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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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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:20241112T141830Z
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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigorios Giotopoulos (NYU Abu Dhabi)
DTSTART;VALUE=DATE-TIME:20240213T160000Z
DTEND;VALUE=DATE-TIME:20240213T173000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/15
DESCRIPTION:Title: S
mooth sets as a convenient setting for Lagrangian field theory\nby Gri
gorios Giotopoulos (NYU Abu Dhabi) as part of Topology and Geometry Semina
r (Texas\, Kansas)\n\n\nAbstract\nIn this talk\, I will indicate how the s
heaf topos of smooth sets serves as a sufficiently powerful and convenient
context to host classical (bosonic) Lagrangian field theory. As motivatio
n\, I will recall the textbook description of variational Lagrangian field
theory\, and list desiderata for an ambient category in which this can ri
gorously be phrased. I will then explain how sheaves over Cartesian spaces
naturally satisfy all the desiderata\, and furthermore allow to rigorousl
y formalize several more field theoretic concepts. Time permitting\, I wil
l indicate how the setting naturally generalizes to include the descriptio
n of (perturbative) infinitesimal structure\, fermionic fields\, and (gaug
e) fields with internal symmetries. This is based on joint work with Hisha
m Sati.\n
LOCATION:https://researchseminars.org/talk/tandg/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Alfonsi (University of Hertfordshire)
DTSTART;VALUE=DATE-TIME:20240319T203000Z
DTEND;VALUE=DATE-TIME:20240319T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/16
DESCRIPTION:Title: B
atalin–Vilkovisky formalism beyond perturbation theory via derived geome
try\nby Luigi Alfonsi (University of Hertfordshire) as part of Topolog
y and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn this talk I will
discuss applications of derived differential geometry to study a non-pert
urbative generalisation of classical Batalin–Vilkovisky (BV-)formalism.
First\, I will describe the current state of the art of the geometry of pe
rturbative BV-theory. Then\, I will introduce a simple model of derived di
fferential geometry\, whose geometric objects are formal derived smooth st
acks (i.e. stacks on formal derived smooth manifolds)\, and which is obtai
ned by applying Töen-Vezzosi’s homotopical algebraic geometry to the th
eory of derived manifolds of Spivak and Carchedi-Steffens. I will show how
derived differential geometry is able to capture aspects of non-perturbat
ive BV-theory by means of examples in the cases of scalar field theory and
Yang-Mills theory.\n
LOCATION:https://researchseminars.org/talk/tandg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pelle Steffens (Technische Universität München)
DTSTART;VALUE=DATE-TIME:20240326T203000Z
DTEND;VALUE=DATE-TIME:20240326T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/17
DESCRIPTION:Title: D
ifferential geometric PDE moduli spaces: derived enhancements\, ellipticit
y and representability\nby Pelle Steffens (Technische Universität Mü
nchen) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst
ract\nAll sorts of algebro-geometric moduli spaces (of stable curves\, sta
ble sheaves on a CY 3-folds\, flat bundles\, Higgs bundles...) are best un
derstood as objects in derived geometry. Derived enhancements of classical
moduli spaces give transparent intrinsic meaning to previously ad-hoc str
uctures pertaining to\, for instance\, enumerative geometry and are indisp
ensable for more advanced constructions\, such as categorification of enum
erative invariants and (algebraic) deformation quantization of derived sym
plectic structures. I will outline how to construct such enhancements for
moduli spaces in global analysis and mathematical physics\, that is\, solu
tion spaces of PDEs in the framework of derived ${\\rm C}^\\infty$ geometr
y and discuss the elliptic representability theorem\, which guarantees tha
t\, for elliptic equations\, these derived moduli stacks are bona fide geo
metric objects (Artin stacks at worst). If time permits some applications
to enumerative geometry (symplectic Gromov-Witten and Floer theory) and de
rived symplectic geometry (the global BV formalism).\n
LOCATION:https://researchseminars.org/talk/tandg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Clough (NYU Abu Dhabi)
DTSTART;VALUE=DATE-TIME:20240416T150000Z
DTEND;VALUE=DATE-TIME:20240416T163000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/18
DESCRIPTION:Title: H
omotopical calculi and the smooth Oka principle\nby Adrian Clough (NYU
Abu Dhabi) as part of Topology and Geometry Seminar (Texas\, Kansas)\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 sheaf X
