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BEGIN:VEVENT
SUMMARY:Julian Kranz (Münster)
DTSTART:20201105T111500Z
DTEND:20201105T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/2
DESCRIPTION:Title: An identification of the Baum-Connes and Davis-Lück as
sembly maps\nby Julian Kranz (Münster) as part of Regensburg Seminar
in Homotopy Theory and related Areas\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Raptis (Regensburg)
DTSTART:20201112T111500Z
DTEND:20201112T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/3
DESCRIPTION:Title: Higher homotopy categories\nby Georgios Raptis (Reg
ensburg) as part of Regensburg Seminar in Homotopy Theory and related Area
s\n\n\nAbstract\nI will review the construction of the higher homotopy cat
egories associated to an infinity-category and discuss some of their prope
rties\, especially in connection with higher weak (co)limits. These object
s define a natural sequence of refinements for the comparison between homo
topy commutativity and homotopy coherence\, but their study seems to have
received less attention than the classical homotopy category. Moreover\, I
will discuss some ongoing work on adjoint functor theorems in this contex
t and a version of the classical Brown representability theorem for higher
homotopy categories. I will then introduce a definition of K-theory for t
hese objects and present some results about the comparison with Waldhausen
K-theory. Lastly\, I will also briefly discuss generalizations of Grothen
dieck derivators and derivator K-theory to the context of (n\,1)-categorie
s\, and present analogous results about the comparison with Waldhausen K-t
heory.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irakli Patchkoria (Aberdeen)
DTSTART:20201119T111500Z
DTEND:20201119T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/4
DESCRIPTION:Title: On the Balmer spectrum of derived Mackey functors\n
by Irakli Patchkoria (Aberdeen) as part of Regensburg Seminar in Homotopy
Theory and related Areas\n\n\nAbstract\nA result of Devinatz-Hopkins-Smith
describes the spectrum of prime ideals of finite spectra. Under this iden
tification the information encoded by the zeroth and infinite chromatic le
vels can be identified with the spectrum of the derived category of intege
rs\, which by a result of Hopkins-Neeman is just equivalent to Spec(Z). I
t turns out that in the equivariant context neither the spectrum of the us
ual derived category of Mackey functors nor the spectrum of the Burnside r
ing play the role of Spec(Z). Given a finite group G\, we show that Kaledi
n's category of derived G-Mackey functors describes the zeroth and infinit
e chromatic levels of the Balmer spectrum of finite G-spectra. We compute
the Balmer spectrum of derived G-Mackey functors. Along the way we will id
entify Kaledin's category with the homotopy category of the stable infinit
y category of HZ-linear spectral Mackey functors in the sense of Barwick.
This is all joint with B. Sanders and C. Wimmer.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calista Bernard (Stanford)
DTSTART:20201203T111500Z
DTEND:20201203T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/5
DESCRIPTION:Title: Twisted Homology Operations\nby Calista Bernard (St
anford) as part of Regensburg Seminar in Homotopy Theory and related Areas
\n\n\nAbstract\nIn the 70s\, Fred Cohen and Peter May gave a description o
f the mod p homology of a free E_n-algebra in terms of certain homology op
erations\, known as Dyer--Lashof operations\, and the Browder bracket. The
se operations capture the failure of the E_n multiplication to be strictly
commutative\, and they prove useful for computations. After reviewing the
main ideas from May and Cohen's work\, I will discuss a framework to gene
ralize these operations to homology with certain twisted coefficient syste
ms and give a complete classification of twisted operations for E_{\\infty
}-algebras. I will also explain computational results that show the existe
nce of new operations for E_2-algebras. Finally\, I will discuss examples
and applications of this theory.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edoardo Lanari (Czech Academy of Sciences)
DTSTART:20201210T111500Z
DTEND:20201210T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/6
DESCRIPTION:Title: Fibrations and lax limits of (oo\,2)-categories\nby
Edoardo Lanari (Czech Academy of Sciences) as part of Regensburg Seminar
in Homotopy Theory and related Areas\n\n\nAbstract\nWe study four types of
(co)cartesian fibrations of oo-bicategories over a given base B\, and pro
ve that they encode the four variance flavors of B-indexed diagrams of oo-
