncerning manifolds which inherit a Poisson structure from an ambient Pois
son manifold\, and among those\, we select a class (coregular submanifolds
) which have particularly nice functorial properties. The second part is d
evoted to Poisson submersions with coregular fibers. Coregular submersions
restrict nicely over symplectic leaves in the base (coupling property)\,
and we determine when they split into commuting vertical and horizontal Po
isson structures. In the last part we present instances in which such core
gular Poisson submersions appear. Our illustrations all revolve around Poi
sson actions of Poisson-Lie groups. This is joint work with L. Brambila an
d P. Frejlich.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Bischoff (University of Oxford)
DTSTART:20210304T161500Z
DTEND:20210304T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/37
DESCRIPTION:Title: Lie Groupoids and differential equations\nby Francis Bi
schoff (University of Oxford) as part of Global Poisson webinar\n\n\nAbstr
act\nThis talk will discuss applications of Lie groupoids to the study of
differential equations with singularities. Several classes of singular dif
ferential equations\, or flat connections\, can be recast as representatio
ns of Lie algebroids\, and by integration\, correspond to Lie groupoid rep
resentations. This perspective allows us to introduce new tools to the stu
dy of these equations. In this talk\, I will give an overview of this appr
oach\, with a focus on the case of differential equations with logarithmic
singularities along certain (possibly singular) submanifolds that are ass
ociated to reductive groups. Whereas the traditional approach to classific
ation relies heavily on the use of power series\, I will explain how the u
se of Lie groupoids gives rise to a more geometric approach.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Hua (University of Hong Kong)
DTSTART:20210311T131500Z
DTEND:20210311T141500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/38
DESCRIPTION:Title: Semiclassical limits of Feigin-Odesskii elliptic algebras vi
a derived geometry\nby Zheng Hua (University of Hong Kong) as part of
Global Poisson webinar\n\n\nAbstract\nIn 1980s\, Feigin and Odesskii const
ructed the elliptic algebras $Q_{n\,k}(C\,\\eta)$ generalizing the constru
ction of Sklyanin and Cherednik. Here n\,k are coprime positive integers\,
$C$ is a complex elliptic curve and $\\eta$ is a point on $C$. Elliptic a
lgebras are quantization of polynomial algebras. They are conjectured to
be regular in the sense of Artin and Schelter for all parameters. Homolo
gical and representation theoretical properties of elliptic algebras are s
tudied via Poisson geometry of their semiclassical limits. We will discuss
various results about these Poisson structures\, e.g. classification of s
ymplectic leaves\, bihamiltonian structures and so on. The main technical
tool is derived geometry\, in particular the work of Calaque-Pantev-Toen-V
aquie-Vezzosi. This is based on the joint work with Alexander Polishchuk.\
n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University)
DTSTART:20210408T121500Z
DTEND:20210408T131500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/39
DESCRIPTION:Title: Deformations\, cohomology and homotopy of relative Rota-Baxt
er Lie algebras\nby Yunhe Sheng (Jilin University) as part of Global P
oisson webinar\n\n\nAbstract\nRota-Baxter operators were originally define
d on a commutative associative algebra by Rota. Then it was defined on Lie
algebras as the operator form of the classical Yang-Baxter equation. Kupe
rshmidt introduced a more general notion called O-operator (later called r
elative Rota-Baxter operator) for arbitrary representation. Rota-Baxter op
erators have fruitful applications in mathematical physics. We determine t
he L-infty-algebra that characterizes relative Rota-Baxter Lie algebras
as Maurer-Cartan elements. As applications\, first we determine the L-inft
y-algebra that controls deformations of a relative Rota-Baxter Lie algebra
and show that it is an extension of the dg Lie algebra controlling deform
ations of the underlying Lie algebra and representation by the dg Lie alge
bra controlling deformations of the relative Rota-Baxter operator. Then we
define the cohomology of relative Rota-Baxter Lie algebras and relate
it to their infinitesimal deformations. In particular the cohomolgoy of
Rota-Baxter Lie algebras and triangular Lie bialgebras are given. Finally
we introduce the notion of homotopy relative Rota-Baxter operators and sh
ow that the underlying structure is pre-Lie-infinity algebras. This talk i
s based on joint works with Chenming Bai\, Li Guo\, Andrey Lazarev and Ron
g Tang.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nigel Higson (Penn State)
DTSTART:20210506T151500Z
DTEND:20210506T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/40
DESCRIPTION:Title: An introduction to the hypoelliptic Laplacian\nby Nigel
Higson (Penn State) as part of Global Poisson webinar\n\n\nAbstract\nJean-
Michel Bismut's hypoelliptic Laplacian is a one-parameter family of linear
differential operators that interpolates between the Laplacian and the ge
odesic flow. It may be constructed in a variety of contexts\, but in thi
s lecture I shall concentrate on symmetric spaces. Here a special mechanis
m comes into play\, as a result of which the heat traces associated to all
the operators in the family remain constant throughout the interpolation.
