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BEGIN:VEVENT
SUMMARY:Urs Schreiber (Czech Academy of Sciences)
DTSTART:20220208T113000Z
DTEND:20220208T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/1
DESCRIPTION:Title: Higher and Equivariant Bundles\nby Urs Schreiber (Czec
h Academy of Sciences) as part of Feza Gursey Center Higher Structures Sem
inars\n\n\nAbstract\nThe natural promotion of the classical concept of (pr
incipal) fiber\nbundles to "higher structures"\, namely to equivariant pri
ncipal infinity-bundles\ninternal to a singular-cohesive infinity-topos\,
turns out to be a natural foundation\nfor generalized cohomology theory in
the full beauty of "twisted\nequivariant differential non-abelian cohomol
ogy of orbifolds"\, and as such for much of the higher homotopical mathema
tics needed at the interface of algebraic topology\, geometry and mathemat
ical quantum physics. This talk gives some introduction and overview\, bas
ed on joint work with H. Sati (arXiv:2008.01101\, arXiv:2112.13654).\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masanori Morishita (Kyushu University)
DTSTART:20220125T113000Z
DTEND:20220125T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/2
DESCRIPTION:Title: Arithmetic topology and arithmetic TQFT\nby Masanori M
orishita (Kyushu University) as part of Feza Gursey Center Higher Structur
es Seminars\n\n\nAbstract\nI will talk about some topics in arithmetic top
ology\, related withclass field theory\,\n and then an arithmetic analog o
f Dijkgraaf-Witten topological quantum field theory.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri Ilker Berktav (Middle East Technical University)
DTSTART:20220222T113000Z
DTEND:20220222T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/3
DESCRIPTION:Title: Symplectic Structures on Derived Schemes\nby Kadri Ilk
er Berktav (Middle East Technical University) as part of Feza Gursey Cente
r Higher Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berkan Üze (Boğaziçi University)
DTSTART:20220308T113000Z
DTEND:20220308T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/4
DESCRIPTION:Title: A Glimpse of Noncommutative Motives\nby Berkan Üze (B
oğaziçi University) as part of Feza Gursey Center Higher Structures Semi
nars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe University)
DTSTART:20220412T113000Z
DTEND:20220412T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/5
DESCRIPTION:Title: Homotopy theory of monoid actions via group actions and an
Elmendorf style theorem\nby Mehmet Akif Erdal (Yeditepe University) a
s part of Feza Gursey Center Higher Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haldun Özgür Bayındır (City University of London)
DTSTART:20220426T113000Z
DTEND:20220426T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/6
DESCRIPTION:Title: Adjoining roots to ring spectra and algebraic K-theory
\nby Haldun Özgür Bayındır (City University of London) as part of Feza
Gursey Center Higher Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Orendain (Universidad Nacional Autónoma de México)
DTSTART:20220510T160000Z
DTEND:20220510T170000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/7
DESCRIPTION:Title: Higher lattice gauge fields and cubical $\\omega$-groupoid
s\nby Juan Orendain (Universidad Nacional Autónoma de México) as par
t of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nGauge fi
elds describe parallel transport of point particles\nalong curves\, with r
espect to connections on principal bundles. This\ndata is captured as a sm
ooth functor from the smooth path groupoid of\nthe base manifold into the
delooping groupoid of the structure group\,\nplus gluing data. Lattice gau
ge fields do this for discretized versions\nof a base manifold. A lattice
gauge field is thus a functor from a\ndiscrete version of the path groupoi
d to a delooping groupoid. Lattice\ngauge fields are meant to serve as dis
crete approximations of regular\ngauge fields.\n\nHigher gauge fields desc
ribe parallel transport of curves along\nsurfaces\, of surfaces along volu
mes\, etc. Several versions of\n2-dimensional gauge field have appeared in
the literature. I will\nexplain how to extend these ideas to lattice gaug
e fields on all\ndimensions\, using Brown's cubical homotopy \\omega-group
oid construction\nassociated to filtered spaces\, implementing a discrete
notion of thin\nhomotopy along the way.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Kyoto University)
DTSTART:20220524T113000Z
DTEND:20220524T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/8
DESCRIPTION:Title: An introduction to perverse schober\nby Tatsuki Kuwaga
ki (Kyoto University) as part of Feza Gursey Center Higher Structures Semi
nars\n\n\nAbstract\nA perverse sheaf is the topological counterpart of a d
ifferential equation with (regular) singularities. A perverse schober is "
a category-valued perverse sheaf". It consists of monodromy of categories
and their behaviors around singularities. The notion of perverse schober q
uite naturally appears in many contexts e.g.\, mirror symmetry. In this ta
lk\, I'll give an introduction to a very elementary part of perverse schob
er and related topics.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Mazel-Gee (California Institute of Technology)
DTSTART:20221108T150000Z
