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BEGIN:VEVENT
SUMMARY:Julian Kranz (Münster)
DTSTART:20201105T111500Z
DTEND:20201105T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/2
DESCRIPTION:Title: An identification of the Baum-Connes and Davis-Lück assembly
maps\nby Julian Kranz (Münster) as part of Regensburg Seminar in Homo
topy Theory and related Areas\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Raptis (Regensburg)
DTSTART:20201112T111500Z
DTEND:20201112T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/3
DESCRIPTION:Title: Higher homotopy categories\nby Georgios Raptis (Regensburg
) as part of Regensburg Seminar in Homotopy Theory and related Areas\n\n\n
Abstract\nI will review the construction of the higher homotopy categories
associated to an infinity-category and discuss some of their properties\,
especially in connection with higher weak (co)limits. These objects defin
e a natural sequence of refinements for the comparison between homotopy co
mmutativity and homotopy coherence\, but their study seems to have receive
d less attention than the classical homotopy category. Moreover\, I will d
iscuss some ongoing work on adjoint functor theorems in this context and a
version of the classical Brown representability theorem for higher homoto
py categories. I will then introduce a definition of K-theory for these ob
jects and present some results about the comparison with Waldhausen K-theo
ry. Lastly\, I will also briefly discuss generalizations of Grothendieck d
erivators and derivator K-theory to the context of (n\,1)-categories\, and
present analogous results about the comparison with Waldhausen K-theory.\
n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irakli Patchkoria (Aberdeen)
DTSTART:20201119T111500Z
DTEND:20201119T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/4
DESCRIPTION:Title: On the Balmer spectrum of derived Mackey functors\nby Irak
li Patchkoria (Aberdeen) as part of Regensburg Seminar in Homotopy Theory
and related Areas\n\n\nAbstract\nA result of Devinatz-Hopkins-Smith descri
bes the spectrum of prime ideals of finite spectra. Under this identificat
ion the information encoded by the zeroth and infinite chromatic levels ca
n be identified with the spectrum of the derived category of integers\, wh
ich by a result of Hopkins-Neeman is just equivalent to Spec(Z). It turns
out that in the equivariant context neither the spectrum of the usual der
ived category of Mackey functors nor the spectrum of the Burnside ring pla
y the role of Spec(Z). Given a finite group G\, we show that Kaledin's cat
egory of derived G-Mackey functors describes the zeroth and infinite chrom
atic levels of the Balmer spectrum of finite G-spectra. We compute the Bal
mer spectrum of derived G-Mackey functors. Along the way we will identify
Kaledin's category with the homotopy category of the stable infinity categ
ory of HZ-linear spectral Mackey functors in the sense of Barwick. This is
all joint with B. Sanders and C. Wimmer.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calista Bernard (Stanford)
DTSTART:20201203T111500Z
DTEND:20201203T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/5
DESCRIPTION:Title: Twisted Homology Operations\nby Calista Bernard (Stanford)
as part of Regensburg Seminar in Homotopy Theory and related Areas\n\n\nA
bstract\nIn the 70s\, Fred Cohen and Peter May gave a description of the m
od p homology of a free E_n-algebra in terms of certain homology operation
s\, known as Dyer--Lashof operations\, and the Browder bracket. These oper
ations capture the failure of the E_n multiplication to be strictly commut
ative\, and they prove useful for computations. After reviewing the main i
deas from May and Cohen's work\, I will discuss a framework to generalize
these operations to homology with certain twisted coefficient systems and
give a complete classification of twisted operations for E_{\\infty}-algeb
ras. I will also explain computational results that show the existence of
new operations for E_2-algebras. Finally\, I will discuss examples and app
lications of this theory.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edoardo Lanari (Czech Academy of Sciences)
DTSTART:20201210T111500Z
DTEND:20201210T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/6
DESCRIPTION:Title: Fibrations and lax limits of (oo\,2)-categories\nby Edoard
o Lanari (Czech Academy of Sciences) as part of Regensburg Seminar in Homo
topy Theory and related Areas\n\n\nAbstract\nWe study four types of (co)ca
rtesian fibrations of oo-bicategories over a given base B\, and prove that
they encode the four variance flavors of B-indexed diagrams of oo-categor
ies. 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 lax\, wei
