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BEGIN:VEVENT
SUMMARY:Christian Blohmann (MPIM Bonn)
DTSTART:20230207T213000Z
DTEND:20230207T230000Z
DTSTAMP:20260417T112119Z
UID:tandg/1
DESCRIPTION:Title: Elastic diffeological spaces\nby Christian Blohmann (MPIM Bonn) a
s part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nI
will introduce a class of diffeological spaces\, called elastic\, on which
the left Kan extension of the tangent functor of smooth manifolds defines
an abstract tangent functor in the sense of Rosický. On elastic spaces t
here is a natural Cartan calculus\, consisting of vector fields and differ
ential forms\, together with the Lie bracket\, de Rham differential\, inne
r derivative\, and Lie derivative\, satisfying the usual graded commutatio
n relations. Elastic spaces are closed under arbitrary coproducts\, finite
products\, and retracts. Examples include manifolds with corners and cusp
s\, diffeological groups and diffeological vector spaces with a mild extra
condition\, mapping spaces between smooth manifolds\, and spaces of secti
ons of smooth fiber bundles.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Mazel-Gee (Caltech)
DTSTART:20230221T213000Z
DTEND:20230221T230000Z
DTSTAMP:20260417T112119Z
UID:tandg/2
DESCRIPTION:Title: Towards knot homology for 3-manifolds\nby Aaron Mazel-Gee (Caltec
h) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract
\nThe Jones polynomial is an invariant of knots in R^3. Following a propos
al of Witten\, it was extended to knots in 3-manifolds by Reshetikhin–Tu
raev using quantum groups. Khovanov homology is a categorification of the
Jones polynomial of a knot in R^3\, analogously to how ordinary homology i
s a categorification of the Euler characteristic of a space. It is a major
open problem to extend Khovanov homology to knots in 3-manifolds. In this
talk\, I will explain forthcoming work towards solving this problem\, joi
nt with Leon Liu\, David Reutter\, Catharina Stroppel\, and Paul Wedrich.
Roughly speaking\, our contribution amounts to the first instance of a bra
iding on 2-representations of a categorified quantum group. More precisely
\, we construct a braided (∞\,2)-category that simultaneously incorporat
es all of Rouquier's braid group actions on Hecke categories in type A\, a
rticulating a novel compatibility among them.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Domenico Fiorenza (Sapienza University of Rome)
DTSTART:20230307T213000Z
DTEND:20230307T230000Z
DTSTAMP:20260417T112119Z
UID:tandg/3
DESCRIPTION:Title: String bordism invariants in dimension 3 from U(1)-valued TQFTs\n
by Domenico Fiorenza (Sapienza University of Rome) as part of Topology and
Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe third string bordism
group is known to be $\\mathbb{Z}/24\\mathbb{Z}$. Using Waldorf's notion
of a geometric string structure on a manifold\, Bunke–Naumann and Redden
have exhibited integral formulas involving the Chern–Weil form represen
tative of the first Pontryagin class and the canonical 3-form of a geometr
ic string structure that realize the isomorphism ${\\rm Bord}_3^{\\rm Stri
ng} \\to \\mathbb{Z}/24\\mathbb{Z}$ (these formulas have been recently red
iscovered by Gaiotto–Johnson-Freyd–Witten). In the talk I will show ho
w these formulas naturally emerge when one considers the U(1)-valued 3d TQ
FTs associated with the classifying stacks of Spin bundles with connection
and of String bundles with geometric structure. Joint work with Eugenio L
andi (arXiv:2209.12933).\
n
LOCATION:https://stable.researchseminars.org/talk/tandg/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Minichiello (CUNY GC)
DTSTART:20230404T203000Z
DTEND:20230404T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/4
DESCRIPTION:Title: Diffeological Principal Bundles\, Čech Cohomology and Principal Infi
nity Bundles\nby Emilio Minichiello (CUNY GC) as part of Topology and
Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThanks to a result of Bae
z and Hoffnung\, the category of diffeological spaces is equivalent to the
category of concrete sheaves on the site of cartesian spaces. By thinkin
g of diffeological spaces as kinds of sheaves\, we can therefore think of
diffeological spaces as kinds of infinity sheaves. We do this by using a
model category presentation of the infinity category of infinity sheaves o
n cartesian spaces\, and cofibrantly replacing a diffeological space withi
n it. By doing this\, we obtain a new generalized cocycle construction fo
r diffeological principal bundles\, a new version of Čech cohomology for
diffeological spaces that can be compared very directly with two other ver
sions appearing in the literature\, which is precisely infinity sheaf coho
mology\, and we show that the nerve of the category of diffeological princ
ipal G-bundles over a diffeological space X for a diffeological group G is
weak equivalent to the nerve of the category of G-principal infinity bund
les over X.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (Wichita State University)
DTSTART:20230411T203000Z
DTEND:20230411T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/5
DESCRIPTION:Title: Fourier analysis in Diophantine approximation\nby Robert Fraser (
Wichita State University) as part of Topology and Geometry Seminar (Texas\
, Kansas)\n\n\nAbstract\nA real number $x$ is said to be normal i
f the sequence $a^n x$ is uniformly distributed modulo 1 for every integer
$a≥2$.\nAlthough Lebesgue-almost all numbers are normal\, the problem d
etermining whether specific irrational numbers such as $e$ and $π$ are no
rmal is extremely difficult.\nHowever\, techniques from Fourier analysis a
nd geometric measure theory can be used to show that certain “thin” su
bsets of $\\mathbb{R}$ must contain normal numbers.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Heine (Hamburg)
DTSTART:20230418T203000Z
DTEND:20230418T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/6
DESCRIPTION:Title: The Dwyer Kan-correspondence and its categorification\nby Till He
ine (Hamburg) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\
n\nAbstract\nExtensions of the Dold-Kan correspondence for the duplicial a
nd (para)cyclic index categories were introduced by Dwyer and Kan.\nBuildi
ng on the categorification of the Dold-Kan correspondence by Dyckerhoff\,
we categorify the duplicial case by establishing an equivalence between th
e $\\infty$-category of $2$-duplicial stable $\\infty$-categories and the
$\\infty$-category of connective chain complexes of stable $\\infty$-categ
ories with right adjoints. \nI will further explain the current prog
ress towards a conjectured correspondence between $2$-paracyclic stable $\
\infty$-categories and connective spherical complexes.\nExamples of the la
tter naturally arise from the study of perverse schobers.