DTEND:20221108T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/10
DESCRIPTION:Title: Towards knot homology for 3-manifolds\nby Aaron Mazel
-Gee (California Institute of Technology) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nThe Jones polynomial is an invaria
nt of knots in $\\mathbb R^3$. Following a proposal of Witten\, it was ext
ended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups.\
nKhovanov homology is a categorification of the Jones polynomial of a knot
in $\\mathbb R^3$\, analogously to how ordinary homology is a categorific
ation of the Euler characteristic of a space. It is a major open problem t
o extend Khovanov homology to knots in 3-manifolds.\nIn this talk\, I will
explain forthcoming work towards solving this problem\, joint with Leon L
iu\,\nDavid Reutter\, Catharina Stroppel\, and Paul Wedrich. Roughly speak
ing\, our contribution amounts\nto the first instance of a braiding on 2-r
epresentations of a categorified quantum group. More\nprecisely\, we const
ruct a braided (∞\,2)-category that simultaneously incorporates all of R
ouquier's\nbraid group actions on Hecke categories in type A\, articulatin
g a novel compatibility among them.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Can Yaylalı (Technische Universität Darmstadt)
DTSTART:20221122T140000Z
DTEND:20221122T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/11
DESCRIPTION:Title: Derived F-zips\nby Can Yaylalı (Technische Universit
ät Darmstadt) as part of Feza Gursey Center Higher Structures Seminars\n\
n\nAbstract\nThe theory of F-zips is a positive characteristic analog of t
he theory of integral Hodge-structures. As shown by Moonen and Wedhorn\, o
ne can associate to any proper smooth scheme with degenerating Hodge-de Rh
am spectral sequence and finite locally free Hodge cohomologies an F-zips
\, via its n-th de Rham cohomology.\nUsing the theory of derived algebraic
geometry\, we can work with the de Rham hypercohomology and show that it
has a derived analog of an F-zip structure. We call these structures deriv
ed F-zips. We can attach to any proper smooth morphism a derived F-zip and
analyze families of proper smooth morphisms via their underlying derived
F-zip.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kürşat Sözer (McMaster University)
DTSTART:20221206T140000Z
DTEND:20221206T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/12
DESCRIPTION:Title: Crossed module graded categories and state-sum homotopy i
nvariants of maps\nby Kürşat Sözer (McMaster University) as part of
Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nA well-known
fact is that groups are algebraic models for 1-types. Generalizing groups
\, crossed modules model 2-types. In this talk\, I will introduce the noti
on of a crossed module graded fusion category which generalizes that of a
fusion category graded by a group. Then\,using such categories\, I will co
nstruct a 3-dimensional state-sum homotopy quantum field theory (HQFT) wit
h a 2-type target. Such an HQFT associates a scalar to a map from a closed
oriented 3-manifold to the fixed 2-type. Moreover\, this scalar is invari
ant under homotopies. This HQFT generalizes the state-sum Turaev-Virelizie
r HQFT with an aspherical target. This is joint work with Alexis Virelizie
r.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ödül Tetik (University of Zurich)
DTSTART:20221220T140000Z
DTEND:20221220T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/13
DESCRIPTION:Title: Field theory from [and] homology via [are] “duals”\nby Ödül Tetik (University of Zurich) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nI will introduce the notion of the
'Poincaré' or 'Koszul' dual of a stratified space with tangential struct
ure (TS)\, whose construction in general is as yet an open problem. Then I
will outline (the finished part of) ongoing work on defining a functorial
field theory\, given\, as input\, a disk-algebra with TS. This recovers t
he framed case\, which was proposed by Lurie (later picked up by Calaque a
nd Scheimbauer): duals of stably-framed bordisms are euclidean spaces with
flag-like stratifications. In particular\, this notion explains the 'shap
e' of the higher Morita category of En-algebras when expressed in terms of
factorization algebras\, and gives a natural definition of Morita categor
ies of disk-algebras with any TS. If time permits\, I will propose a simpl
e Poisson-structured version of this procedure which should construct\, us
ing Poisson additivity\, extended classical gauge theories given only the
1-shifted Poisson algebra of bulk observables.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (University of Zurich)
DTSTART:20221025T113000Z
DTEND:20221025T123000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/14
DESCRIPTION:Title: Geometric structures as stacks and geometric field theori
es\nby Kadri İlker Berktav (University of Zurich) as part of Feza Gur
sey Center Higher Structures Seminars\n\n\nAbstract\nIn this talk\, we out
line a general framework for geometric field theories formulated by Ludewi
g and Stoffel. In brief\, functorial field theories (FFTs) can be formaliz
ed as certain functors from an appropriate bordism category Bord to a suit
able target category. Atiyah's topological field theories and Segal's con
formal field theories are the two important examples of such formulation.