By studying the limits at both ends of the family\, remarkable formulas
are obtained\, including for example the Selberg trace formula. All thi
s requires a heavy dose of analysis in the spirit of\, but more complicate
d than\, the local index theory of Dirac operators. But in this talk I sha
ll mostly ignore the analysis and concentrate on a few basic ideas\, in th
e hope that they may eventually lead to a more geometric understanding of
the hypoelliptic Laplacian.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Jun Chen (Sichuan University)
DTSTART:20210610T121500Z
DTEND:20210610T131500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/41
DESCRIPTION:Title: Batalin-Vilkovisky and gravity algebras on Poisson manifold
s with semisimple modular symmetry\nby Xiao-Jun Chen (Sichuan Universi
ty) as part of Global Poisson webinar\n\n\nAbstract\nIn this talk\, we stu
dy the "twisted" Poincare duality of smooth Poisson manifolds\, and show
that\, if the modular symmetry is semisimple\, that is\, the modular vect
or is diagonalizable\, there is a mixed complex associated to the Poisson
complex which\, combining with the twisted Poincare duality\, gives a Ba
talin-Vilkovisky algebra structure on the Poisson cohomology\, and a grav
ity algebra structure on the negative cyclic Poisson homology. This gener
alizes the previous results obtained by Xu et al for unimodular Poisson a
lgebras. We also show that these two algebraic structures are preserved u
nder Kontsevich's deformation quantization\, and in the case of polynomia
l algebras they are also preserved by Koszul duality. This talk is based
on a joint work with Liu\, Yu and Zeng.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Diez (TU Delft)
DTSTART:20210318T161500Z
DTEND:20210318T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/42
DESCRIPTION:Title: Group-valued momentum maps for diffeomorphism groups\nby
Tobias Diez (TU Delft) as part of Global Poisson webinar\n\n\nAbstract\n
In mathematical physics\, some conserved quantities have a discrete nature
\, for example because they have a topological origin. These conservation
laws cannot be captured by the usual momentum map. I will present a genera
lized notion of a momentum map taking values in a Lie group\, which is abl
e to include discrete conversed quantities. It is inspired by the Lu-Weins
tein momentum map for Poisson Lie group actions\, but the groups involved
do not necessarily have to be Poisson Lie groups. The most interesting app
lications include momentum maps for diffeomorphism groups which take value
s in groups of Cheeger-Simons differential characters. As an important exa
mple\, I will show that the Teichmüller space with the Weil-Petersson sym
plectic form can be realized as symplectic orbit reduced space.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Scheimbauer (TU München)
DTSTART:20210325T161500Z
DTEND:20210325T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/43
DESCRIPTION:Title: Derived symplectic geometry and AKSZ topological field theor
ies\nby Claudia Scheimbauer (TU München) as part of Global Poisson w
ebinar\n\n\nAbstract\nDerived algebraic geometry and derived symplectic ge
ometry in the sense of Pantev-Toen-Vaquié-Vezzosi allows for a reinterpre
tation/analog of the classical AKSZ construction for certain $\\sigma$-mod
els. After recalling this procedure I will explain how it can be extended
to give a fully extended oriented TFT in the sense of Lurie with values in
a higher category whose objects are $n$-shifted symplectic derived stacks
and (higher) morphisms are (higher) Lagrangian correspondences. It is giv
en by taking mapping stacks with a fixed target building and describes ``s
emi-classical TFTs". This is joint work in progress with Damien Calaque an
d Rune Haugseng.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Fock (IRMA\, Strasbourg)
DTSTART:20210401T151500Z
DTEND:20210401T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/44
DESCRIPTION:Title: Momentum map of general relativity\nby Vladimir Fock (IR
MA\, Strasbourg) as part of Global Poisson webinar\n\n\nAbstract\nWe study
an approach to general relativity using vielbein with values in a Cliffor
d algebra. This approach allows to simplify computations and in particular
define a hidden $\\mathfrak{sl}(2) \\times \\mathfrak{sl}(2)$ symmetry (a
nd even affine $\\mathfrak{sl}(4)$ one in the Kaehler case). This formal
ism allows to compute in simple terms the phase space of the theory and th
e action of the diffeomorphisms on it. The main feature of this situation
is that diffeomorphisms do not form a group\, but a groupoid. We will disc
uss the reason for this situation and suggest an analogue of the momentum
map. Joint work with P. Goussard.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Zambon (KU Leuven)
DTSTART:20210415T151500Z
DTEND:20210415T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/45
DESCRIPTION:Title: Deformations of Lagrangian submanifolds in log-symplectic ge
ometry\nby Marco Zambon (KU Leuven) as part of Global Poisson webinar
\n\n\nAbstract\nLog-symplectic manifolds constitute a class of Poisson man
ifolds that in many respects behave like symplectic ones. We address the q
uestion of whether Lagrangian submanifolds and their deformations are as w
ell-behaved as in symplectic geometry. Since the case of Lagrangians trans
versal to the singular locus is well understood\, we focus on Lagrangian s
ubmanifolds contained in the singular locus. We establish a normal form th
eorem around such submanifolds\, and show that their deformations are gove
rned by a DGLA. The latter allows to draw geometric consequences: we discu
ss when a Lagrangian admits deformations not contained in the singular loc
us\, and we give precise criteria for unobstructedness of first order defo
rmations.\n\nThis talk is based on joint work with Stephane Geudens.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (University of Angers)
DTSTART:20210422T151500Z
DTEND:20210422T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/46
DESCRIPTION:Title: Associative Yang-Baxter equation: from double Poisson struct
ures to modular forms\nby Vladimir Rubtsov (University of Angers) as p
art of Global Poisson webinar\n\n\nAbstract\nI shall give a survey of vari
ous avatars of Associative Yang-Baxter Equations from (double) Poisson s
tructure existence conditions to a form of the trisecant Fay identity and
as some equations on generating functions for period polynomials of (quasi
-)modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Eliashberg (Stanford)
DTSTART:20210429T151500Z
DTEND:20210429T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/47
DESCRIPTION:Title: Topology of the space of tight contact structures on $\\math
bb{R}^3$\nby Yakov Eliashberg (Stanford) as part of Global Poisson web
inar\n\n\nAbstract\n30 years ago I proved that any tight contact structure
on $\\mathbb{R}^3$ is equivalent to the standard one. In the same paper I
suggested that one can establish along the same lines the contractibility
of the space of fixed at infinity tight contact structure on $\\mathbb{
R}^3$. Recently we proved this claim in our joint work with N. Mishachev.