\narXiv:2303.03653.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Wierstra (Korteweg-de Vries Institute for Mathematics\, Univ
ersity of Amsterdam)
DTSTART:20230425T203000Z
DTEND:20230425T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/7
DESCRIPTION:Title: A recognition principle for iterated suspensions as coalgebras over t
he little cubes operad\nby Felix Wierstra (Korteweg-de Vries Institute
for Mathematics\, University of Amsterdam) as part of Topology and Geomet
ry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I will discus a re
cognition principle for iterated suspensions as coalgebras over the little
cubes operad.\nThis is joint work with Oisín Flynn-Connolly and José Mo
reno-Fernádez.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kinard
DTSTART:20231003T180000Z
DTEND:20231003T195000Z
DTSTAMP:20260417T112119Z
UID:tandg/8
DESCRIPTION:Title: Sheaves as a Data Structure\nby Rachel Kinard as part of Topology
and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe word “Topology
”\, best known for its association to the study of invariants of an abst
ract space\, is a branch of Pure Mathematics whose best known applications
are found in Physics (Quantum Mechanics\, Quantum Field Theory). Very rar
ely does a Pure Math Field find such as Topology find relevance in a world
of Big Data and computer automation. Data Science utilizes these powerful
topological invariants to quickly gather information about complex data s
paces in a brave new area of study called “Topological Data Analysis”
or TDA. Given a set of data points\, the nerve construction produces a sim
plicial complex that can be analyzed to understand important characteristi
cs of the data. I will provide an introduction to TDA and a few examples o
f surprising Data Science applications.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kinard
DTSTART:20231005T190000Z
DTEND:20231005T195000Z
DTSTAMP:20260417T112119Z
UID:tandg/9
DESCRIPTION:Title: Sheaves as a Data Structure (Part 2)\nby Rachel Kinard as part of
Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nWe continue
our discussion with an example of “Path-Optimization Sheaves” (https:
//arxiv.org/abs/2012.05974)\;\nan alternative approach to classical Dijkst
ra’s Algorithm\, paths from a source vertex to sink vertex in a graph ar
e revealed as Sections of the Path-finding Sheaf.\n\nTables\, Arrays\, and
Matrices are useful in data storage and manipulation\, employing operatio
ns and methods from Numerical Linear Algebra for computer algorithm develo
pment.\nRecent advances in computer hardware and high performance computin
g invite us to explore more advanced data structures\,\nsuch as sheaves an
d the use of sheaf operations for more sophisticated computations.\nAbstra
ctly\, Mathematical Sheaves can be used to track data associated to the op
en sets of a topological space\;\npractically\, sheaves as an advanced dat
a structure provide a framework for the manipulation and optimization of c
omplex systems of interrelated information.\nDo we ever really get to see
a concrete example?\nI will point to several recent examples of (1) the us
e of sheaves as a tool for data organization\, and (2) the use of sheaves
to gain additional information about a system.\n\nNotice the nonstandard d
ay (Thursday) and the nonstandard time slot (2 pm Central Time).\n\nContin
uation of the talk given on October 3 (https://researchseminars.org/talk/t
andg/8/).\n\nRecording of Part I is available here: https://dmitripavlov.o
rg/2023-10-03.mp4\n
LOCATION:https://stable.researchseminars.org/talk/tandg/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Debray (Purdue University)
DTSTART:20231024T180000Z
DTEND:20231024T195000Z
DTSTAMP:20260417T112119Z
UID:tandg/10
DESCRIPTION:Title: Constructing the Virasoro groups using differential cohomology\n
by Arun Debray (Purdue University) as part of Topology and Geometry Semina
r (Texas\, Kansas)\n\n\nAbstract\nAbstract: The Virasoro groups are a fami
ly of central extensions of ${\\rm Diff}^+(S^1)$ by the circle group $\\bf
T$.\nIn this talk I will discuss recent work\, joint with Yu Leon Liu and
Christoph Weis\,\nconstructing these groups by beginning with a lift of t
he first Pontrjagin class to "off-diagonal" differential cohomology\,\nthe
n transgressing it to obtain a central extension.\nAlong the way\, I will
discuss what the Virasoro extensions are and how to recognize them\;\na br
ief introduction to differential cohomology\; and lifts of characteristic
classes to differential cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Bunk (University of Oxford)
DTSTART:20231107T190000Z
DTEND:20231107T205000Z
DTSTAMP:20260417T112119Z
UID:tandg/11
DESCRIPTION:Title: Smooth higher symmetries groups and the geometry of Deligne cohomolo
gy\nby Severin Bunk (University of Oxford) as part of Topology and Geo
metry Seminar (Texas\, Kansas)\n\n\nAbstract\nWe construct the smooth high
er group of symmetries of any higher geometric structure on manifolds. Via
a universal property\, this classifies equivariant structures on the geom
etry. We present a general construction of moduli stacks of solutions in h
igher-geometric field theories and provide a criterion for when two such m
oduli stacks are equivalent. We then apply this to the study of generalise