Given an FFT\, one can also require the source category to endow with a ''
geometric structure''. Of course\, the meaning of ''geometry'' must be cla
rified in this new context. To introduce geometric field theories in an ap
propriate way\, therefore\, we first explain how to define ''geometries''
using the language of stacks\, and then we provide the so-called geometric
bordism category GBord. Finally\, we give the definition of a geometric f
ield theory as a suitable functor on GBord.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neslihan Güğümcü (İzmir Institute of Technology)
DTSTART:20230117T140000Z
DTEND:20230117T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/15
DESCRIPTION:Title: On a quantum invariant of multi-knotoids\nby Neslihan
Güğümcü (İzmir Institute of Technology) as part of Feza Gursey Cente
r Higher Structures Seminars\n\n\nAbstract\nKnotoids are immersed arcs in
surfaces\, introduced by Vladimir Turaev.\nKnotoids in the 2-sphere can be
considered as open knot diagrams with\ntwo endpoints that can lie anywher
e in S2. In this sense\, the theory of\nspherical knotoids extends the the
ory of knots in the Euclidean 3-space\,\nand the classification problem of
knots generalizes to knotoids in an\ninteresting way with the existence o
f open ends. In this talk we will\npresent multi-knotoids and an Alexander
polynomial type invariant for\nthem by utilizing a partition function inv
olving a solution of the\nYang-Baxter equation. This talk is a joint work
with Louis Kauffman.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Roberts (University of Adelaide)
DTSTART:20230131T070000Z
DTEND:20230131T080000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/16
DESCRIPTION:Title: Low-dimensional higher geometry: a case study\nby Dav
id Roberts (University of Adelaide) as part of Feza Gursey Center Higher S
tructures Seminars\n\n\nAbstract\nConsiderations from several different ar
eas of mathematics have prompted\nthe development of so- called higher geo
metry: the study of categorified\nanalogues of geometric structures. Despi
te being studied for nearly two\ndecades\, few examples that capture non-a
belian phenomena have been\nconstructed. And here by "constructed"\, we me
an to the level that would\nsatisfy traditional differential geometers\, a
s opposed to the kind of\nconstruction that category theorists are comfort
able with.\nTo this end\, I will describe a new framework to work with bun
dle\n2-gerbes\, which from a higher- category point of view are certain ty
pes\nof truncated descent data for $\\infty$-stacks on a manifold. The\nde
scription is sufficient to undertake concrete computations more\nsatisfyin
g to traditional differential geometers and mathematical\nphysicists. I al
so describe explicit geometric examples that can be\nconstructed using our
framework\, including infinite families of explicit\ngeometric string str
uctures.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University\, Bloomington)
DTSTART:20230228T140000Z
DTEND:20230228T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/17
DESCRIPTION:Title: On the classification of modular categories\nby Julia
Plavnik (Indiana University\, Bloomington) as part of Feza Gursey Center
Higher Structures Seminars\n\n\nAbstract\nModular categories are intricate
organizing algebraic structures\nappearing in a variety of mathematical s
ubjects including topological\nquantum field theory\, conformal field theo
ry\, representation theory of\nquantum groups\, von Neumann algebras\, and
vertex operator algebras. They\nare fusion categories with additional bra
iding and pivotal structures\nsatisfying a non- degeneracy condition. The
problem of classifying\nmodular categories is motivated by applications to
topological quantum\ncomputation as algebraic models for topological phas
es of matter.\n\nIn this talk\, we will start by introducing some of the b
asic definitions\nand properties of fusion\, braided\, and modular categor
ies\, and we will\nalso give some concrete examples to have a better under
standing of their\nstructures. I will give an overview of the current situ
ation of the\nclassification program for modular categories\, with a parti
cular focus\non the results for odd-dimensional modular categories\, and w
e will\nmention some open directions in this field.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Caramello (Institut des Hautes Études Scientifiques)
DTSTART:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/18
DESCRIPTION:Title: Gröthendieck toposes as unifying “bridges” in mathem
atics.\nby Olivia Caramello (Institut des Hautes Études Scientifiques
) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\n
I will explain the sense in which Gröthendieck toposes can act as unifyin
g 'bridges' for relating different mathematical theories to each other and
studying them from a multiplicity of points of view. I shall first presen
t the general techniques underpinning this theory and then discuss a numbe
r of selected applications in different mathematical fields.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics)
DTSTART:20230411T150000Z
DTEND:20230411T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/19