ghted and pseudo limits. When the oo-bicategory at hand arises from a mode
l 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 homotop
y limit on the model categorical level\, thus showing in particular the ex
istence of these 2-(co)limits in a wide range of examples.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Voigt (Glasgow)
DTSTART:20201217T111500Z
DTEND:20201217T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/7
DESCRIPTION:Title: Bicategorical constructions with C^*-categories\nby Christ
ian Voigt (Glasgow) as part of Regensburg Seminar in Homotopy Theory and r
elated Areas\n\n\nAbstract\nC^*-categories are a useful tool in operator a
lgebras\, appearing naturally in the study of quantum groups\, subfactors\
, and K-theory\, among other things. Some constructions which are relevan
t in these applications can be phrased in terms of bicolimits. In this tal
k I will discuss a general approach to deal with bicolimits of C^*-categor
ies\, illustrate this with a few examples\, and point out some peculiariti
es. \n\n(Based on joint work with J. Antoun)\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyne Moser (EPFL)
DTSTART:20201126T111500Z
DTEND:20201126T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/10
DESCRIPTION:Title: A double (∞\,1)-categorical nerve for double categories
\nby Lyne Moser (EPFL) as part of Regensburg Seminar in Homotopy Theory an
d related Areas\n\n\nAbstract\nA 2-category can be seen as an internal cat
egory to categories with discrete category of objects\, i.e.\, a horizonta
l double category with only trivial vertical morphisms. Some aspects of 2-
category theory\, such as 2-limits\, benefit from a passage to double cate
gories. Going to the ∞-world\, we expect to have a similar picture\, whi
ch would allow one to develop aspects of (∞\,2)-category\, such as (∞\
,2)-limits\, using double (∞\,1)-categories.\nA double (∞\,1)-category
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 space can
be interpreted as a ``horizontal double (∞\,1)-category. In this talk\,
I will consider a slightly modified version of these double (∞\,1)-cate
gories and will give a nerve construction from double categories into doub
le (∞\,1)-categories. This nerve is right Quillen and homotopically full
y faithful from a model structure on the category of double categories con
structed in a joint work with Maru Sarazola and Paula Verdugo. By restrict
ing 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 faithful. I w
ill show that these nerves are further compatible in a precise sense with
the horizontal embedding of 2-categories into double categories\, and this
says that the ∞-setting indeed extends the strict setting.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sosnilo (Steklov Institute St. Petersburg)
DTSTART:20210107T111500Z
DTEND:20210107T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/13
DESCRIPTION:Title: On nilpotent extensions of ∞-categories and the cyclotomic
trace\nby Vladimir Sosnilo (Steklov Institute St. Petersburg) as part
of Regensburg Seminar in Homotopy Theory and related Areas\n\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Spakula (Southampton)
DTSTART:20210114T111500Z
DTEND:20210114T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/14
DESCRIPTION:Title: Quasi-locality and rigidity of Roe algebras\nby Jan Spaku
la (Southampton) as part of Regensburg Seminar in Homotopy Theory and rela
ted 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. Band opera
tors are ones whose matrix is supported on a "band" along the main diagona
l\; all norm-limits of these form a C*-algebra\, called uniform Roe algebr
a of X. This algebra "encodes" the large-scale (a.k.a. coarse) structure o
f X. Quasi-locality\, coined by John Roe in '88\, is a property of an oper
ator on l^{2}(X)\, designed as a condition to check whether the operator b
elongs to the uniform Roe algebra (without producing band operators nearby
). The talk is about our attempt to make this work\, and find counterexamp
les.\nAfter an introduction about coarse geometry and Roe algebras\, I wil
l explain quasi-locality and a result in the 'positive' direction. Next\,
I will introduce asymptotic expanders and make a connection with recent re
sults about rigidity of Roe algebras\, and counterexamples to the coarse B
aum-Connes conjecture. Finally\, if time permits\, I will talk about Prope
rty A and some ingredients of some of the proofs. (Based on joint work wit
h A Tikuisis\, K Li\, P Nowak\, and J Zhang.)\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charanya Ravi (Regensburg)
DTSTART:20210121T111500Z
DTEND:20210121T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/15
DESCRIPTION:Title: Equivariant virtual fundamental classes\nby Charanya Ravi