d Ricci solitons\, or NSNS supergravity: this theory has two different for
mulations\, originating in higher geometry and generalised geometry\, resp
ectively. These formulations produce inequivalent field configurations and
inequivalent symmetries. We resolve this discrepancy by showing that thei
r moduli stacks are equivalent. This is joint work with C. Shahbazi.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Araminta Amabel (Northwestern University)
DTSTART:20231114T190000Z
DTEND:20231114T205000Z
DTSTAMP:20260417T112119Z
UID:tandg/12
DESCRIPTION:Title: A factorization homology approach to line operators\nby Araminta
Amabel (Northwestern University) as part of Topology and Geometry Seminar
(Texas\, Kansas)\n\n\nAbstract\nThere are several mathematical models for
field theories\, including the functorial approach of Atiyah–Segal and
the factorization algebra approach of Costello–Gwilliam.\nI'll discuss h
ow to think about line operators in these contexts\, and the different str
engths of each method.\nMotivated by work of Freed–Moore–Teleman\, I'l
l explain how to exploit both models to say something about certain gauge
theories.\nThis is based on joint work with Owen Gwilliam.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Tooby-Smith (Cornell University)
DTSTART:20231121T190000Z
DTEND:20231121T205000Z
DTSTAMP:20260417T112119Z
UID:tandg/13
DESCRIPTION:Title: Smooth generalized symmetries of quantum field theories\nby Jose
ph Tooby-Smith (Cornell University) as part of Topology and Geometry Semin
ar (Texas\, Kansas)\n\n\nAbstract\nIn this talk\, based on joint work with
Ben Gripaios and Oscar Randal-Williams (arXiv:2209.13524 and 2310.16090)\
, we will\, with help from the geometric cobordism hypothesis\, define and
study invertible smooth generalized symmetries of field theories within t
he framework of higher category theory. We will show the existence of a ne
w type of anomaly that afflicts global symmetries even before trying to ga
uge\, we call these anomalies “smoothness anomalies”. In addition\, we
will see that d-dimensional QFTs when considered collectively can have d-
form symmetries\, which goes beyond the (d-1)-form symmetries known to phy
sicists for individual QFTs. We will also touch on aspects of gauging glob
al symmetries in the case of topological quantum field theories.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Berwick-Evans (University of Illinois Urbana-Champaign)
DTSTART:20231128T190000Z
DTEND:20231128T205000Z
DTSTAMP:20260417T112119Z
UID:tandg/14
DESCRIPTION:Title: Twisted equivariant Thom classes in topology and physics\nby Dan
iel Berwick-Evans (University of Illinois Urbana-Champaign) as part of Top
ology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their semina
l work\, Mathai and Quillen explained how free fermion theories can be use
d to construct cocycle representatives of Thom classes in de Rham cohomolo
gy. After reviewing this idea\, I will describe several avenues of general
ization that lead to cocycle representatives of Thom classes in twisted eq
uivariant KR-theory and (conjecturally) in equivariant elliptic cohomology
. I will further describe nice properties enjoyed by these cocycle represe
ntatives\, e.g.\, compatibility with (twisted) power operations. This is j
oint work with combinations of Tobi Barthel\, Millie Deaton\, Meng Guo\, Y
igal Kamel\, Hui Langwen\, Kiran Luecke\, Alex Pacun\, and Nat Stapleton.\
n
LOCATION:https://stable.researchseminars.org/talk/tandg/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigorios Giotopoulos (NYU Abu Dhabi)
DTSTART:20240213T160000Z
DTEND:20240213T173000Z
DTSTAMP:20260417T112119Z
UID:tandg/15
DESCRIPTION:Title: Smooth sets as a convenient setting for Lagrangian field theory\
nby Grigorios Giotopoulos (NYU Abu Dhabi) as part of Topology and Geometry
Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk\, I will indicate ho
w the sheaf topos of smooth sets serves as a sufficiently powerful and con
venient context to host classical (bosonic) Lagrangian field theory. As mo
tivation\, I will recall the textbook description of variational Lagrangia
n field theory\, and list desiderata for an ambient category in which this
can rigorously be phrased. I will then explain how sheaves over Cartesian
spaces naturally satisfy all the desiderata\, and furthermore allow to ri
gorously formalize several more field theoretic concepts. Time permitting\
, I will indicate how the setting naturally generalizes to include the des
cription of (perturbative) infinitesimal structure\, fermionic fields\, an
d (gauge) fields with internal symmetries. This is based on joint work wit
h Hisham Sati.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Alfonsi (University of Hertfordshire)
DTSTART:20240319T203000Z
DTEND:20240319T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/16
DESCRIPTION:Title: Batalin–Vilkovisky formalism beyond perturbation theory via derive
d geometry\nby Luigi Alfonsi (University of Hertfordshire) as part of
Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk
I will discuss applications of derived differential geometry to study a n
on-perturbative generalisation of classical Batalin–Vilkovisky (BV-)form
alism. First\, I will describe the current state of the art of the geometr
y of perturbative BV-theory. Then\, I will introduce a simple model of der