DESCRIPTION:Title: Higher algebraic closure\nby Theo Johnson-Freyd (Peri
meter Institute for Theoretical Physics) as part of Feza Gursey Center Hig
her Structures Seminars\n\n\nAbstract\nDeligne's work on Tannakian duality
identifies the category sVec of super vector spaces as the "algebraic clo
sure" of the category Vec of vector spaces (over C). I will describe my co
nstruction\, joint with David Reutter\, of the higher-categorical analog o
f sVec: the algebraic closure of the n-category of "n-vector spaces". The
construction mixes ideas from Galois theory\, quantum physics\, homotopy t
heory\, and fusion category theory. Time permitting\, I will describe the
higher-categorical\nGalois group\, which turns out to have a surgery-theor
etic description through which it is almost\, but not quite\, the group PL
.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Scheimbauer (Technische Universität München)
DTSTART:20230509T150000Z
DTEND:20230509T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/20
DESCRIPTION:Title: A universal property of the higher category of spans and
finite Gauge theory as an extended TFT\nby Claudia Scheimbauer (Techni
sche Universität München) as part of Feza Gursey Center Higher Structure
s Seminars\n\n\nAbstract\nI will explain how to generalize Harpaz’ unive
rsal property of the $(\\infty\,1)$-category of spans to the higher catego
ry thereof. The crucial property is “m-semiadditivity”\, which general
izes usual semiadditivity of categories. Combining this with the finite pa
th integral construction of Freed- Hopkins-Lurie-Teleman this yields finit
e gauge theory as a fully extended TFT. This is joint work in progress wit
h Tashi Walde.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (İstanbul Technical University)
DTSTART:20230523T140000Z
DTEND:20230523T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/21
DESCRIPTION:Title: Dold-Kan equivalence and its extensions\nby Atabey Ka
ygun (İstanbul Technical University) as part of Feza Gursey Center Higher
Structures Seminars\n\n\nAbstract\nThe Dold-Kan Correspondence is an equi
valence between the category of differential graded objects and the catego
ry of simplicial objects on an abelian category. This equivalence is best
understood within the context of Quillen model categories. However\, a mor
e straightforward interpretation using the representation theory of small
categories is possible. We will demonstrate that the Dold-Kan equivalence
can be expressed through specific induction and restriction functors\, pav
ing the way for similar equivalences for crossed-simplicial objects. There
are extensions to the Dold-Kan Correspondence in this context\, with the
Dwyer-Kan equivalence between the category of duplicial objects and the ca
tegory of cyclic objects over an abelian category being a notable example.
We will also show that the Dwyer-Kan equivalence can be incorporated into
the framework we initially developed for the Dold-Kan Correspondence. Las
tly\, we will discuss further extensions.\n\nThis research is a joint work
with my PhD student\, Haydar Can Kaya.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20230328T140000Z
DTEND:20230328T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/23
DESCRIPTION:Title: A simplicial category for higher correspondences\nby
Redi Haderi (Bilkent University) as part of Feza Gursey Center Higher Stru
ctures Seminars\n\n\nAbstract\nCorrespondences between simplicial sets (an
d oo-categories) are a generalization of the notion of profunctor between
categories. It is known that functors between categories are classified by
lax\ndiagram of profunctors. We will present this fact from the lens of d
ouble category theory.\nThen\, we will show how simplicial sets\, simplici
al maps and correspondences are organized in a simplicial category (this i
s a weak simplicial object in categories). A simplicial category may\nbe r
egarded as a 2-fold version of a simplicially enriched category\, and henc
e some ideas from double category theory apply. In particular we formulate
the fact that simplicial maps are classified by diagrams of correspondenc
es. As a corollary\, we obtain a formulation of Lurie's prediction that in
ner fibrations are classified by diagrams of correspondences between oo-ca
tegories.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuf Barış Kartal (University of Edinburgh)
DTSTART:20230221T140000Z
DTEND:20230221T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/24
DESCRIPTION:Title: Frobenius operators in symplectic topology\nby Yusuf
Barış Kartal (University of Edinburgh) as part of Feza Gursey Center Hig
her Structures Seminars\n\n\nAbstract\nOne can define the Frobenius operat
or on a commutative ring of characteristic p as the p th power operation\,
and this has generalizations to a larger class of commutative rings\, and
even to topological spaces and spectra. Spectra with circle actions and F
robenius operators are called cyclotomic spectra. The simplest example is
the free loop space\, and important examples arise in algebraic and arithm
etic geometry as topological Hochschild homology of rings and categories.