(Regensburg) as part of Regensburg Seminar in Homotopy Theory and related
Areas\n\n\nAbstract\nWe give a brief introduction to virtual fundamental
classes\, which play an important role in Gromov-Witten theory. We then di
scuss virtual versions of the equivariant Grothendieck-Riemann-Roch theore
m and the non-abelian Atiyah-Bott localization theorem for the Borel-style
equivariant Chow groups defined by Totaro-Edidin-Graham. This is a report
on joint work with Bhamidi Sreedhar.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Wulf (Göttingen)
DTSTART:20210128T111500Z
DTEND:20210128T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/16
DESCRIPTION:Title: Secondary cup and cap products in coarse geometry\nby Chr
istopher Wulf (Göttingen) as part of Regensburg Seminar in Homotopy Theor
y and related Areas\n\n\nAbstract\nAbstract:\nI present a construction of
secondary cup and cap products on coarse (co-)homology theories from given
cross and slant products. They are defined for coarse spaces relative to
weak generalized controlled deformation retracts.\nOn ordinary coarse coho
mology\, the secondary cup product agrees with a secondary product defined
by Roe. For coarsifications of topological coarse (co-)homology theories\
, the secondary cup and cap products correspond to the primary cup and cap
products on Higson dominated coronas via transgression maps. And in the c
ase of coarse K-theory and -homology\, the secondary products correspond t
o canonical primary products between the K-theories of the stable Higson c
orona and the Roe algebra under assembly and co-assembly.\n(arXiv:2012.112
96\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drew Heard (Trondheim)
DTSTART:20210204T111500Z
DTEND:20210204T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/17
DESCRIPTION:Title: Support theory for triangulated categories in algebra and top
ology\nby Drew Heard (Trondheim) as part of Regensburg Seminar in Homo
topy Theory and related Areas\n\n\nAbstract\nAbstract: We will survey 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 Balm
er of the spectrum of a tensor-triangulated category\, and the relation be
tween the two. We will then discuss a recent application to the category o
f derived Mackey functors.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Rovelli (ANU)
DTSTART:20210211T111500Z
DTEND:20210211T124500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/18
DESCRIPTION:Title: Exploring (∞\, n)-categories through n-complicial sets\
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 those and
understand them as much as possible. In these talks we will discuss the m
odel of n-complicial sets\, and study how one can realize convenient repre
sentatives 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 general ca
se. This is joint work with Viktoriya Ozornova.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (Trondheim)
DTSTART:20210415T101500Z
DTEND:20210415T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/19
DESCRIPTION:Title: Algebraic K-theory of Lawvere theories\nby Markus Szymik
(Trondheim) as part of Regensburg Seminar in Homotopy Theory and related A
reas\n\n\nAbstract\nThe algebraic K-theory of Lawvere theories unifies old
and new group homology computations. I will review this in the first part
of the talk. Then I will explain how the basic assembly maps in higher al
gebraic K-theory can be understood from this perspective. Many examples il
lustrate the theory. This is joint work with Anna Marie Bohmann.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Raptis (Regensburg)
DTSTART:20210422T101500Z
DTEND:20210422T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/20
DESCRIPTION:Title: Thinking about the Transfer Index Conjecture\nby Georgios
Raptis (Regensburg) as part of Regensburg Seminar in Homotopy Theory and
related Areas\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff)
DTSTART:20210429T101500Z
DTEND:20210429T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/21
DESCRIPTION:Title: Equivariant higher twisted K-theory of SU(n) via exponential
functors\nby Ulrich Pennig (Cardiff) as part of Regensburg Seminar in
Homotopy Theory and related Areas\n\n\nAbstract\nTwisted K-theory is a var
iant of topological K-theory that allows local coefficient systems called
twists. For spaces and twists equipped with an action by a group\, equivar
iant twisted K-theory provides an even finer invariant. Equivariant twists
over Lie groups gained increasing importance in the subject due to a resu
lt by Freed\, Hopkins and Teleman that relates the corresponding K-groups
to the Verlinde ring of the associated loop group. From the point of view
of homotopy theory only a small subgroup of all possible twists is conside