The proof is based on the study of topology of 1-dimensional foliations
and functions on the 2-sphere.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210513T121500Z
DTEND:20210513T131500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/48
DESCRIPTION:Title: Moduli spaces of $G$-local systems and Poisson geometry\
nby Linhui Shen (Michigan State University) as part of Global Poisson webi
nar\n\n\nAbstract\nLet $G$ be a split semi-simple algebraic group over $\\
mathbb{Q}$. We introduce a natural cluster structure on moduli spaces of f
ramed $G$-local systems over surfaces with marked points. As a consequence
\, the moduli spaces of $G$-local systems admit natural Poisson structures
\, and can be further quantized. We will study the principal series repres
entations of such quantum spaces. If time permits\, I will discuss its app
lications in the study of quantum groups. This talk will mainly be based o
n joint work with A.B. Goncharov (arXiv:1904.10491).\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adriano Tomassini (Parma)
DTSTART:20210520T151500Z
DTEND:20210520T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/49
DESCRIPTION:Title: $\\overline{\\partial}$ Harmonic forms on compact almost Her
mitian manifolds\nby Adriano Tomassini (Parma) as part of Global Poiss
on webinar\n\n\nAbstract\n"Let $M$ be a smooth manifold of dimension $2n$
and let $J$ be an almost-complex structure on $M$. Then\, $J$ induces on t
he space of forms $A^\\bullet(M)$ a natural bigrading\, namely\n$$\nA^\\bu
llet(M)=\\bigoplus_{p+q=\\bullet}A^{p\,q}(M).\n$$\nAccordingly\, the exter
ior derivative $d$ splits into four operators\n$$\nd:A^{p\,q}(M)\\to A^{p+
2\,q-1}(M)\\oplus A^{p+1\,q}(M)\\oplus A^{p\,q+1}(X)\\oplus A^{p-1\,q+2}(M
)\n$$\n$$\nd=\\mu+\\partial+\\overline{\\partial}+\\bar\\mu\,\n$$\nwhere $
\\mu$ and $\\bar\\mu$ are differential operators that are linear over func
tions.\n\nLet $g$ be a Hermitian metric on $(M\,J)$. Denote by $$\\Delta_{
\\overline{\\partial}}:=\\overline{\\partial}\\\,\\overline{\\partial}^*+\
\overline{\\partial}^*\\overline{\\partial}$$ the $\\overline{\\partial}$-
Laplacian. Then $\\Delta_{\\overline{\\partial}}$ is an elliptic different
ial operator. We study the space of $\\overline{\\partial}$-harmonic forms
on $(M\,J\,g)$. Some explicit examples will be discussed. Special results
are obtained for $\\dim_\\mathbb{R} M=4$. This a joint work with Nicolett
a Tardini."\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Bonechi (INFN\, Florence)
DTSTART:20210527T151500Z
DTEND:20210527T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/50
DESCRIPTION:Title: Bihamiltonian systems and invariant polynomials\nby Fran
cesco Bonechi (INFN\, Florence) as part of Global Poisson webinar\n\n\nAbs
tract\nMotivated by the problem of quantization of the symplectic groupoid
we study a class of bihamiltonian systems defined on compact hermitian sy
mmetric spaces. Indeed\, a Poisson Nijenhuis (PN) structure defines a (sin
gular) real polarization of the symplectic groupoid integrating any of the
Poisson structures appearing in the bihamiltonian hierarchy. Despite its
singularity\, this polarization leads to the quantization of complex proje
ctive spaces. We will discuss in some detail a way to discuss this polariz
ation in terms of invariant polynomials of a certain Thimm chain of subalg
ebras. This approach works for the classical cases\; time permitting\, I w
ill discuss some partial results about the exceptional cases.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Balibanu (Harvard)
DTSTART:20210603T151500Z
DTEND:20210603T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/51
DESCRIPTION:Title: Steinberg slices and group-valued moment maps\nby Ana Ba
libanu (Harvard) as part of Global Poisson webinar\n\n\nAbstract\nWe defin
e a class of transversal slices in spaces which are quasi-Poisson for the
action of a complex semisimple group $G$. This is a multiplicative analogu
e of Whittaker reduction. One example is the multiplicative universal cent
ralizer of $G$\, which is equipped with the usual symplectic structure in
this way. We construct a smooth partial compactification of $Z$ by taking
the closure of each centralizer fiber in the wonderful compactification of
$G$. By realizing this partial compactification as a transversal in a lar
ger quasi-Poisson variety\, we show that it is smooth and log-symplectic.\
n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Kirchhoff-Lukat (KU Leuven)
DTSTART:20210617T151500Z
DTEND:20210617T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/52
DESCRIPTION:Title: Exploring the modular class of Dirac structures\nby Char
lotte Kirchhoff-Lukat (KU Leuven) as part of Global Poisson webinar\n\n\nA
bstract\nThe concept of modular class is best known for Poisson structures
\, but is naturally defined for any Lie algebroid: It is a class in the fi
rst Lie algebroid cohomology. Poisson structures as Lie algebroids have th
e special feature that their dual is isomorphic to the tangent bundle and
thus representatives are vector fields\, which allows for the definition o
f the so-called modular foliation\, locally spanned by Hamiltonian vector
fields and the modular vector field. This modular foliation can in turn be
viewed as the foliation of a Poisson structure on the total space of the
real line bundle $\\det (T^\\ast M)$ (Gualtieri-Pym). In this talk\, I wil
l show how to extend these concepts to general real or complex Dirac struc
tures in exact Courant algebroids and discuss the information contained in
the modular class of a Dirac structure in some non-Poisson examples. (Thi
s is joint work in progress with Ralph Klaasse.)\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Frejlich (UFRGS)