By topological reasons and mirror symmetry\, it is natural to expect such
a structure to arise in symplectic topology-- more precisely in ``closed s
tring Floer theory''. In this talk\, we will explain how to construct such
spectra using Hamiltonian Floer theory\, i.e. by using holomorphic cylind
ers in symplectic manifolds. Joint work in progress with Laurent Cote.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erdal Ulualan (Kütahya Dumlupınar Üniversitesi)
DTSTART:20230425T133000Z
DTEND:20230425T143000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/26
DESCRIPTION:Title: Simplisel gruplardan yüksek boyutlu cebirsel modellere
funktorlar\nby Erdal Ulualan (Kütahya Dumlupınar Üniversitesi) as p
art of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nBu ç
alışmada bir simplisel grubun Moore kompleksinde tanımlı olan hiper c
̧aprazlanmış kompleks çiftleri kullanılarak parçalanmış simpli
sel gruplar ile cebirsel modeller arasındaki ilişkiler verilecektir. 1-
parçalanmış simplisel grubun bir çaprazlanmış modülü nasıl
modellediği ve 1- parçalanmış bisimplisel grubun bir çaprazlanmı
ş kareyi nasıl modellediği gösterilecektir. Sonuç olarak\, bu ili
şkileri genelleştirerek 1-parçalanmış n-boyutlu multisimplisel gr
ubun bir çaprazlanmış n-küpü nasıl modellediğini göstereceg
̆iz.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lakshya Bhardwaj (University of Oxford)
DTSTART:20230926T120000Z
DTEND:20230926T130000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/27
DESCRIPTION:Title: TQFTs and Gapped Phases with Non-Invertible Symmetries\nby Lakshya Bhardwaj (University of Oxford) as part of Feza Gursey Cente
r Higher Structures Seminars\n\n\nAbstract\nI will discuss classification
of topological quantum field theories (TQFTs) with non-invertible generali
zed/categorical symmetries. From a condensed matter point of view\, this i
s related to the classification of gapped phases of systems with non-inver
tible symmetries. Although the general formalism will be applicable to any
spacetime dimension\, I will provide concrete details in spacetime dimens
ion $d=2$. As main examples\, I will describe the only $(1+1)d$ gapped pha
se with Ising symmetry which carries 3 vacua along with relative Euler ter
ms\, and four possible $(1+1)d$ gapped phases with $Rep(S_3)$ symmetry. Al
ong the way\, I will also discuss the order parameters for such gapped pha
ses\, which carry generalized charges under non-invertible symmetries.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Rumynin (University of Warwick)
DTSTART:20231010T150000Z
DTEND:20231010T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/28
DESCRIPTION:Title: C_2-Graded groups\, their Real representations and Dyson'
s tenfold way\nby Dmitriy Rumynin (University of Warwick) as part of F
eza Gursey Center Higher Structures Seminars\n\n\nAbstract\nA $C_2$-graded
group is a pair: a group $G$ and its index two subgroup $H$.\nIts Real re
presentation is a complex representation of $H$ with an action of the othe
r coset $G\\H$ of odd elements in another way that needs to be chosen. Dif
ferent choices lead to different theories.\nSuch representations appeared
independently in three different disciplines: Algebra\, Physics and Topolo
gy.\n\nThe goal of the talk is to review the formalism and various choices
\, including resulting theories.\nThe talk is based on my recent works wit
h James Taylor (Oxford) and Matthew B. Young (Utah State).\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Street (Macquarie University)
DTSTART:20231024T090000Z
DTEND:20231024T100000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/29
DESCRIPTION:Title: Could representations of your category be those of a grou
poid?\nby Ross Street (Macquarie University) as part of Feza Gursey Ce
nter Higher Structures Seminars\n\n\nAbstract\nBy a representation of a ca
tegory ℱ here is meant a functor from ℱ to a category V of modules ove
r a commutative ring R. The question is whether there is a groupoid G whos
e category [G\,V] of representations is equivalent to the category [ℱ\,V
] of representations of the given category ℱ. That is to say\, is there
a groupoid G such that the free V - category RG on G is Morita V - equival
ent to the free V - category Rℱ on ℱ? The groupoid G could be the core
groupoid ℱinv of ℱ\; that is\, the subcategory of ℱ with the same o
bjects but with only the invertible morphisms. Motivating examples come fr
om Dold-Kan-type theorems and a theorem of Nicholas Kuhn [see “Generic r
epresentation theory of finite fields in nondescribing characteristic”\,
Advances in Math 272 (2015) 598–610]. The plan is to describe structure
on ℱ which leads to such a result\, and includes these and other exampl