categories. We then use this machinery to set up a general theory of 2-(co
)limits for diagrams valued in an oo-bicategory\, capable of expressing la
x\, weighted and pseudo limits. When the oo-bicategory at hand arises from
a model category tensored over marked simplicial sets\, we show that this
notion of 2-(co)limit can be calculated as a suitable form of a weighted
homotopy limit on the model categorical level\, thus showing in particular
the existence of these 2-(co)limits in a wide range of examples.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (Glasgow)
DTSTART:20201217T111500Z
DTEND:20201217T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/7
DESCRIPTION:Title: Bicategorical constructions with C^*-categories\nby
Christian Voigt (Glasgow) as part of Regensburg Seminar in Homotopy Theor
y and related Areas\n\n\nAbstract\nC^*-categories are a useful tool in ope
rator algebras\, appearing naturally in the study of quantum groups\, subf
actors\, and K-theory\, among other things. Some constructions which are
relevant in these applications can be phrased in terms of bicolimits. In t
his talk I will discuss a general approach to deal with bicolimits of C^*-
categories\, illustrate this with a few examples\, and point out some pecu
liarities. \n\n(Based on joint work with J. Antoun)\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyne Moser (EPFL)
DTSTART:20201126T111500Z
DTEND:20201126T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/10
DESCRIPTION:Title: A double (∞\,1)-categorical nerve for double categor
ies\nby Lyne Moser (EPFL) as part of Regensburg Seminar in Homotopy Th
eory and related Areas\n\n\nAbstract\nA 2-category can be seen as an inter
nal category to categories with discrete category of objects\, i.e.\, a ho
rizontal double category with only trivial vertical morphisms. Some aspect
s of 2-category theory\, such as 2-limits\, benefit from a passage to doub
le categories. Going to the ∞-world\, we expect to have a similar pictur
e\, which would allow one to develop aspects of (∞\,2)-category\, such a
s (∞\,2)-limits\, using double (∞\,1)-categories.\nA double (∞\,1)-c
ategory was defined by Haugseng as a Segal object in complete Segal spaces
\, and then an (∞\,2)-category in the form of a 2-fold complete Segal sp
ace can be interpreted as a ``horizontal double (∞\,1)-category. In this
talk\, I will consider a slightly modified version of these double (∞\,
1)-categories and will give a nerve construction from double categories in
to double (∞\,1)-categories. This nerve is right Quillen and homotopical
ly fully faithful from a model structure on the category of double categor
ies constructed in a joint work with Maru Sarazola and Paula Verdugo. By r
estricting along a ``homotopical horizontal embedding of 2-categories into
double categories\, we get a nerve from 2-categories into 2-fold complete
Segal spaces\, which is also right Quillen and homotopically fully faithf
ul. I will show that these nerves are further compatible in a precise sens
e with the horizontal embedding of 2-categories into double categories\, a
nd this says that the ∞-setting indeed extends the strict setting.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sosnilo (Steklov Institute St. Petersburg)
DTSTART:20210107T111500Z
DTEND:20210107T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/13
DESCRIPTION:Title: On nilpotent extensions of ∞-categories and the cycl
otomic trace\nby Vladimir Sosnilo (Steklov Institute St. Petersburg) a
s part of Regensburg Seminar in Homotopy Theory and related Areas\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Spakula (Southampton)
DTSTART:20210114T111500Z
DTEND:20210114T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/14
DESCRIPTION:Title: Quasi-locality and rigidity of Roe algebras\nby Ja
n Spakula (Southampton) as part of Regensburg Seminar in Homotopy Theory a
nd related Areas\n\n\nAbstract\nLet X be a countable discrete metric space
\, and think of operators on l^{2}(X) in terms of their X-by-X matrix. Ban
d operators are ones whose matrix is supported on a "band" along the main
diagonal\; all norm-limits of these form a C*-algebra\, called uniform Roe
algebra of X. This algebra "encodes" the large-scale (a.k.a. coarse) stru
cture of X. Quasi-locality\, coined by John Roe in '88\, is a property of
an operator on l^{2}(X)\, designed as a condition to check whether the ope
rator belongs to the uniform Roe algebra (without producing band operators
nearby). The talk is about our attempt to make this work\, and find count
erexamples.\nAfter an introduction about coarse geometry and Roe algebras\
, I will explain quasi-locality and a result in the 'positive' direction.
