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BEGIN:VEVENT
SUMMARY:Christian Blohmann (MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20230207T213000Z
DTEND;VALUE=DATE-TIME:20230207T230000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/1
DESCRIPTION:Title: El
astic diffeological spaces\nby Christian Blohmann (MPIM Bonn) as part
of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nI will in
troduce a class of diffeological spaces\, called elastic\, on which the le
ft Kan extension of the tangent functor of smooth manifolds defines an abs
tract tangent functor in the sense of Rosický. On elastic spaces there is
a natural Cartan calculus\, consisting of vector fields and differential
forms\, together with the Lie bracket\, de Rham differential\, inner deriv
ative\, and Lie derivative\, satisfying the usual graded commutation relat
ions. Elastic spaces are closed under arbitrary coproducts\, finite produc
ts\, and retracts. Examples include manifolds with corners and cusps\, dif
feological groups and diffeological vector spaces with a mild extra condit
ion\, mapping spaces between smooth manifolds\, and spaces of sections of
smooth fiber bundles.\n
LOCATION:https://researchseminars.org/talk/tandg/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Mazel-Gee (Caltech)
DTSTART;VALUE=DATE-TIME:20230221T213000Z
DTEND;VALUE=DATE-TIME:20230221T230000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/2
DESCRIPTION:Title: To
wards knot homology for 3-manifolds\nby Aaron Mazel-Gee (Caltech) as p
art of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe J
ones polynomial is an invariant of knots in R^3. Following a proposal of W
itten\, it was extended to knots in 3-manifolds by Reshetikhin–Turaev us
ing quantum groups. Khovanov homology is a categorification of the Jones p
olynomial of a knot in R^3\, analogously to how ordinary homology is a cat
egorification of the Euler characteristic of a space. It is a major open p
roblem to extend Khovanov homology to knots in 3-manifolds. In this talk\,
I will explain forthcoming work towards solving this problem\, joint with
Leon Liu\, David Reutter\, Catharina Stroppel\, and Paul Wedrich. Roughly
speaking\, our contribution amounts to the first instance of a braiding o
n 2-representations of a categorified quantum group. More precisely\, we c
onstruct a braided (∞\,2)-category that simultaneously incorporates all
of Rouquier's braid group actions on Hecke categories in type A\, articula
ting a novel compatibility among them.\n
LOCATION:https://researchseminars.org/talk/tandg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Domenico Fiorenza (Sapienza University of Rome)
DTSTART;VALUE=DATE-TIME:20230307T213000Z
DTEND;VALUE=DATE-TIME:20230307T230000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/3
DESCRIPTION:Title: St
ring bordism invariants in dimension 3 from U(1)-valued TQFTs\nby Dome
nico Fiorenza (Sapienza University of Rome) as part of Topology and Geomet
ry 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 ge
ometric string structure on a manifold\, Bunke–Naumann and Redden have e
xhibited integral formulas involving the Chern–Weil form representative
of the first Pontryagin class and the canonical 3-form of a geometric stri
ng structure that realize the isomorphism ${\\rm Bord}_3^{\\rm String} \\t
o \\mathbb{Z}/24\\mathbb{Z}$ (these formulas have been recently rediscover
ed by Gaiotto–Johnson-Freyd–Witten). In the talk I will show how these
formulas naturally emerge when one considers the U(1)-valued 3d TQFTs ass
ociated with the classifying stacks of Spin bundles with connection and of
String bundles with geometric structure. Joint work with Eugenio Landi (<
a href="https://arxiv.org/abs/2209.12933v2">arXiv:2209.12933).\n
LOCATION:https://researchseminars.org/talk/tandg/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Minichiello (CUNY GC)
DTSTART;VALUE=DATE-TIME:20230404T203000Z
DTEND;VALUE=DATE-TIME:20230404T220000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/4
DESCRIPTION:Title: Di
ffeological Principal Bundles\, Čech Cohomology and Principal Infinity Bu
ndles\nby Emilio Minichiello (CUNY GC) as part of Topology and Geometr
y Seminar (Texas\, Kansas)\n\n\nAbstract\nThanks to a result of Baez and H
offnung\, the category of diffeological spaces is equivalent to the catego
ry of concrete sheaves on the site of cartesian spaces. By thinking of di
ffeological spaces as kinds of sheaves\, we can therefore think of diffeol
ogical spaces as kinds of infinity sheaves. We do this by using a model c
ategory presentation of the infinity category of infinity sheaves on carte
sian spaces\, and cofibrantly replacing a diffeological space within it.