red in classical treatments of twisted K-theory. In this talk I will discu
ss an operator-algebraic model for equivariant higher (i.e. non-classical)
twists over SU(n) induced by exponential functors on the category of vect
or spaces and isomorphisms. These twists are represented by Fell bundles a
nd the C*-algebraic picture allows a full computation of the associated 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://researchseminars.org/talk/AGSeminarRegensburg/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Hebestreit (Bonn)
DTSTART:20210506T101500Z
DTEND:20210506T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/22
DESCRIPTION:Title: Stable moduli spaces of hermitian forms\nby Fabian Hebest
reit (Bonn) as part of Regensburg Seminar in Homotopy Theory and related A
reas\n\n\nAbstract\nIn recent joint work with Calmès\, Dotto\, Harpaz\, L
and\, Moi\, Nardin and Nikolaus we developed a formalism for Grothendieck-
Witt spectra of stable categories\, that is very amenable to computation\,
in particular enjoying a tight relation to Witt-(or L-)spectra. After bri
efly recalling the set-up\, I will explain how this theory recovers the cl
assical Grothendieck-Witt animae of ordinary rings\, which are defined as
group completions of moduli spaces of unimodular forms over R. In combinat
ion these statements allow us to solve a number of open problems\, and all
ow access to the stable homology of orthogonal and symplectic groups over
the integers for example.\n\nThe comparison itself is a hermitian analogue
of Quillen's `+=Q´ theorem and the Gillet-Waldhausen theorem\, though ou
r proof proceeds very differently: It is based on ideas from the theory of
cobordism categories in manifold topology\, of which we provide an algebr
aic analog based on Ranicki's algebraic surgery theory.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Grady (Texas Tech. Univ.)
DTSTART:20210520T101500Z
DTEND:20210520T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/23
DESCRIPTION:Title: Extended field theories are local and have classifying spaces
\nby Daniel Grady (Texas Tech. Univ.) as part of Regensburg Seminar in
Homotopy Theory and related Areas\n\n\nAbstract\nA central ingredient in
quantum field theory that is usually expected\, or demanded\, is that it i
s 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 theories nat
urally leads to this type of locality\, however no proof of this fact has
emerged in the literature. In this talk\, I will discuss joint work with D
mitri Pavlov in which we formulate the notion of locality for extended fie
ld theories and prove that all extended field theories are local in this s
ense. Since we do not restrict to the case of topological field theories\,
this requires defining a smooth variant of the fully extended bordism cat
egory\, which is amenable to geometric structures. I will also discuss app
lications to the Stolz--Teichner program\, including a classifying space c
onstruction for field theories and the construction of power operations fr
om field theories (following the recent work of Barthel\, Berwick-Evans\,
and Stapleton).\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tashi Walde (TUM)
DTSTART:20210527T101500Z
DTEND:20210527T114500Z
DTSTAMP:20260422T230716Z
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 Areas\n\
n\nAbstract\nHigher Segal spaces form an interesting hierarchy of higher s
tructures\nwhich generalize the classical Segal spaces used to encode homo
topy\ncoherent associative structures. In this talk I explain some basic\n
aspects of their theory and show how one can understand higher Segal\nspac
es conceptually in analogy to functor/manifold calculus\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadrian Heine (Osnabrück)
DTSTART:20210610T101500Z
DTEND:20210610T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/25
DESCRIPTION:Title: Algebraic models of p-adic homotopy types\nby Hadrian Hei
ne (Osnabrück) as part of Regensburg Seminar in Homotopy Theory and relat
ed Areas\n\n\nAbstract\nIn this talk I will recall Mandell's theorem class
ifying connected p-complete nilpotent spaces of finite p-type by E_infty-a
lgebras over the algebraic closure of the field with p-elements. After tha
t I will discuss a variant of Mandell's theorem via E_infty-coalgebras\, w
hich is joint work in progress with Manfred Stelzer.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Porta (Stasbourg)
DTSTART:20210617T101500Z
DTEND:20210617T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/26
DESCRIPTION:Title: Topological exodromy with coefficients\nby Mauro Porta (S
tasbourg) as part of Regensburg Seminar in Homotopy Theory and related Are
as\n\n\nAbstract\nI will survey ongoing work with Jean-Baptiste Teyssier.