ived differential geometry\, whose geometric objects are formal derived sm
ooth stacks (i.e. stacks on formal derived smooth manifolds)\, and which i
s obtained by applying Töen-Vezzosi’s homotopical algebraic geometry to
the theory of derived manifolds of Spivak and Carchedi-Steffens. I will s
how how derived differential geometry is able to capture aspects of non-pe
rturbative BV-theory by means of examples in the cases of scalar field the
ory and Yang-Mills theory.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pelle Steffens (Technische Universität München)
DTSTART:20240326T203000Z
DTEND:20240326T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/17
DESCRIPTION:Title: Differential geometric PDE moduli spaces: derived enhancements\, ell
ipticity and representability\nby Pelle Steffens (Technische Universit
ät München) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\
n\nAbstract\nAll sorts of algebro-geometric moduli spaces (of stable curve
s\, stable sheaves on a CY 3-folds\, flat bundles\, Higgs bundles...) are
best understood as objects in derived geometry. Derived enhancements of cl
assical moduli spaces give transparent intrinsic meaning to previously ad-
hoc structures pertaining to\, for instance\, enumerative geometry and are
indispensable for more advanced constructions\, such as categorification
of enumerative invariants and (algebraic) deformation quantization of deri
ved symplectic structures. I will outline how to construct such enhancemen
ts for moduli spaces in global analysis and mathematical physics\, that is
\, solution spaces of PDEs in the framework of derived ${\\rm C}^\\infty$
geometry and discuss the elliptic representability theorem\, which guarant
ees that\, for elliptic equations\, these derived moduli stacks are bona f
ide geometric objects (Artin stacks at worst). If time permits some applic
ations to enumerative geometry (symplectic Gromov-Witten and Floer theory)
and derived symplectic geometry (the global BV formalism).\n
LOCATION:https://stable.researchseminars.org/talk/tandg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Clough (NYU Abu Dhabi)
DTSTART:20240416T150000Z
DTEND:20240416T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/18
DESCRIPTION:Title: Homotopical calculi and the smooth Oka principle\nby Adrian Clou
gh (NYU Abu Dhabi) as part of Topology and Geometry Seminar (Texas\, Kansa
s)\n\n\nAbstract\nI will present a new proof of Berwick-Evans\, Boavida de
Brito\, and Pavlov’s theorem that for any smooth manifold A\, and any s
heaf X on the site of smooth manifolds\, the mapping sheaf Hom(A\,X) has t
he correct homotopy type. The talk will focus on the main innovation of th
is proof\, namely the use of test categories to construct homotopical calc
uli on locally contractible ∞-toposes. With this tool in hand I will exp
lain how a suitable homotopical calculus may be constructed on the ∞-top
os of sheaves on the site of smooth manifolds using a new diffeology on th
e standard simplices due to Kihara. The main theorem follows using a simil
ar argument that for any CW-complex A\, and any topological space X the se
t of continuous maps Hom(A\,X) equipped with compact-open topology models
the mapping-homotopy-type map(A\,X).\n
LOCATION:https://stable.researchseminars.org/talk/tandg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (University of Oxford)
DTSTART:20240423T150000Z
DTEND:20240423T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/19
DESCRIPTION:Title: Characterizing paths and surfaces via (higher) holonomy\nby Darr
ick Lee (University of Oxford) as part of Topology and Geometry Seminar (T
exas\, Kansas)\n\n\nAbstract\nClassical vector valued paths are widespread
across pure and applied mathematics: from stochastic processes in probabi
lity to time series data in machine learning. Parallel transport of such p
aths in principal G-bundles have provided an effective method to character
ise such paths. In this talk\, we provide a brief overview of these result
s and their applications. We will then discuss recent work on extending th
is framework to characterizing random and possibly nonsmooth surfaces usin
g surface holonomy. This is based on joint work with Harald Oberhauser.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Lebovic (University of Oregon)
DTSTART:20240430T203000Z
DTEND:20240430T220000Z
DTSTAMP:20260417T112119Z
UID:tandg/20
DESCRIPTION:Title: Iterated K-theory and Functorial Field Theory\nby Jacob Lebovic
(University of Oregon) as part of Topology and Geometry Seminar (Texas\, K
ansas)\n\n\nAbstract\nUsing previous work by Bass\, Dundas\, and Rognes gi
ving a geometric model of the iterated K-theory spectrum K(ku) in terms of
bundles of Kapranov-Voevodsky 2-vector spaces\, and recent work by Grady
and Pavlov providing a rigorous foundation for fully-extended functorial f
ield theories\, we construct a model of K(ku) in terms of 2-dimensional fu
nctorial field theories valued in KV 2-vector spaces.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Grady (Wichita State University)
DTSTART:20240910T200000Z
DTEND:20240910T210000Z
DTSTAMP:20260417T112119Z
UID:tandg/21
DESCRIPTION:Title: Deformation classes of invertible field theories and the Freed–Hop
kins conjecture\nby Dan Grady (Wichita State University) as part of To