By doing this\, we obtain a new generalized cocycle construction for diffe
ological principal bundles\, a new version of Čech cohomology for diffeol
ogical spaces that can be compared very directly with two other versions a
ppearing in the literature\, which is precisely infinity sheaf cohomology\
, and we show that the nerve of the category of diffeological principal G-
bundles over a diffeological space X for a diffeological group G is weak e
quivalent to the nerve of the category of G-principal infinity bundles ove
r X.\n
LOCATION:https://researchseminars.org/talk/tandg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (Wichita State University)
DTSTART;VALUE=DATE-TIME:20230411T203000Z
DTEND;VALUE=DATE-TIME:20230411T220000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/5
DESCRIPTION:Title: Fo
urier analysis in Diophantine approximation\nby Robert Fraser (Wichita
State University) as part of Topology and Geometry Seminar (Texas\, Kansa
s)\n\n\nAbstract\nA real number $x$ is said to be *normal* if the s
equence $a^n x$ is uniformly distributed modulo 1 for every integer $a≥2
$.\nAlthough Lebesgue-almost all numbers are normal\, the problem determin
ing whether specific irrational numbers such as $e$ and $π$ are normal is
extremely difficult.\nHowever\, techniques from Fourier analysis and geom
etric measure theory can be used to show that certain “thin” subsets o
f $\\mathbb{R}$ must contain normal numbers.\n
LOCATION:https://researchseminars.org/talk/tandg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Heine (Hamburg)
DTSTART;VALUE=DATE-TIME:20230418T203000Z
DTEND;VALUE=DATE-TIME:20230418T220000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/6
DESCRIPTION:Title: Th
e Dwyer Kan-correspondence and its categorification\nby Till Heine (Ha
mburg) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst
ract\nExtensions of the Dold-Kan correspondence for the duplicial and (par
a)cyclic index categories were introduced by Dwyer and Kan.\nBuilding on t
he categorification of the Dold-Kan correspondence by Dyckerhoff\, we cate
gorify the duplicial case by establishing an equivalence between the $\\in
fty$-category of $2$-duplicial stable $\\infty$-categories and the $\\inft
y$-category of connective chain complexes of stable $\\infty$-categories w
ith right adjoints. \nI will further explain the current progress to
wards a conjectured correspondence between $2$-paracyclic stable $\\infty$
-categories and connective spherical complexes.\nExamples of the latter na
turally arise from the study of perverse schobers. \narXiv:2303.03653.\n
LOCATION:https://researchseminars.org/talk/tandg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Wierstra (Korteweg-de Vries Institute for Mathematics\, Univ
ersity of Amsterdam)
DTSTART;VALUE=DATE-TIME:20230425T203000Z
DTEND;VALUE=DATE-TIME:20230425T220000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/7
DESCRIPTION:Title: A
recognition principle for iterated suspensions as coalgebras over the litt
le cubes operad\nby Felix Wierstra (Korteweg-de Vries Institute for Ma
thematics\, University of Amsterdam) as part of Topology and Geometry Semi
nar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I will discus a recogniti
on principle for iterated suspensions as coalgebras over the little cubes
operad.\nThis is joint work with Oisín Flynn-Connolly and José Moreno-Fe
rnádez.\n
LOCATION:https://researchseminars.org/talk/tandg/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kinard
DTSTART;VALUE=DATE-TIME:20231003T180000Z
DTEND;VALUE=DATE-TIME:20231003T195000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/8
DESCRIPTION:Title: Sh
eaves as a Data Structure\nby Rachel Kinard as part of Topology and Ge
ometry Seminar (Texas\, Kansas)\n\n\nAbstract\nThe word “Topology”\, b
est known for its association to the study of invariants of an abstract sp
ace\, is a branch of Pure Mathematics whose best known applications are fo
und in Physics (Quantum Mechanics\, Quantum Field Theory). Very rarely doe
s a Pure Math Field find such as Topology find relevance in a world of Big
Data and computer automation. Data Science utilizes these powerful topolo
gical invariants to quickly gather information about complex data spaces i
n a brave new area of study called “Topological Data Analysis” or TDA.