Motivated by the study of wild character varieties\, we were led to revisi
t and improve Treumann-Lurie's results on exodromy in the topological sett
ing. In this seminar I will explain how to realize the exodromy equivalenc
e via an explicit push-pull \; as an intermediate step\, we establish (fol
kloristic) formulas for the stalks of the constructible sheaves obtained v
ia exodromy. As a consequence\, we manage to drop many assumptions require
d in the approach described in Higher Algebra. If time permits\, I'll sket
ch a couple of applications to the construction of algebraic moduli spaces
.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Krannich (Cambridge)
DTSTART:20210708T101500Z
DTEND:20210708T114500Z
DTSTAMP:20260422T230716Z
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://researchseminars.org/talk/AGSeminarRegensburg/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimo Pippi (University College London)
DTSTART:20210624T101500Z
DTEND:20210624T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/28
DESCRIPTION:Title: Cohomology of singularity categories and equivariant vanishin
g cycles\nby Massimo Pippi (University College London) as part of Rege
nsburg Seminar in Homotopy Theory and related Areas\n\n\nAbstract\nGiven a
regular scheme X over a strictly henselian trait S\, one can regard the g
eneric 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 invariant
s reflecting the singularities of X_0 : the sheaf of vanishing cycles and
the category of singularities of X_0 . It is known that these two objects
are strictly related. We will discuss the situation where X is a regular s
cheme over a regular local ring of dimension n ≥ 1. Even more generally\
, we will consider the case where X is a regular scheme endowed with a glo
bal section of a vector bundle of rank n≥1 and we will see how the conne
ction between vanishing cycles and singularity categories generalizes in t
his case. We will see that a theorem of D. Orlov and J. Burke- M. Walker a
llows us to reduce to the case of a regular scheme with a global section o
f a line bundle. The fact that the line bundle may be non-trivial forces u
s to consider a G_m-equivariant version of (inertia invariant) vanishing c
ycles. This talk covers the work carried out in the preprint arXiv:2009.13
359.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Leygonie (Oxford)
DTSTART:20210701T101500Z
DTEND:20210701T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/29
DESCRIPTION:Title: The fiber of Persistent Homology\nby Jacob Leygonie (Oxfo
rd) as part of Regensburg Seminar in Homotopy Theory and related Areas\n\n
\nAbstract\nAbstract: Persistent Homology (PH) is a central descriptor in
Topological Data Analysis (TDA) that encodes the topological properties 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 PH and w
hat information is lost\; formally this means that the fiber of PH is not
understood. Apart from its relevance to the numerous applications of Persi
stent Homology\, we will see that this fiber is a beautiful object.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Prigge (ETH Zürich)
DTSTART:20210715T101500Z
DTEND:20210715T114500Z
DTSTAMP:20260422T230716Z
UID:AGSeminarRegensburg/30
DESCRIPTION:Title: Characteristic classes of framed fibre bundles\nby Nils P
rigge (ETH Zürich) as part of Regensburg Seminar in Homotopy Theory and r
elated Areas\n\n\nAbstract\nIn this talk I will discuss ongoing work to ge
neralize Kontsevich's construction of characteristic classes of certain fi
bre bundles\, and I will highlight the connection to the rational homotopy
theory of modules over the little disk operad and embedding calculus.\n
LOCATION:https://researchseminars.org/talk/AGSeminarRegensburg/30/
END:VEVENT
END:VCALENDAR