Next\, I will introduce asymptotic expanders and make a connection with re
cent results about rigidity of Roe algebras\, and counterexamples to the c
oarse Baum-Connes conjecture. Finally\, if time permits\, I will talk abou
t Property A and some ingredients of some of the proofs. (Based on joint w
ork with A Tikuisis\, K Li\, P Nowak\, and J Zhang.)\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charanya Ravi (Regensburg)
DTSTART:20210121T111500Z
DTEND:20210121T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/15
DESCRIPTION:Title: Equivariant virtual fundamental classes\nby Charan
ya Ravi (Regensburg) as part of Regensburg Seminar in Homotopy Theory and
related Areas\n\n\nAbstract\nWe give a brief introduction to virtual funda
mental classes\, which play an important role in Gromov-Witten theory. We
then discuss virtual versions of the equivariant Grothendieck-Riemann-Roch
theorem and the non-abelian Atiyah-Bott localization theorem for the Bore
l-style equivariant Chow groups defined by Totaro-Edidin-Graham. This is a
report on joint work with Bhamidi Sreedhar.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Wulf (Göttingen)
DTSTART:20210128T111500Z
DTEND:20210128T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/16
DESCRIPTION:Title: Secondary cup and cap products in coarse geometry\
nby Christopher Wulf (Göttingen) as part of Regensburg Seminar in Homotop
y Theory and related Areas\n\n\nAbstract\nAbstract:\nI present a construct
ion of secondary cup and cap products on coarse (co-)homology theories fro
m given cross and slant products. They are defined for coarse spaces relat
ive to weak generalized controlled deformation retracts.\nOn ordinary coar
se cohomology\, the secondary cup product agrees with a secondary product
defined by Roe. For coarsifications of topological coarse (co-)homology th
eories\, the secondary cup and cap products correspond to the primary cup
and cap products on Higson dominated coronas via transgression maps. And i
n the case of coarse K-theory and -homology\, the secondary products corre
spond to canonical primary products between the K-theories of the stable H
igson corona and the Roe algebra under assembly and co-assembly.\n(arXiv:2
012.11296\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drew Heard (Trondheim)
DTSTART:20210204T111500Z
DTEND:20210204T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/17
DESCRIPTION:Title: Support theory for triangulated categories in algebra
and topology\nby Drew Heard (Trondheim) as part of Regensburg Seminar
in Homotopy Theory and related Areas\n\n\nAbstract\nAbstract: We will surv
ey the support theory of triangulated categories through the machinery of
tensor-triangulated geometry. We will discuss the stratification theory of
Benson—Iyengar—Krause for triangulated categories\, the construction
by Balmer of the spectrum of a tensor-triangulated category\, and the rela
tion between the two. We will then discuss a recent application to the cat
egory of derived Mackey functors.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Rovelli (ANU)
DTSTART:20210211T111500Z
DTEND:20210211T124500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/18
DESCRIPTION:Title: Exploring (∞\, n)-categories through n-complicial se
ts\nby Martina Rovelli (ANU) as part of Regensburg Seminar in Homotopy
Theory and related Areas\n\n\nAbstract\nWith the rising significance of (
∞\, n)-categories\, it is important to have easy-to-handle models for th
ose and understand them as much as possible. In these talks we will discus
s the model of n-complicial sets\, and study how one can realize convenien
t representatives of strict n-categories\, which encode universal indexing
shapes for diagrams valued in (∞\, n)-categories. We will focus on n =
2\, for which more results are available\, but keep an eye towards the gen
eral case. This is joint work with Viktoriya Ozornova.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (Trondheim)
DTSTART:20210415T101500Z
DTEND:20210415T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/19
DESCRIPTION:Title: Algebraic K-theory of Lawvere theories\nby Markus
Szymik (Trondheim) as part of Regensburg Seminar in Homotopy Theory and re
lated Areas\n\n\nAbstract\nThe algebraic K-theory of Lawvere theories unif
ies old and new group homology computations. I will review this in the fir
st part of the talk. Then I will explain how the basic assembly maps in hi
gher algebraic K-theory can be understood from this perspective. Many exam
ples illustrate the theory. This is joint work with Anna Marie Bohmann.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Raptis (Regensburg)
DTSTART:20210422T101500Z
DTEND:20210422T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/20
DESCRIPTION:Title: Thinking about the Transfer Index Conjecture\nby G
eorgios Raptis (Regensburg) as part of Regensburg Seminar in Homotopy Theo
ry and related Areas\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff)