Given a set of data points\, the nerve construction produces a simplicial
complex that can be analyzed to understand important characteristics of t
he data. I will provide an introduction to TDA and a few examples of surpr
ising Data Science applications.\n
LOCATION:https://researchseminars.org/talk/tandg/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Kinard
DTSTART;VALUE=DATE-TIME:20231005T190000Z
DTEND;VALUE=DATE-TIME:20231005T195000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/9
DESCRIPTION:Title: Sh
eaves as a Data Structure (Part 2)\nby Rachel Kinard as part of Topolo
gy and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nWe continue our di
scussion with an example of “Path-Optimization Sheaves” (https://arxiv
.org/abs/2012.05974)\;\nan alternative approach to classical Dijkstra’s
Algorithm\, paths from a source vertex to sink vertex in a graph are revea
led as Sections of the Path-finding Sheaf.\n\nTables\, Arrays\, and Matric
es are useful in data storage and manipulation\, employing operations and
methods from Numerical Linear Algebra for computer algorithm development.\
nRecent advances in computer hardware and high performance computing invit
e us to explore more advanced data structures\,\nsuch as sheaves and the u
se of sheaf operations for more sophisticated computations.\nAbstractly\,
Mathematical Sheaves can be used to track data associated to the open sets
of a topological space\;\npractically\, sheaves as an advanced data struc
ture provide a framework for the manipulation and optimization of complex
systems of interrelated information.\nDo we ever really get to see a concr
ete example?\nI will point to several recent examples of (1) the use of sh
eaves as a tool for data organization\, and (2) the use of sheaves to gain
additional information about a system.\n\nNotice the nonstandard day (Thu
rsday) and the nonstandard time slot (2 pm Central Time).\n\nContinuation
of the talk given on October 3 (https://researchseminars.org/talk/tandg/8/
).\n\nRecording of Part I is available here: https://dmitripavlov.org/2023
-10-03.mp4\n
LOCATION:https://researchseminars.org/talk/tandg/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Debray (Purdue University)
DTSTART;VALUE=DATE-TIME:20231024T180000Z
DTEND;VALUE=DATE-TIME:20231024T195000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/10
DESCRIPTION:Title: C
onstructing the Virasoro groups using differential cohomology\nby Arun
Debray (Purdue University) as part of Topology and Geometry Seminar (Texa
s\, Kansas)\n\n\nAbstract\nAbstract: The Virasoro groups are a family of c
entral extensions of ${\\rm Diff}^+(S^1)$ by the circle group $\\bf T$.\nI
n this talk I will discuss recent work\, joint with Yu Leon Liu and Christ
oph Weis\,\nconstructing these groups by beginning with a lift of the firs
t Pontrjagin class to "off-diagonal" differential cohomology\,\nthen trans
gressing it to obtain a central extension.\nAlong the way\, I will discuss
what the Virasoro extensions are and how to recognize them\;\na brief int
roduction to differential cohomology\; and lifts of characteristic classes
to differential cohomology.\n
LOCATION:https://researchseminars.org/talk/tandg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Bunk (University of Oxford)
DTSTART;VALUE=DATE-TIME:20231107T190000Z
DTEND;VALUE=DATE-TIME:20231107T205000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/11
DESCRIPTION:Title: S
mooth higher symmetries groups and the geometry of Deligne cohomology\
nby Severin Bunk (University of Oxford) as part of Topology and Geometry S
eminar (Texas\, Kansas)\n\n\nAbstract\nWe construct the smooth higher grou
p of symmetries of any higher geometric structure on manifolds. Via a univ
ersal property\, this classifies equivariant structures on the geometry. W