es.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Gurski (Case Western Reserve University)
DTSTART:20231107T120000Z
DTEND:20231107T130000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/30
DESCRIPTION:Title: Computing with symmetric monoidal functors\nby Nick G
urski (Case Western Reserve University) as part of Feza Gursey Center High
er Structures Seminars\n\n\nAbstract\nCoherence theorems\, while often tec
hnically complicated\, serve a simple role: to make computations easier on
the user. Abstract forms of coherence theorems often take one of two form
s\, either a strictification form or a diagrammatic form. The general\, ab
stract kinds of coherence theorems that would apply to symmetric or braide
d monoidal functors are of the strictification variety\, but in practice t
he diagrammatic versions are often what one might need. I will present a g
eneral form of\na diagrammatic coherence theorem applicable to monoidal fu
nctors (of any variety) or any other structure governed by a reasonably ni
ce 2-monad. This is joint work with Niles Johnson.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Donovan (Yau Mathematical Sciences Center\, Tsinghua Unive
rsity)
DTSTART:20231128T110000Z
DTEND:20231128T120000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/31
DESCRIPTION:Title: Homological comparison of resolution and smoothing\nb
y William Donovan (Yau Mathematical Sciences Center\, Tsinghua University)
as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nA
singular space often comes equipped with (1) a resolution\, given by a mo
rphism from a smooth space\, and (2) a smoothing\, namely a deformation wi
th smooth generic fibre. I will discuss work in progress on how these may
be related homologically.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Institut de Mathématiques de Jussieu – Paris Ri
ve Gauche)
DTSTART:20231205T150000Z
DTEND:20231205T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/32
DESCRIPTION:Title: Complexes of stable infinity-categories\nby Merlin Ch
rist (Institut de Mathématiques de Jussieu – Paris Rive Gauche) as par
t of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nA comple
x of stable infinity-categories is a categorification of a chain complex\,
meaning a sequence of stable infinity-categories together with a differen
tial that squares to the zero functor. We refer to such categorified compl
exes as categorical complexes. We give a categorification of the totalizat
ion construction\, which associates a categorical complex with a categoric
al multi-complex. Special cases include the totalizations of commutative s
quares or higher cubes of stable infinity categories. This can be used to
construct interesting examples of categorical complexes\, for instance com
ing from normal crossing divisors.\nThe study of categorical complexes can
be seen as part of the conjectural/emerging subject of categorified homol
ogical algebra. We will also indicate a partial formalisation of this\, ba
sed on the notion of a lax additive (infinity\,2)-category\, categorifying
the notion of an additive 1-category.\nThis talk is based on joint work w
ith T. Dyckerhoff and T. Walde\, see https://arxiv.org/abs/2301.02606.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Félix Loubaton (MPIM\, Bonn)
DTSTART:20231219T150000Z
DTEND:20231219T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/33
DESCRIPTION:Title: Lax univalence for $(\\infty\,\\omega)$-categories\nb
y Félix Loubaton (MPIM\, Bonn) as part of Feza Gursey Center Higher Struc
tures Seminars\n\n\nAbstract\nThe classical Grothendieck construction esta
blishes an isomorphism between the (pseudo)functor $F:C\\to Cat$ and the l
eft Cartesian fibration $E\\to C$. We can then show that $E$ is the lax co
limit of the\nfunctor $F$.\n\nThis presentation is dedicated to the genera
lization of this result for $(\\infty\,\\omega)$-categories. After definin
g $(\\infty\,\\omega)$-categories\, we will state the lax univalence for $
(\\infty\,\\omega)$- categories. We'll then explain how this result allows
us to express a strong link between Grothendieck construction for $(\\inf
ty\,\\omega)$-categories and the lax-colimits of $(\\infty\,\\omega)$-cate
gories\, similar to the classical case.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent Üniversitesi)
DTSTART:20240116T150000Z
DTEND:20240116T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/35
DESCRIPTION:Title: Shifted contact structures on derived stacks\nby Kadr
i İlker Berktav (Bilkent Üniversitesi) as part of Feza Gursey Center Hig
her Structures Seminars\n\n\nAbstract\nIn this talk\, we outline our progr