DTSTART:20210624T151500Z
DTEND:20210624T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/53
DESCRIPTION:Title: The bundle picture of Poisson transversals\nby Pedro Fre
jlich (UFRGS) as part of Global Poisson webinar\n\n\nAbstract\nIn this tal
k\, we describe the nonlinear Grassmannian $PT(M\,\\pi)$ of all closed Poi
sson transversals of a given Poisson manifold $(M\,\\pi)$\, and show that
the tautological bundle over it carries a canonical coupling Dirac structu
re. Our main result is that a choice of invariant volume form on the ambie
nt manifold induces a weak symplectic structure on the nonlinear Grassmann
ian\, which is a coadjoint orbit for the (infinitesimal) action of a certa
in central extension of the Hamiltonian group -- generalizing the result o
f Haller-Vizman in the symplectic case. This is joint work with I. Marcut.
\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Waldmann (Würzburg)
DTSTART:20210916T151500Z
DTEND:20210916T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/54
DESCRIPTION:Title: KMS Functionals in Poisson Geometry\nby Stefan Waldmann
(Würzburg) as part of Global Poisson webinar\n\n\nAbstract\nIn this talk
I will report on some old results about KMS states in symplectic geometry
and present new results in the general Poisson case. The classical KMS con
dition captures thermodynamical states in classical mechanical systems as
a semi-classical limit of the (original) quantum KMS condition used in alg
ebraic quantum field theory. In the symplectic case the classification of
KMS functionals is rather simple. In the general Poisson case\, the invest
igation of the KMS condition for volume forms can be seen as one of the ma
in motivations for the definition of the modular class by Alan Weinstein.
Considering more general functionals gives new and interesting structures
where in some simple cases a full classification is available. While the c
lassical situation is already very rich\, the quantization of classical KM
S states is yet to be explored. The results are a joint work with Nicolò
Drago.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Voronov (Manchester)
DTSTART:20210923T151500Z
DTEND:20210923T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/55
DESCRIPTION:Title: Thick morphisms of supermanifolds and bracket structures
\nby Theodore Voronov (Manchester) as part of Global Poisson webinar\n\n\n
Abstract\nA “thick morphism” of supermanifolds is a generalization of
a smooth map that I introduced in 2014. It is NOT a map\, but it induces a
pull-back of smooth functions. A peculiar feature of such pull-back is th
at it is NONLINEAR --- actually\, it is a formal mapping of the algebras o
f smooth functions regarded as infinite-dimensional (super)manifolds. Comp
are with ordinary pull-backs\, which are algebra homomorphisms\, in partic
ular linear. In the talk\, I will give the definition of thick morphisms a
nd explain the construction of nonlinear pull-backs. Actually\, because of
the non-linearity\, there are two parallel versions of thick morphisms a
nd the corresponding pull-backs: “bosonic” (acting on even functions)
and “fermionic” (acting on odd functions). Each of them gives rise to
a formal category containing the category of ordinary maps.\n\nMy original
motivation was constructing L-infinity morphisms for homotopy Poisson or
homotopy Schouten brackets. Thick morphisms also make it possible to give
adjoints for nonlinear vector bundle maps (useful for L-infinity algebroid
s). There is a nonlinear analog of “functional-algebraic duality” with
certain “nonlinear algebra homomorphisms” taking place of ordinary ho
momorphisms. In the bosonic case\, thick morphisms also have a quantum ver
sion given by particular Fourier integral operators\, which provide L-infi
nity morphisms for “quantum brackets” generated by BV- type operators.
\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Geun Oh (IBS Center for Geometry and Physics & POSTECH)
DTSTART:20210930T131500Z
DTEND:20210930T141500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/56
DESCRIPTION:Title: Non-archimedian deformation of Landau-Ginzburg potentials an
d Gelfand-Cetlin systems\nby Yong-Geun Oh (IBS Center for Geometry and
Physics & POSTECH) as part of Global Poisson webinar\n\n\nAbstract\nUsing
the bulk-deformation of Floer cohomology by Schubert classes and non-Arch
imedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential functi
on\, we prove that every complete flag manifold with a monotone Kirillov--
Kostant--Souriau symplectic form carries a continuum of non-displaceable L
agrangian tori which degenerates to a non-torus fiber in the Hausdorff lim
it. This talk is based on a joint work with Yunhyung Cho and Yoosik Kim.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiro Tanaka (Texas State University)
DTSTART:20211007T151500Z
DTEND:20211007T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/57
DESCRIPTION:Title: Stable Weinstein geometry through localizations\nby Hiro
Tanaka (Texas State University) as part of Global Poisson webinar\n\n\nAb
stract\nMuch of computational math is formula-driven\, while much of categ
orical math is formalism-driven. Mirror symmetry is rich in part because m
any of its results are driven by both. With the advent of stable-homotopy-
theoretic invariants in symplectic geometry--such as Nadler-Shende's micro
local categories and (on the horizon) spectrally enriched wrapped Fukaya c
ategories--there has been a real need for better-behaved formalisms in sym
plectic geometry. (This is because\, now-a-days\, much of stable homotopy
theory is possible only thanks to extremely well-constructed formalisms.)