pology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their semin
al work\, Freed and Hopkins studied the moduli space of topological\, refl
ection positive\, invertible\, Euclidean field theories\, providing a comp
lete classification in terms of certain objects arising in stable homotopy
theory. In this work\, it was also conjectured that a similar classifica
tion holds in the case of nontopological field theories\, and this conject
ure is already being used in a variety of applications to condensed matter
physics. In this talk\, I will discuss a recent result which provides an
affirmative answer to this conjecture. I will begin by reviewing motivat
ion and background on reflection positive theories. Then I will state the
conjecture and sketch of the proof.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaqi Fu (Université Paul Sabatier\, Toulouse\, France)
DTSTART:20241106T160000Z
DTEND:20241106T173000Z
DTSTAMP:20260417T112119Z
UID:tandg/22
DESCRIPTION:Title: A filtered Koszul duality of partition Lie algebras(-oids)\nby J
iaqi Fu (Université Paul Sabatier\, Toulouse\, France) as part of Topolog
y and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nPartition Lie algeb
ras are sophisticated algebraic objects introduced by Brantner–Mathew to
control infinitesimal deformations in positive characteristics. This talk
will present a Koszul duality between partition Lie algebras and specific
complete filtered derived rings. This duality helps to understand the hom
otopy operations on partition Lie algebras. Additionally\, a “many-objec
t” version of this duality connects partition Lie algebroids with infini
tesimal derived foliations in the sense of Toën–Vezzosi.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kern (KTH)
DTSTART:20241119T213000Z
DTEND:20241119T230000Z
DTSTAMP:20260417T112119Z
UID:tandg/23
DESCRIPTION:Title: Categorical spectra and ℤ-categories\nby David Kern (KTH) as p
art of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nCateg
orical spectra\, developed by Stefanich\, are a directed version of\nspect
ra where the suspension of pointed ∞-groupoids is replaced by that\nof p
ointed ω-categories. They are very useful for capturing stability\nphenom
ena in iterated categorifications\, or for defining “∞-vector\nspaces
”. In this talk\, I will explain that they can be understood as a\nweak
version of Lessard's ℤ-categories\, a kind of category with arrows\nin a
ll negative as well as positive dimensions\, which allows for a more\ndire
ct study of their structure.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luuk Stehouwer (Dalhousie University)
DTSTART:20250212T160000Z
DTEND:20250212T173000Z
DTSTAMP:20260417T112119Z
UID:tandg/24
DESCRIPTION:Title: The Unitary Cobordism Hypothesis\nby Luuk Stehouwer (Dalhousie U
niversity) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\n
Abstract\nThe cobordism hypothesis classifies extended topological quantum
\nfield theories (TQFTs) in terms of algebraic information in the target\n
category. One of the core principles in quantum field theory - unitarity -
\nsays that state spaces are not just vector spaces\, but Hilbert spaces.\
nRecently in joint work with many others\, we have defined unitarity for\n
extended TQFTs\, inspired by Freed and Hopkins. Our main technical tool is
a\nhigher-categorical version of dagger categories\; categories $C$ equip
ped\nwith a strict anti-involution $\\dagger: C \\to C^{op}$ which is the
identity\non objects. I explain joint work in progress with Theo Johnson-F
reyd\,\nCameron Krulewski and Lukas Müller in which we prove a version of
the\ncobordism hypothesis for unitary TQFTs. The main observation is that
the\nstably framed bordism $n$-category is freely generated as a
symmetric\nmonoidal dagger $n$-category with unitary duals by a single ob
ject: the point.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Müller (Perimeter Institute for Theoretical Physics)
DTSTART:20250305T160000Z
DTEND:20250305T173000Z
DTSTAMP:20260417T112119Z
UID:tandg/25
DESCRIPTION:Title: A Higher Spin Statistics Theorem for Invertible Quantum Field Theori
es\nby Lukas Müller (Perimeter Institute for Theoretical Physics) as
part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe
spin-statistics theorem asserts that in a unitary quantum field theory\, t
he spin of a particle—characterized by its transformation under the cent
ral element of the spin group\, which corresponds to a 360-degree rotation
—determines whether it obeys bosonic or fermionic statistics. This relat
ionship can be formalized mathematically as equivariance for a geometric a
nd algebraic action of the 2-group ${\\rm B}{\\bf Z}_2$. In my talk\, I wi
ll present a refinement of these actions\, extending from ${\\rm B}{\\bf Z
}_2$ to appropriate actions of the stable orthogonal group ${\\rm O}$\, an
d demonstrate that every unitary invertible quantum field theory intertwin
es these ${\\rm O}$-actions.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Rot (Vrije Universiteit Amsterdam)
DTSTART:20250312T150000Z
DTEND:20250312T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/26
DESCRIPTION:Title: The topology of infinite dimensional spaces and nonlinear proper Fre
dholm mappings\nby Thomas Rot (Vrije Universiteit Amsterdam) as part o
f Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this ta