am for the development of shifted contact structures in the context of der
ived algebraic geometry. We start by recalling some key notions and result
s from derived algebraic/symplectic geometry. Next\, we discuss shifted co
ntact structures on derived Artin stacks and report our results regarding
their local theory\, together with some future directions.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Baas (Norwegian University of Science and Technology)
DTSTART:20240213T150000Z
DTEND:20240213T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/37
DESCRIPTION:Title: Beyond Categories\nby Nils Baas (Norwegian University
of Science and Technology) as part of Feza Gursey Center Higher Structure
s Seminars\n\n\nAbstract\nMy talk will be philosophical. I will motivate t
he need to go beyond higher categories in order to get a good framework fo
r many types of higher structures. This leads me to the notion of hyperstr
uctures which I will motivate and explain. Initially this is a very genera
l concept in order to cover both mathematical and applied aspects which I
will explain. I will also relate to extended Field Theories.\n\nMeeting ID
: 828 0129 1723\nPasscode: 530129\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meng-Chwan Tan (National University of Singapore)
DTSTART:20240227T090000Z
DTEND:20240227T100000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/38
DESCRIPTION:Title: Vafa-Witten Theory: Invariants\, Floer Homologies\, Higgs
Bundles\, a Geometric Langlands Correspondence\, and Categorification
\nby Meng-Chwan Tan (National University of Singapore) as part of Feza Gur
sey Center Higher Structures Seminars\n\n\nAbstract\nWe revisit Vafa-Witte
n theory in the more general setting whereby the underlying moduli space i
s not that of instantons\, but of the full Vafa-Witten equations. We physi
cally derive (i) a novel Vafa-Witten four-manifold invariant associated wi
th this moduli space\, (ii) their relation to Gromov-Witten invariants\, (
iii) a novel Vafa-Witten Floer homology assigned to three-manifold boundar
ies\, (iv) a novel Vafa-Witten Atiyah-Floer correspondence\, (v) a proof a
nd generalization of a conjecture by Abouzaid-Manolescu in [1] about the h
ypercohomology of a perverse sheaf of vanishing cycles\, (vi) a Langlands
duality of these invariants\, Floer homologies and hypercohomology\, and (
vii) a quantum geometric Langlands correspondence with purely imaginary pa
rameter that specializes to the classical correspondence in the zero-coupl
ing limit\, where Higgs bundles feature in (ii)\, (iv)\, (vi) and (vii). W
e also explain how these invariants and homologies will be categorified in
the process\, and discuss their higher categorification. In essence\, we
will relate differential and enumerative geometry\, topology and geometric
representation theory in mathematics\, via a maximally-supersymmetric top
ological quantum field theory with electric-magnetic duality in physics.\n
\nMeeting ID: 892 5026 2628\nPasscode: 521946\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Dimitriadis Bermejo (Paul Sabatier University)
DTSTART:20240312T150000Z
DTEND:20240312T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/39
DESCRIPTION:Title: A new model for dg-categories\nby Elena Dimitriadis B
ermejo (Paul Sabatier University) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nDg-categories have been very important in
Algebraic Geometry for a really long time\; but they are not without their
issues. In order to solve these\, current researchers have been turning t
o different models of infinity-categories for inspiration. Enriched infini
ty categories\, dg-Segal categories\, enriched quasi-categories... Followi
ng this flourishing field\, in this talk we will define a new model for dg
-categories inspired in Rezk's complete Segal spaces model for infinity-ca
tegories.\n\nDuring this talk we will define dg-Segal spaces\, give its re
lationship to classical Segal spaces\, use this to define complete dg-Sega
l spaces and its model structure and give a sketch of the proof of its equ
ivalence to Tabuada's model structure of dg-categories. If time allows\, w
e will say a word about some possible refinements of the model\, and menti
on some work in progress surrounding its relationship to Mertens and Borge
s Marques' model of dg-Segal spaces.\n\nMeeting ID: 817 3634 5226\nPasscod
e: 458243\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240326T150000Z
DTEND:20240326T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/40
DESCRIPTION:Title: Commutative and Frobenius algebras in span categories
\nby Walker Stern (Bilkent University) as part of Feza Gursey Center Highe
r Structures Seminars\n\n\nAbstract\nIn this talk\, I will discuss the rel