In this talk\, we will talk about recent success in constructing the forma
lism\, especially in the setting of certain non-compact symplectic manifol
ds called Weinstein sectors. The results have concrete geometric consequen
ces\, like showing that spaces of embeddings of these manifolds map contin
uously to spaces of maps between certain invariants. (And in particular\,
leads to higher-homotopy-group generalizations\, in the Weinstein setting\
, of the Seidel homomorphism\, similar to works of Savelyev and Oh-Tanaka.
) The main result we'll discuss is that the infinity-category of stabilize
d sectors can be constructed using the categorically formal process of loc
alization. Most of what we discuss is joint with Oleg Lazarev and Zachary
Sylvan.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dusa McDuff (Barnard College)
DTSTART:20211014T151500Z
DTEND:20211014T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/58
DESCRIPTION:Title: Embedding ellipsoids into Hirzebruch surfaces\nby Dusa M
cDuff (Barnard College) as part of Global Poisson webinar\n\n\nAbstract\n"
This talk will report on joint work with Magill and Weiler concerning the
question of when an ellipsoid symplectically embeds into the \none-point
blowup of CP^2. The precise size of the blowup has a great effect on the c
orresponding embedding capacity function. Indeed\, as discovered in earli
er work with collaborators\nBertozzi\, Holm\, Maw\, Mwakyoma\, Pires\, and
Weiler\, for certain blowup parameters there are infinitely many signifi
cant obstructive classes\, which implies that the capacity function has a
staircase. We have now found that the set of these parameters\, though sti
ll not fully understood\, displays some very interesting symmetries and re
cursive patterns."\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiumars Kaveh (Pittsburgh)
DTSTART:20211021T151500Z
DTEND:20211021T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/59
DESCRIPTION:Title: On almost toric degenerations of projective varieties and ap
plications to Hamiltonian torus actions\nby Kiumars Kaveh (Pittsburgh)
as part of Global Poisson webinar\n\n\nAbstract\nRoughly speaking\, a tor
ic degeneration of a variety X is a (flat) one-parameter family of irreduc
ible varieties X_t such that for nonzero t\, X_t is isomorphic to X and X_
0 is a (not necessarily normal) toric variety. I will present the recent r
esult that any projective variety has an "almost" toric degeneration and w
ill discuss applications in constructing Hamiltonian torus actions as well
as estimating Gromov widths. I will try to cover needed definitions\, mot
ivations and background in the talk. This is a joint work with Chris Manon
and Takuya Murata.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Li (Tsinghua)
DTSTART:20211028T131500Z
DTEND:20211028T141500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/60
DESCRIPTION:Title: Elliptic chiral homology and quantum master equation\nby
Si Li (Tsinghua) as part of Global Poisson webinar\n\n\nAbstract\nWe pres
ent an effective BV quantization theory for chiral deformation of two dime
nsional conformal field theories. We explain a connection between the quan
tum master equation and the chiral homology for vertex operator algebras.
As an application\, we construct correlation functions of the curved beta-
gamma/b-c system and establish a coupled equation relating to chiral homol
ogy groups of chiral differential operators. This can be viewed as the ver
tex algebra analogue of the trace map in algebraic index theory.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykola Matviichuk (McGill)
DTSTART:20211104T151500Z
DTEND:20211104T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/61
DESCRIPTION:by Mykola Matviichuk (McGill) as part of Global Poisson webina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yael Karshon (Toronto)
DTSTART:20211111T151500Z
DTEND:20211111T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/62
DESCRIPTION:Title: Complexity one Hamiltonian torus actions\nby Yael Karsho
n (Toronto) as part of Global Poisson webinar\n\n\nAbstract\nI will report
on my classification\, joint with Sue Tolman\, of Hamiltonian torus actio
ns with two dimensional quotients.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Izosimov (University of Arizona)
DTSTART:20211118T161500Z
DTEND:20211118T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/63
DESCRIPTION:Title: Lie groupoids in fluid dynamics\nby Anton Izosimov (Uni
versity of Arizona) as part of Global Poisson webinar\n\n\nAbstract\nIn 19
66\, V. Arnold showed that the Euler equation describing the motion of an
ideal fluid on a Riemannian manifold can be regarded as the geodesic flow
of a right-invariant metric on the Lie group of volume-preserving diffeomo
rphisms. This insight turned out to be indispensable for the study of Hami
ltonian properties and conservation laws in hydrodynamics\, fluid instabil
ities\, topological properties of flows\, as well as a powerful tool for o
btaining sharper existence and uniqueness results for Euler-type equations
. However\, the scope of application of Arnold’s approach is limited to
problems whose symmetries form a group. At the same time\, there are many
problems in fluid dynamics\, such as free boundary problems\, fluid-struct
ure interactions\, as well as discontinuous fluid flows\, whose symmetries
should instead be regarded as a groupoid. In the talk\, I will discuss an
extension of Arnold's theory from Lie groups to Lie groupoids. The exampl
e of vortex sheet motion (i.e. fluids with discontinuities) will be addres
sed in detail. The talk is based on ongoing work with B. Khesin.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanpeng Li (Sichuan University)
DTSTART:20211125T131500Z
DTEND:20211125T141500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/64