lk I will discuss the differential topology of non-linear proper Fredholm
mappings. In applications these mappings arise as non-linear PDE problems
(of elliptic type). I will discuss work with Lauran Toussaint that relate
s these mappings to the stable homotopy groups of spheres\, and if time pe
rmits\, I will discuss an ongoing project on defining a new homology theor
y of singular type for infinite dimensional spaces. This is joint work wit
h Alberto Abbondandolo\, Michael Jung and Lauran Toussaint.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urs Schreiber (NYU Abu Dhabi)
DTSTART:20250326T150000Z
DTEND:20250326T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/27
DESCRIPTION:Title: Non-Lagrangian construction of abelian CS/FQH-theory via flux quanti
zation in 2-Cohomotopy\nby Urs Schreiber (NYU Abu Dhabi) as part of To
pology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nAfter briefly
recalling how the analog of Dirac charge quantization in exotic (effective
\, higher) gauge theories\, providing their global topological completion\
, is encoded in a choice of classifying space $𝒜$ whose rationalization
reflects the flux Bianchi identities\, I explain how the choice $𝒜 ≔
S^2$ (“flux quantization in 2-Cohomotopy”) implements effective corre
ctions to ordinary Dirac flux quantization\, which over surfaces yields ex
actly the topological quantum observables of fractional quantum Hall syste
ms\, traditionally described by abelian Chern-Simons theory. I close by br
iefly indicating how this situation is geometrically engineered on probe M
5-branes if the M-theory C-field is flux-quantized in 4-Cohomotopy (“Hyp
othesis H”).\nThis is joint work with Hisham Sati\; for more pointers se
e ncatlab.org/schreibe
r/show/ISQS25.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lory Aintablian (MPIM Bonn)
DTSTART:20250402T150000Z
DTEND:20250402T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/28
DESCRIPTION:Title: Differentiation of groupoid objects in tangent categories\nby Lo
ry Aintablian (MPIM Bonn) as part of Topology and Geometry Seminar (Texas\
, Kansas)\n\n\nAbstract\nThe infinitesimal counterpart of a Lie group(oid)
is its Lie algebra(oid). I will show that the differentiation procedure w
orks in any category with an abstract tangent structure in the sense of Ro
sicky\, which was later rediscovered by Cockett and Cruttwell. Mainly\, I
will construct the abstract Lie algebroid of a differentiable groupoid in
a cartesian tangent category $C$ with a scalar $R$-multiplication\, where
$R$ is a ring object of $C$. Examples include differentiation of infinite-
dimensional Lie groups\, elastic diffeological groupoids\, etc. This is jo
int work with Christian Blohmann.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mayuko Yamashita (Perimeter Institute)
DTSTART:20250430T150000Z
DTEND:20250430T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/29
DESCRIPTION:Title: Topological elliptic genera\nby Mayuko Yamashita (Perimeter Inst
itute) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst
ract\nThere is a classical notion of elliptic genera\, which assigns Jacob
i forms to SU-manifolds. In this talk\, I explain my work with Ying-Hsuan
Lin (arXiv:2412.02298) to
give its homotopy-theoretical refinements and variants\, which we call “
topological elliptic genera”. The codomain becomes genuinely equivarian
t twisted Topological Modular Forms. In this talk\, I explain the constru
ction and physical idea behind\, and discuss an application where we deriv
e an interesting divisibility result of Euler numbers for Sp-manifolds. A
lso I explain a recent update with Tilman Bauer (in preparation) proving t
he surjectivity results of topological elliptic genera.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Sanford (Ohio State University)
DTSTART:20250409T150000Z
DTEND:20250409T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/30
DESCRIPTION:Title: Manifestly unitary higher Hilbert spaces\nby Sean Sanford (Ohio
State University) as part of Topology and Geometry Seminar (Texas\, Kansas
)\n\n\nAbstract\nA key aspect of quantum theory its insistence that states
evolve via unitary transformations. In order to understand the symmetries
of higher dimensional quantum field theory\, we need to develop higher di
mensional analogues of unitarity. The language and theory of higher catego
ries has greatly clarified the way we express these higher symmetries\, bu
t unfortunately this language imposes a certain dogma seems to be in confl
ict with various attempts at describing unitarity. In the nLab for example
\, there is a great debate over whether or not unitary structures on a (hi
gher) category are `evil’\; at term which is both dogmatic and technical
ly precise.\n\nVarious attempts have been made to force these structures t
o `play nice’ with one another\, to varying degrees of success. In this
talk I will present our most recent contribution to these efforts: definin
g the notion of a 3-Hilbert space. Our work aims to encode a kind of evalu
ation on spheres of every dimension that plays nicely with duality structu
res that are imposed by the cobordism hypothesis. I will show how this com
patibility is stronger than simply having daggers at all levels\, thus dif
ferentiating our construction from previous attempts at higher unitarity.