on the site of smooth manifolds\, the mapping sheaf Hom(A\,X) has the corr
ect homotopy type. The talk will focus on the main innovation of this proo
f\, namely the use of test categories to construct homotopical calculi on
locally contractible ∞-toposes. With this tool in hand I will explain ho
w a suitable homotopical calculus may be constructed on the ∞-topos of s
heaves on the site of smooth manifolds using a new diffeology on the stand
ard simplices due to Kihara. The main theorem follows using a similar argu
ment that for any CW-complex A\, and any topological space X the set of co
ntinuous maps Hom(A\,X) equipped with compact-open topology models the map
ping-homotopy-type map(A\,X).\n
LOCATION:https://researchseminars.org/talk/tandg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (University of Oxford)
DTSTART;VALUE=DATE-TIME:20240423T150000Z
DTEND;VALUE=DATE-TIME:20240423T163000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/19
DESCRIPTION:Title: C
haracterizing paths and surfaces via (higher) holonomy\nby Darrick Lee
(University of Oxford) as part of Topology and Geometry Seminar (Texas\,
Kansas)\n\n\nAbstract\nClassical vector valued paths are widespread across
pure and applied mathematics: from stochastic processes in probability to
time series data in machine learning. Parallel transport of such paths in
principal G-bundles have provided an effective method to characterise suc
h paths. In this talk\, we provide a brief overview of these results and t
heir applications. We will then discuss recent work on extending this fram
ework to characterizing random and possibly nonsmooth surfaces using surfa
ce holonomy. This is based on joint work with Harald Oberhauser.\n
LOCATION:https://researchseminars.org/talk/tandg/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Lebovic (University of Oregon)
DTSTART;VALUE=DATE-TIME:20240430T203000Z
DTEND;VALUE=DATE-TIME:20240430T220000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/20
DESCRIPTION:Title: I
terated K-theory and Functorial Field Theory\nby Jacob Lebovic (Univer
sity of Oregon) as part of Topology and Geometry Seminar (Texas\, Kansas)\
n\n\nAbstract\nUsing previous work by Bass\, Dundas\, and Rognes giving a
geometric model of the iterated K-theory spectrum K(ku) in terms of bundle
s of Kapranov-Voevodsky 2-vector spaces\, and recent work by Grady and Pav
lov providing a rigorous foundation for fully-extended functorial field th
eories\, we construct a model of K(ku) in terms of 2-dimensional functoria
l field theories valued in KV 2-vector spaces.\n
LOCATION:https://researchseminars.org/talk/tandg/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Grady (Wichita State University)
DTSTART;VALUE=DATE-TIME:20240910T200000Z
DTEND;VALUE=DATE-TIME:20240910T210000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/21
DESCRIPTION:Title: D
eformation classes of invertible field theories and the Freed–Hopkins co
njecture\nby Dan Grady (Wichita State University) as part of Topology
and Geometry Seminar (Texas\, Kansas)\n\n\nAbstract\nIn their seminal work
\, Freed and Hopkins studied the moduli space of topological\, reflection
positive\, invertible\, Euclidean field theories\, providing a complete cl
assification in terms of certain objects arising in stable homotopy theory
. In this work\, it was also conjectured that a similar classification ho
lds in the case of nontopological field theories\, and this conjecture is
already being used in a variety of applications to condensed matter physic
s. In this talk\, I will discuss a recent result which provides an affirm
ative answer to this conjecture. I will begin by reviewing motivation and
background on reflection positive theories. Then I will state the conjec
ture and sketch of the proof.\n
LOCATION:https://researchseminars.org/talk/tandg/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaqi Fu (Université Paul Sabatier\, Toulouse\, France)
DTSTART;VALUE=DATE-TIME:20241106T160000Z
DTEND;VALUE=DATE-TIME:20241106T173000Z
DTSTAMP;VALUE=DATE-TIME:20241112T141830Z
UID:tandg/22
DESCRIPTION:Title: A
filtered Koszul duality of partition Lie algebras(-oids)\nby Jiaqi Fu
(Université Paul Sabatier\, Toulouse\, France) as part of Topology and G
eometry Seminar (Texas\, Kansas)\n\n\nAbstract\nPartition Lie algebras are
sophisticated algebraic objects introduced by Brantner–Mathew to contro
l infinitesimal deformations in positive characteristics. This talk will p
resent a Koszul duality between partition Lie algebras and specific comple
te filtered derived rings. This duality helps to understand the homotopy o
perations on partition Lie algebras. Additionally\, a “many-object” ve
rsion of this duality connects partition Lie algebroids with infinitesimal
derived foliations in the sense of Toën–Vezzosi.\n
LOCATION:https://researchseminars.org/talk/tandg/22/
END:VEVENT
END:VCALENDAR