DTSTART:20210429T101500Z
DTEND:20210429T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/21
DESCRIPTION:Title: Equivariant higher twisted K-theory of SU(n) via expon
ential functors\nby Ulrich Pennig (Cardiff) as part of Regensburg Semi
nar in Homotopy Theory and related Areas\n\n\nAbstract\nTwisted K-theory i
s a variant of topological K-theory that allows local coefficient systems
called twists. For spaces and twists equipped with an action by a group\,
equivariant twisted K-theory provides an even finer invariant. Equivariant
twists over Lie groups gained increasing importance in the subject due to
a result by Freed\, Hopkins and Teleman that relates the corresponding K-
groups to the Verlinde ring of the associated loop group. From the point o
f view of homotopy theory only a small subgroup of all possible twists is
considered in classical treatments of twisted K-theory. In this talk I wil
l discuss an operator-algebraic model for equivariant higher (i.e. non-cla
ssical) twists over SU(n) induced by exponential functors on the category
of vector spaces and isomorphisms. These twists are represented by Fell bu
ndles and the C*-algebraic picture allows a full computation of the associ
ated K-groups at least in low dimensions. I will also draw some parallels
of our results with the FHT theorem. This is joint work with D. Evans.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Hebestreit (Bonn)
DTSTART:20210506T101500Z
DTEND:20210506T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/22
DESCRIPTION:Title: Stable moduli spaces of hermitian forms\nby Fabian
Hebestreit (Bonn) as part of Regensburg Seminar in Homotopy Theory and re
lated Areas\n\n\nAbstract\nIn recent joint work with Calmès\, Dotto\, Har
paz\, Land\, Moi\, Nardin and Nikolaus we developed a formalism for Grothe
ndieck-Witt spectra of stable categories\, that is very amenable to comput
ation\, in particular enjoying a tight relation to Witt-(or L-)spectra. Af
ter briefly recalling the set-up\, I will explain how this theory recovers
the classical Grothendieck-Witt animae of ordinary rings\, which are defi
ned as group completions of moduli spaces of unimodular forms over R. In c
ombination these statements allow us to solve a number of open problems\,
and allow access to the stable homology of orthogonal and symplectic group
s over the integers for example.\n\nThe comparison itself is a hermitian a
nalogue of Quillen's `+=Q´ theorem and the Gillet-Waldhausen theorem\, th
ough our proof proceeds very differently: It is based on ideas from the th
eory of cobordism categories in manifold topology\, of which we provide an
algebraic analog based on Ranicki's algebraic surgery theory.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Grady (Texas Tech. Univ.)
DTSTART:20210520T101500Z
DTEND:20210520T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/23
DESCRIPTION:Title: Extended field theories are local and have classifying
spaces\nby Daniel Grady (Texas Tech. Univ.) as part of Regensburg Sem
inar in Homotopy Theory and related Areas\n\n\nAbstract\nA central ingredi
ent in quantum field theory that is usually expected\, or demanded\, is th
at it is local (meaning there is no ``spooky action at a distance" and all
large-scale phenomena are determined by their behavior at small scales).
It has long been expected that the formalism of fully extended field theor
ies naturally leads to this type of locality\, however no proof of this fa
ct has emerged in the literature. In this talk\, I will discuss joint work
with Dmitri Pavlov in which we formulate the notion of locality for exten
ded field theories and prove that all extended field theories are local in
this sense. Since we do not restrict to the case of topological field the
ories\, this requires defining a smooth variant of the fully extended bord
ism category\, which is amenable to geometric structures. I will also disc
uss applications to the Stolz--Teichner program\, including a classifying
space construction for field theories and the construction of power operat
ions from field theories (following the recent work of Barthel\, Berwick-E
vans\, and Stapleton).\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tashi Walde (TUM)
DTSTART:20210527T101500Z
DTEND:20210527T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/24
DESCRIPTION:Title: Higher Segal spaces via higher excision\nby Tashi
Walde (TUM) as part of Regensburg Seminar in Homotopy Theory and related A
reas\n\n\nAbstract\nHigher Segal spaces form an interesting hierarchy of h
igher structures\nwhich generalize the classical Segal spaces used to enco
de homotopy\ncoherent associative structures. In this talk I explain some
basic\naspects of their theory and show how one can understand higher Sega
l\nspaces conceptually in analogy to functor/manifold calculus\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadrian Heine (Osnabrück)
DTSTART:20210610T101500Z