If time permits\, we will discuss a roadmap for unitarity in any dimension
via a unitary version of condensation completion.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita (University of Oxford)
DTSTART:20250423T150000Z
DTEND:20250423T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/31
DESCRIPTION:Title: Bicommutant categories from conformal nets\nby Nivedita (Univers
ity of Oxford) as part of Topology and Geometry Seminar (Texas\, Kansas)\n
\n\nAbstract\nTwo-dimensional chiral conformal field theories (CFTs) admit
three distinct mathematical formulations: vertex operator algebras (VOAs)
\, conformal nets\, and Segal (functorial) chiral CFTs. With the broader a
im to build fully extended Segal chiral CFTs\, we start with the input of
a conformal net.\n\nIn this talk\, we focus on presenting three equivalent
constructions of the category of solitons\, i.e. the category of solitoni
c representations of the net\, which we propose is what theory (chiral CFT
) assigns to a point. Solitonic representations of the net are one of the
primary class of examples of bicommutant categories (a categorified analog
ue of a von Neumann algebras). The Drinfel’d centre of solitonic represe
ntations is the representation category of the conformal net which has bee
n studied before\, particularly in the context of rational CFTs (finite-in
dex nets). If time permits\, we will briefly outline ongoing work on bicom
mutant category modules (which are the structures assigned by the Segal Ch
iral CFT at the level of 1-manifolds)\, hinting towards a categorified ana
logue of Connes fusion of von Neumann algebra modules.\n\n(Bicommutant cat
egories act on W*-categories analogous to von Neumann algebras acting on H
ilbert spaces.)\n
LOCATION:https://stable.researchseminars.org/talk/tandg/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Simon Pacaud Lemay (Macquarie University)
DTSTART:20250923T220000Z
DTEND:20250923T233000Z
DTSTAMP:20260417T112119Z
UID:tandg/32
DESCRIPTION:Title: The world of differential categories\nby Jean-Simon Pacaud Lemay
(Macquarie University) as part of Topology and Geometry Seminar (Texas\,
Kansas)\n\n\nAbstract\nDifferential categories use category theory to prov
ide the foundations of differential calculus. In this talk\, I will give
you guided tour of the world of differential categories. We will see (1) d
ifferential categories\, which give the algebraic foundations of different
iation\; Cartesian differential categories\, which give the foundations of
multivariable differential calculus\; and (3) tangent categories\, which
give the foundations of differential geometry. In particular we will look
at the map of differential categories and see how these three concepts rel
ate to each other. Moreover\, the theory of differential categories has be
en successful in formalising various important concepts related to differe
ntiation. In particular\, this talk will set the table for next week’s t
alk\, where Chiara Sava will explain how differential categories capture d
ifferential graded algebras.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Sava (Charles University\, Prague)
DTSTART:20250930T150000Z
DTEND:20250930T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/33
DESCRIPTION:Title: Differential graded algebras in differential categories\nby Chia
ra Sava (Charles University\, Prague) as part of Topology and Geometry Sem
inar (Texas\, Kansas)\n\n\nAbstract\nDifferential categories\, introduced
in last week's talk by Jean-Simon Pacaud Lemay\, provide a categorical fra
mework for the algebraic foundations of differential calculus. Within this
setting we can capture familiar notions such as derivations\, Kähler dif
ferentials\, differential algebras and de Rham cohomology. Along this line
\, in this talk\, we will show how to define differential graded algebras
in a differential category. In the case of polynomial differentiation\, th
is construction recovers the classical commutative differential graded alg
ebras\, while for smooth functions it yields differential graded $C^\\inft
y$-rings in the sense of Dmitri Pavlov. To further justify our definition\
, we will explain how the monad of a differential category can be lifted t
o its category of chain complexes and how the algebras of the lifted monad
correspond precisely to differential graded algebras of the base category
\, with the free ones given by the de Rham complexes. Finally\, we will di
scuss how the category of chain complexes of a differential category is it
self a differential category\, pointing towards the prospect of differenti
al dg-categories. This is joint work with Jean-Simon Pacaud Lemay.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georg Lehner (University of Münster)
DTSTART:20251021T150000Z
DTEND:20251021T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/34
DESCRIPTION:Title: Measure theory via locales\nby Georg Lehner (University of Müns
ter) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstra
ct\nThere are two oftentimes unspoken truths in measure theory. 1) Practic