DESCRIPTION:Title: On tropical Poisson-Lie theory\nby Yanpeng Li (Sichuan
University) as part of Global Poisson webinar\n\n\nAbstract\nFor a compact
Lie group $K$ with the standard Poisson structure\, we first construct a
tropical version for the dual Poisson-Lie group $K^\\ast$. This constructi
on will then help us 1) to establish a relation between $K^\\ast$ and the
Langlands dual group $G^\\vee$ of the complexification $G:=K^\\mathbb{C}$\
; 2) to construct an exhaustion by symplectic embeddings of toric domains
for each regular coadjoint orbit of $K$. We combine ideas from Poisson-Lie
groups\, cluster algebras and the geometric crystals of Berenstein-Kazhda
n.\n\nThe talk is based on joint works with A. Alekseev\, A. Berenstein\,
B. Hoffman\, and J. Lane.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (Oxford)
DTSTART:20211209T161500Z
DTEND:20211209T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/66
DESCRIPTION:Title: Moment maps for non-reductive group actions in Kähler geome
try\nby Frances Kirwan (Oxford) as part of Global Poisson webinar\n\n\
nAbstract\nWhen a complex reductive group $G$ acts linearly on a projectiv
e variety $X$\, the GIT quotient $X//G$ can be identified with a symplecti
c quotient of $X$ by a Hamiltonian action of a maximal compact subgroup $K
$ of $G$. Here the moment map takes values in the (real) dual of the Lie a
lgebra of $K$\, which embeds naturally in the complex dual of the Lie alge
bra of $G$ (as those complex linear maps taking real values on $\\mathfrak
{k}$). The aim of this talk is to discuss an analogue of this description
for GIT quotients by suitable non-reductive actions\, where the analogue o
f the moment map takes values in the complex dual of the Lie algebra of th
e non-reductive group. This is joint work with Gergely Berczi.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Stasheff (University of Pennsylvania)
DTSTART:20211216T161500Z
DTEND:20211216T171500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/67
DESCRIPTION:Title: Higher holonomy and representations up to homotopy\nby J
im Stasheff (University of Pennsylvania) as part of Global Poisson webinar
\n\n\nAbstract\n"Given a connection for a smooth vector bundle $p:E\\to
M$\, parallel transport with respect to smooth paths in the base space $M$
provides a correspondence between smooth vector bundles with flat conn
ection on $M$ and representations of $\\pi_1(M)$ . Based in part on earli
er groundbreaking work of K.T. Chen\, recently this correspondence has bee
n enhanced to the level of smooth paths (not homotopy classes) in the base
space $M$ and differential graded vector bundles with generalized flat
connections.\n\nClassical parallel transport with respect to smooth paths
in the base space $M$ and the correspondence with representations of $\\pi
_1(M)$ will be recalled briefly\, but no familiarity with differential gra
ded vector bundles with generalized flat connections will be assumed."\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiang Tang (Washington)
DTSTART:20200618T151500Z
DTEND:20200618T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/68
DESCRIPTION:Title: An index theorem on the tempered dual of a real reductive Li
e group\nby Xiang Tang (Washington) as part of Global Poisson webinar\
n\n\nAbstract\nLet $G$ be a (real reductive) Lie group. The tempered dual
of $G$ is the space of isomorphism classes of irreducible unitary $G$-repr
esentations that are contained in the (left) regular representation of $G$
on $L^2(G)$. In this talk\, we will report our study on the geometry of
the tempered dual. As an application\, we will present an index theorem f
or proper cocompact $G$-actions. This talk is based on the joint works wit
h Peter Hochs\, Markus Pflaum\, Hessel Posthuma\, and Yanli Song.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Gekhtman (Notre Dame)
DTSTART:20200625T151500Z
DTEND:20200625T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/69
DESCRIPTION:Title: Generalized cluster structures related to the Drinfeld doubl
e of $\\mathrm{GL}(n)$\nby Michael Gekhtman (Notre Dame) as part of Gl
obal Poisson webinar\n\n\nAbstract\nAs is well-known\, cluster transformat
ions in cluster algebras of geometric type are often modeled on determinan
t identities\, such short Plucker relations\, Desnanot-Jacobi identiti
es and their generalizations. I will present a construction that plays a s
imilar role in a description of generalized cluster transformations and di
scuss its applications to generalized cluster structures in $\\mathrm{GL}(
n)$ compatible with a certain subclass of Belavin-Drinfeld Poisson-Lie bac
kers\, in the Drinfeld double of $\\mathrm{GL}(n)$ and in spaces of period
ic difference operators. Based on a joint work with M. Shapiro and A. Vain
shtein.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camille Laurent-Gengoux (Lorraine)
DTSTART:20200702T151500Z
DTEND:20200702T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/70
DESCRIPTION:Title: About singular leaves of singular foliations\nby Camille
Laurent-Gengoux (Lorraine) as part of Global Poisson webinar\n\n\nAbstrac
t\nJoint work with Leonid Ryvkin. For singular foliations\, e.g. symplect
ic leaves of a Poisson structure or Lie group orbits\, the dimension of th
e leaves may vary: When it does\, the leaf is said to be singular. We wil
l explain why (formal) neighborhoods of simply connected leaves have surpr
isingly simple local models. This is in sharp contrast with Poisson struct
ures or Lie algebroids. We will derive some consequences (sometimes conje
ctural) of these facts in terms of first return map\, Androulidakis-Skanda
lis holonomy groupoid\, and the universal Q-manifold that Lavau\, Strobl