DTEND:20210610T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/25
DESCRIPTION:Title: Algebraic models of p-adic homotopy types\nby Hadr
ian Heine (Osnabrück) as part of Regensburg Seminar in Homotopy Theory an
d related Areas\n\n\nAbstract\nIn this talk I will recall Mandell's theore
m classifying connected p-complete nilpotent spaces of finite p-type by E_
infty-algebras over the algebraic closure of the field with p-elements. Af
ter that I will discuss a variant of Mandell's theorem via E_infty-coalgeb
ras\, which is joint work in progress with Manfred Stelzer.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Porta (Stasbourg)
DTSTART:20210617T101500Z
DTEND:20210617T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/26
DESCRIPTION:Title: Topological exodromy with coefficients\nby Mauro P
orta (Stasbourg) as part of Regensburg Seminar in Homotopy Theory and rela
ted Areas\n\n\nAbstract\nI will survey ongoing work with Jean-Baptiste Tey
ssier. Motivated by the study of wild character varieties\, we were led to
revisit and improve Treumann-Lurie's results on exodromy in the topologic
al setting. In this seminar I will explain how to realize the exodromy equ
ivalence via an explicit push-pull \; as an intermediate step\, we establi
sh (folkloristic) formulas for the stalks of the constructible sheaves obt
ained via exodromy. As a consequence\, we manage to drop many assumptions
required in the approach described in Higher Algebra. If time permits\, I'
ll sketch a couple of applications to the construction of algebraic moduli
spaces.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Krannich (Cambridge)
DTSTART:20210708T101500Z
DTEND:20210708T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/27
DESCRIPTION:by Manuel Krannich (Cambridge) as part of Regensburg Seminar i
n Homotopy Theory and related Areas\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimo Pippi (University College London)
DTSTART:20210624T101500Z
DTEND:20210624T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/28
DESCRIPTION:Title: Cohomology of singularity categories and equivariant v
anishing cycles\nby Massimo Pippi (University College London) as part
of Regensburg Seminar in Homotopy Theory and related Areas\n\n\nAbstract\n
Given a regular scheme X over a strictly henselian trait S\, one can regar
d the generic fiber X_η as a regular variety degenerating to the special
fiber X_0 \, that may be singular. Then\, one can consider at least two in
variants reflecting the singularities of X_0 : the sheaf of vanishing cycl
es and the category of singularities of X_0 . It is known that these two o
bjects are strictly related. We will discuss the situation where X is a re
gular scheme over a regular local ring of dimension n ≥ 1. Even more gen
erally\, we will consider the case where X is a regular scheme endowed wit
h a global section of a vector bundle of rank n≥1 and we will see how th
e connection between vanishing cycles and singularity categories generaliz
es in this case. We will see that a theorem of D. Orlov and J. Burke- M. W
alker allows us to reduce to the case of a regular scheme with a global se
ction of a line bundle. The fact that the line bundle may be non-trivial f
orces us to consider a G_m-equivariant version of (inertia invariant) vani
shing cycles. This talk covers the work carried out in the preprint arXiv:
2009.13359.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Leygonie (Oxford)
DTSTART:20210701T101500Z
DTEND:20210701T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/29
DESCRIPTION:Title: The fiber of Persistent Homology\nby Jacob Leygoni
e (Oxford) as part of Regensburg Seminar in Homotopy Theory and related Ar
eas\n\n\nAbstract\nAbstract: Persistent Homology (PH) is a central descrip
tor in Topological Data Analysis (TDA) that encodes the topological proper
ties of a real-valued function on a space by means of its sub-level sets.
But in fact it remains mysterious what information is really captured by P
H and what information is lost\; formally this means that the fiber of PH
is not understood. Apart from its relevance to the numerous applications o
f Persistent Homology\, we will see that this fiber is a beautiful object.
\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Prigge (ETH Zürich)
DTSTART:20210715T101500Z
DTEND:20210715T114500Z
DTSTAMP:20260404T111445Z
UID:AGSeminarRegensburg/30
DESCRIPTION:Title: Characteristic classes of framed fibre bundles\nby
Nils Prigge (ETH Zürich) as part of Regensburg Seminar in Homotopy Theor
y and related Areas\n\n\nAbstract\nIn this talk I will discuss ongoing wor
k to generalize Kontsevich's construction of characteristic classes of cer
tain fibre bundles\, and I will highlight the connection to the rational h
omotopy theory of modules over the little disk operad and embedding calcul
us.\n
LOCATION:https://stable.researchseminars.org/talk/AGSeminarRegensburg/30/
END:VEVENT
END:VCALENDAR