ally all useful measures in practice are given by Radon measures. 2) One d
oes not really care so much about the sigma-algebra of measurable sets\, b
ut rather about its quotient by the ideal of null sets.\n\nThe quotient of
measurable sets by null sets is\, in the case of a given Radon measure\,
an example of what is called a measurable locale\, and can be treated like
a (usually point-free) space. We argue that this measurable locale can be
constructed directly from a Grothendieck topology on the poset of compact
sets. This opens the door to a purely sheaf-theoretic perspective on meas
ure theory. As an application\, we show that the locale of sublocales of a
given Hausdorff space X equipped with a Radon measure can be equipped wit
h a natural extension of the measure\, invariant under measure preserving
homeomorphisms.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Riva (CMSA\, Harvard University)
DTSTART:20251111T160000Z
DTEND:20251111T173000Z
DTSTAMP:20260417T112119Z
UID:tandg/35
DESCRIPTION:Title: Zigzags and free adjunctions\nby Lorenzo Riva (CMSA\, Harvard Un
iversity) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nA
bstract\nThe cobordism hypothesis tells us that the process of freely addi
ng adjoints to the $k$-morphisms of a symmetric monoidal $(\\infty\,n)$-ca
tegory can be roughly described as follows: treat one such $k$-morphism as
an $n$-framed $k$-dimensional cube and change the framing appropriately t
o obtain its left/right adjoint. At the very least\, this description is c
orrect if we start with the the commutative monoid generated by a single o
bject. But what happens with more complicated examples? Motivated by work
of Dawson-Paré-Pronk\, we explicitly construct the functor that freely ad
ds right adjoints to the morphisms of an infinity-category\; we also exten
d the construction to arbitrary dimensions and speculate on what its unive
rsal property should be. This is based on joint work with Martina Rovelli.
\n
LOCATION:https://stable.researchseminars.org/talk/tandg/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fei Han (National University of Singapore)
DTSTART:20260211T000000Z
DTEND:20260211T013000Z
DTSTAMP:20260417T112119Z
UID:tandg/36
DESCRIPTION:Title: Differential Models for Anderson Dual to Twisted Spin(^c) Bordism an
d the Twisted Anomaly Map\nby Fei Han (National University of Singapor
e) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract
\nSpin(^c) bordism is an important bordism theory with many connections an
d applications in topology\, geometry\, and physics. In this talk\, we exp
lain the construction of models for twisted Spin(^c) bordism and its Ander
son dual\, in homotopy-theoretic\, geometric\, and differential settings.
The talk is based on joint work with Yuanchu Li.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Bustillo Vazquez (Northwestern University)
DTSTART:20260414T150000Z
DTEND:20260414T163000Z
DTSTAMP:20260417T112119Z
UID:tandg/37
DESCRIPTION:Title: Fully-Dualizable and Invertible E_n-Algebras\nby Pablo Bustillo
Vazquez (Northwestern University) as part of Topology and Geometry Seminar
(Texas\, Kansas)\n\n\nAbstract\nThe easiest source of fully extended TQFT
s is found in E_n-algebras: for any symmetric monoidal category V and E_n-
algebra A in V\, one automatically obtains an n-dimensional TQFT given by
factorization homology. Sometimes\, however\, these TQFTs can be extended
to (n+1)-dimensional ones. In this talk\, I will explain how to characteri
ze precisely when this extension is possible and when the resulting theory
is invertible.\n
LOCATION:https://stable.researchseminars.org/talk/tandg/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kensuke Arakawa (Kyoto University)
DTSTART:20260421T230000Z
DTEND:20260422T003000Z
DTSTAMP:20260417T112119Z
UID:tandg/38
DESCRIPTION:Title: On the equivalence of two approaches to multiplicative homotopy theo
ries\nby Kensuke Arakawa (Kyoto University) as part of Topology and Ge
ometry Seminar (Texas\, Kansas)\n\n\nAbstract\nLocally presentable (\\infi
nity\,1) categories admit two popular models: Presentable quasicategories
and combinatorial model categories. Building on the foundational work of D
ugger and Lurie\, Pavlov proved that their associated (\\infty\,1)-categor
ies are equivalent\, confirming a long-standing expectation. He then went
on to conjecture that this should also hold multiplicatively\, i.e.\, for
presentably symmetric monoidal quasicategories and combinatorial symmetric
monoidal model categories. Such an equivalence would be of foundational i
mportance in higher algebra.\n\nIn arXiv:2603.23018\, I proved this conjec
ture. The main difficulty is that existing techniques to rigidify quasicat
egories often break down multiplicatively. In the talk\, I will explain ho
w to overcome this. If time permits\, I will also explain applications to
enriched infinity operads (arXiv:2603.23019).\n
LOCATION:https://stable.researchseminars.org/talk/tandg/38/
END:VEVENT
END:VCALENDAR