e present a general construction of moduli stacks of solutions in higher-g
eometric field theories and provide a criterion for when two such moduli s
tacks are equivalent. We then apply this to the study of generalised Ricci
solitons\, or NSNS supergravity: this theory has two different formulatio
ns\, originating in higher geometry and generalised geometry\, respectivel
y. These formulations produce inequivalent field configurations and inequi
valent symmetries. We resolve this discrepancy by showing that their modul
i stacks are equivalent. This is joint work with C. Shahbazi.\n
LOCATION:https://researchseminars.org/talk/tandg/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Araminta Amabel (Northwestern University)
DTSTART;VALUE=DATE-TIME:20231114T190000Z
DTEND;VALUE=DATE-TIME:20231114T205000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
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 fac
torization algebra approach of Costello–Gwilliam.\nI'll discuss how to t
hink about line operators in these contexts\, and the different strengths
of each method.\nMotivated by work of Freed–Moore–Teleman\, I'll expla
in how to exploit both models to say something about certain gauge theorie
s.\nThis is based on joint work with Owen Gwilliam.\n
LOCATION:https://researchseminars.org/talk/tandg/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Tooby-Smith (Cornell University)
DTSTART;VALUE=DATE-TIME:20231121T190000Z
DTEND;VALUE=DATE-TIME:20231121T205000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/13
DESCRIPTION:Title: S
mooth generalized symmetries of quantum field theories\nby Joseph Toob
y-Smith (Cornell University) as part of Topology and Geometry Seminar (Tex
as\, Kansas)\n\n\nAbstract\nIn this talk\, based on joint work with Ben Gr
ipaios and Oscar Randal-Williams (arXiv:2209.13524 and 2310.16090)\, we wi
ll\, with help from the geometric cobordism hypothesis\, define and study
invertible smooth generalized symmetries of field theories within the fram
ework of higher category theory. We will show the existence of a new type
of anomaly that afflicts global symmetries even before trying to gauge\, w
e call these anomalies “smoothness anomalies”. In addition\, we will s
ee that d-dimensional QFTs when considered collectively can have d-form sy
mmetries\, which goes beyond the (d-1)-form symmetries known to physicists
for individual QFTs. We will also touch on aspects of gauging global symm
etries in the case of topological quantum field theories.\n
LOCATION:https://researchseminars.org/talk/tandg/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Berwick-Evans (University of Illinois Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20231128T190000Z
DTEND;VALUE=DATE-TIME:20231128T205000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083547Z
UID:tandg/14
DESCRIPTION:Title: T
wisted equivariant Thom classes in topology and physics\nby Daniel Ber
wick-Evans (University of Illinois Urbana-Champaign) as part of Topology a
nd Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their seminal work\
, Mathai and Quillen explained how free fermion theories can be used to co
nstruct cocycle representatives of Thom classes in de Rham cohomology. Aft
er reviewing this idea\, I will describe several avenues of generalization
that lead to cocycle representatives of Thom classes in twisted equivaria
nt KR-theory and (conjecturally) in equivariant elliptic cohomology. I wil
l further describe nice properties enjoyed by these cocycle representative
s\, e.g.\, compatibility with (twisted) power operations. This is joint wo
rk with combinations of Tobi Barthel\, Millie Deaton\, Meng Guo\, Yigal Ka
mel\, Hui Langwen\, Kiran Luecke\, Alex Pacun\, and Nat Stapleton.\n
LOCATION:https://researchseminars.org/talk/tandg/14/
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