and myself have previously associated to a singular foliation.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susan Tolman (Urbana-Champaign)
DTSTART:20200709T151500Z
DTEND:20200709T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/71
DESCRIPTION:Title: Beyond semitoric\nby Susan Tolman (Urbana-Champaign) as
part of Global Poisson webinar\n\n\nAbstract\nA compact four dimensional
completely integrable system $f \\colon M \\to \\mathbb R^2$ is {\\bf semi
toric}\nif it has only non-degenerate singularities\, without hyperbolic b
locks\, and one of the components of $f$\ngenerates a circle action. Semi
toric systems have been extensively studied and have many nice properties:
for example\, the preimages $f^{-1}(x)$ are all connected. Unfortunate
ly\, although there are many interesting examples of semitoric systems\, t
he class has some limitation. For example\, there are blowups of $S^2 \\t
imes S^2$ with Hamiltonian circle actions which cannot be extended to semi
toric systems. We expand the class of semitoric systems by allowing certa
in degenerate singularities\, which we call {\\bf ephemeral} singularities
. We prove that the preimage $f^{-1}(x)$ is still connected for this larg
er class. We hope that this class will be large enough to include not onl
y all compact four manifolds with Hamiltonian circle actions\, but more ge
nerally all complexity one spaces.\nBased on joint work with D. Sepe.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiang-Hua Lu (Hong Kong)
DTSTART:20200924T151500Z
DTEND:20200924T161500Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/72
DESCRIPTION:Title: Some examples of algebraic symplectic groupoids\nby Jian
g-Hua Lu (Hong Kong) as part of Global Poisson webinar\n\n\nAbstract\nWe
construct Poisson and symplectic groupoids over a class of polynomial Pois
son structures on $\\mathbb{C}^n$ whose total spaces are certain configura
tion spaces of flags. This is joint work with Victor Mouquin and ShiZhuo Y
u.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough University)
DTSTART:20220120T160000Z
DTEND:20220120T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/73
DESCRIPTION:by Alexey Bolsinov (Loughborough University) as part of Global
Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matias del Hoyo (Universidade Federal Fluminense)
DTSTART:20220127T160000Z
DTEND:20220127T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/74
DESCRIPTION:Title: Vector bundles over Lie groupoids and related structures
\nby Matias del Hoyo (Universidade Federal Fluminense) as part of Global
Poisson webinar\n\n\nAbstract\nThe differentiation of a Lie groupoid yiel
ds a Lie algebroid and the transverse geometry of a Lie groupoid is encode
d in a differentiable stack. These two constructions admit partial inverse
s\, thus setting a bridge between the theories of algebroids and stacks\,
which has shown to be useful when dealing for instance with representation
s and cohomology. In this talk\, I will overview vector bundles over Lie g
roupoids\, Lie algebroids\, and differentiable stacks\, explain their key
role in Poisson and Dirac geometries\, discuss their behavior when crossin
g through that bridge\, and mention some of my contributions to the subjec
t.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Mnev (University of Notre Dame)
DTSTART:20220203T160000Z
DTEND:20220203T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/75
DESCRIPTION:Title: Two field-theoretic viewpoints on the Fukaya-Morse $A_\\inft
y$-category\nby Pavel Mnev (University of Notre Dame) as part of Globa
l Poisson webinar\n\n\nAbstract\nWe study an enhanced version of the Morse
degeneration of the Fukaya $A_\\infty$-category with higher compositions
given by counts of gradient flow trees. The enhancement consists in allowi
ng morphisms from an object to itself to be chains on the manifold. Higher
compositions correspond to counting Morse trees passing through a given s
et of chains. We provide two viewpoints on the construction and on the pro
of of the $A_\\infty$-relations for the composition maps. One viewpoint is
via an effective action for the BF theory computed in a special gauge. Th
e other is via higher topological quantum mechanics. This is a report on a
joint work with O. Chekeres\, A. Losev and D. Youmans\, preprint availabl
e at arXiv:2112.12756.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Evens (University of Notre Dame)
DTSTART:20220217T160000Z
DTEND:20220217T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/76
DESCRIPTION:Title: On the variety of coisotropic subalgebras\nby Samuel Eve
ns (University of Notre Dame) as part of Global Poisson webinar\n\n\nAbstr
act\nI will discuss some results due mostly to my students Nicole Kroeger
and Doan Le on classifying coisotropic subalgebras in a complex semisimple
Lie algebra with standard Lie bialgebra structure. This work builds on p
revious results of Zambon\, and uses my previous work with Jiang-Hua Lu on
the variety of Lagrangian subalgebras\, along with additional results of
Lu on spherical conjugacy classes.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hsuan-Yi Liao (National Tsing Hua University)
DTSTART:20220224T130000Z
DTEND:20220224T140000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/77
DESCRIPTION:Title: Homotopy fiber product of manifolds\nby Hsuan-Yi Liao (N
ational Tsing Hua University) as part of Global Poisson webinar\n\n\nAbstr
act\nA main motivation of developing derived differential geometry is to d
eal with singularities arising from zero loci or intersections of submanif
olds. Both zero loci and intersections can be considered as fiber products
of manifolds which may not be manifolds. Thus\, we extend the category of
differentiable manifolds to a larger category in which one has "homotopy
fiber products". In this talk\, I would like to show a construction\, usin
g vector bundles\, sections and connections\, of homotopy fiber products o
f manifolds and explain structures behind the construction. The talk is m
ainly based on a joint work with Kai Behrend and Ping Xu.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Orsay)
DTSTART:20220303T160000Z
DTEND:20220303T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/78
DESCRIPTION:Title: Chiral symplectic leaves and arc spaces of Slodowy slices\nby Anne Moreau (Orsay) as part of Global Poisson webinar\n\n\nAbstract\
nIn this talk\, I will present various applications of the notion of chira
l symplectic leaves: to quasi-lisse vertex algebras\, to the arc spaces of
Slodowy slices\, to the affine W-algebra at the critical level and the Fe
igin-Frenkel center\, etc. This is based on several joint works with Tomoy
uki Arakawa.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Gutt (Université libre de Bruxelles)
DTSTART:20220310T160000Z
DTEND:20220310T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/79
DESCRIPTION:by Simone Gutt (Université libre de Bruxelles) as part of Glo
bal Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (Caltech)
DTSTART:20220317T160000Z
DTEND:20220317T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/80
DESCRIPTION:by Sergei Gukov (Caltech) as part of Global Poisson webinar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Li (MPI)
DTSTART:20220331T120000Z
DTEND:20220331T130000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/81
DESCRIPTION:by Yu Li (MPI) as part of Global Poisson webinar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern)
DTSTART:20220407T150000Z
DTEND:20220407T160000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/82
DESCRIPTION:by Milen Yakimov (Northeastern) as part of Global Poisson webi
nar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Strobl (Lyon 1)
DTSTART:20220421T150000Z
DTEND:20220421T160000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/83
DESCRIPTION:by Thomas Strobl (Lyon 1) as part of Global Poisson webinar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (Sheffield)
DTSTART:20220505T160000Z
DTEND:20220505T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/84
DESCRIPTION:by Nikita Nikolaev (Sheffield) as part of Global Poisson webin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART:20211202T160000Z
DTEND:20211202T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/85
DESCRIPTION:Title: Symplectic reduction along a submanifold\nby Peter Crook
s (Northeastern University) as part of Global Poisson webinar\n\n\nAbstrac
t\nNoether's perspective on conserved quantities gives rise to quotient co
nstructions in symplectic geometry. The most classical such construction i
s Marsden-Weinstein-Meyer reduction\, while more modern variants include G
inzburg-Kazhdan reduction\, Kostant-Whittaker reduction\, Mikami-Weinstein
reduction\, symplectic cutting\, and symplectic implosion.\n\nI will outl
ine a generalization of the quotient constructions mentioned above. This g
eneralization will be shown to have versions in the smooth\, holomorphic\,
complex algebraic\, and derived symplectic contexts. As a corollary\, I w
ill derive a concrete and Lie-theoretic construction of "universal" symple
ctic quotients.\n\nThis represents joint work with Maxence Mayrand.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allen Knutson (Cornell University)
DTSTART:20220324T160000Z
DTEND:20220324T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/86
DESCRIPTION:by Allen Knutson (Cornell University) as part of Global Poisso
n webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aissa Wade (Penn State University)
DTSTART:20220414T150000Z
DTEND:20220414T160000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/87
DESCRIPTION:by Aissa Wade (Penn State University) as part of Global Poisso
n webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhangju Liu (Peking University)
DTSTART:20220428T120000Z
DTEND:20220428T130000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/88
DESCRIPTION:by Zhangju Liu (Peking University) as part of Global Poisson w
ebinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cédric Oms (École normale supérieure de Lyon)
DTSTART:20220512T160000Z
DTEND:20220512T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/89
DESCRIPTION:by Cédric Oms (École normale supérieure de Lyon) as part of
Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Roytenberg (Utrecht University)
DTSTART:20220519T160000Z
DTEND:20220519T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/90
DESCRIPTION:by Dmitry Roytenberg (Utrecht University) as part of Global Po
isson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20220526T120000Z
DTEND:20220526T130000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/91
DESCRIPTION:by TBA as part of Global Poisson webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Behrend (Univercity of British Columbia)
DTSTART:20220210T160000Z
DTEND:20220210T170000Z
DTSTAMP:20260404T111244Z
UID:globalpoisson/92
DESCRIPTION:Title: Some remarks on Lagrangian intersections in the algebraic ca
se\nby Kai Behrend (Univercity of British Columbia) as part of Global
Poisson webinar\n\n\nAbstract\nSome years ago\, in joint work with B. Fant
echi\, we constructed brackets on the higher structure sheaves of Lagrangi
an intersections\, and compatible Batalin-Vilkovisky operators\, when cert
ain orientations are chosen (see our contribution to Manin’s 70th birthd
ay festschrift). This lead to a de-Rham type cohomology theory for Lagrang
ian intersections. In the interim\, much progress has been made on a bette
r understanding of the origin of these structures\, and some related conje
ctures have been proved. We will explain some of these results.\n
LOCATION:https://stable.researchseminars.org/talk/globalpoisson/92/
END:VEVENT
END:VCALENDAR