ation of span categories to various versions of the symplectic category. I
will then expose the connection between simplicial objects and algebras i
n span categories\, focusing on the 1- and 2-categorical cases to explicat
e the underlying intuitions. Finally\, I will discuss recent work (joint w
ith Ivan Contreras and Rajan Mehta) generalizing this correspondence to al
gebras with further structure\, that is\, to commutative and Frobenius alg
ebras.\n\nMeeting ID: 865 0047 9193\nPasscode: 850569\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Huerta (Instituto Superior Técnico)
DTSTART:20240409T150000Z
DTEND:20240409T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/41
DESCRIPTION:Title: Poincaré duality for families of supermanifolds\nby
John Huerta (Instituto Superior Técnico) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nIt is well known to experts\, but
seldom discussed explicitly\, that smooth supergeometry is best done in fa
milies. This is also called the relative setting\, and it implies that we
need relative versions of standard supergeometric constructions. Such cons
tructions include the de Rham complex familiar from ordinary differential
geometry\, but in the supergeometric setting\, they also include more exot
ic objects\, such as the Berezinian line bundle (whose sections are the co
rrect objects to integrate over supermanifolds) and the related complex of
integral forms\, where the super version of Stokes' theorem lives. To wor
k in families\, we introduce relative versions of the de Rham complex and
the integral form complex\, and we prove that they satisfy a relative vers
ion of Poincaré duality. No background in supergeometry will be assumed f
or this talk.\n\nThis is joint work with Konstantin Eder and Simone Noja.\
n\nMeeting ID: 859 9026 1915\nPasscode: 578799\n\n--\nSeminar time has bee
n updated.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tubbenhauer (University of Sydney)
DTSTART:20240507T080000Z
DTEND:20240507T090000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/42
DESCRIPTION:Title: Counting in tensor products\nby Daniel Tubbenhauer (U
niversity of Sydney) as part of Feza Gursey Center Higher Structures Semin
ars\n\n\nAbstract\nThis talk is an introduction to analytic methods in ten
sor categories with the focus on quantifying the number of summands in ten
sor products of representations and related structures. Along the way\, we
'll throw in plenty of examples to keep things interesting!\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shulman (University of California – San Diego)
DTSTART:20240521T170000Z
DTEND:20240521T180000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/43
DESCRIPTION:Title: Higher Observational type theory\nby Michael Shulman
(University of California – San Diego) as part of Feza Gursey Center Hig
her Structures Seminars\n\n\nAbstract\nHomotopy Type Theory is a new appro
ach to the foundations of mathematics\, in which the basic objects of math
ematics are not sets but homotopy types. It is natively isomorphism-invari
ant and well-adapted to computer formalization\, and can be interpreted in
higher toposes to give a synthetic language for internal constructions an
d proofs. It can also be explained intuitively to students\, giving them a
ccess to higher structures while avoiding the complicated machinery of com
binatorial homotopy theory\; and it can be used as a programming language\
, to compute certain invariants of higher structures by simply running cod
e derived from their definitions. However\, until recently it was not know
n how to achieve both of these latter two properties simultaneously with a
single formal system. In this talk I will introduce Homotopy Type Theory
and its applications to higher structures from perspective of Higher Obser
vational Type Theory\; this is a new formal system for Homotopy Type Theor
y that\, we hope\, is both intuitively natural and computationally adequat
e. This is joint work in progress with Thorsten Altenkirch and Ambrus Kapo
si.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgün Ünlü (Bilkent University)
DTSTART:20240604T150000Z
DTEND:20240604T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/44
DESCRIPTION:Title: Infinity operads as simplicial lists\nby Özgün Ünl
ü (Bilkent University) as part of Feza Gursey Center Higher Structures Se
minars\n\n\nAbstract\nIn this talk\, we will present a model for infinity
operads. We will start by discussing how the category of colored nonsymmet
ric operads can be embedded in a category which we call the category of si
mplicial lists. Within this category\, our model for infinity operads will
generalize colored nonsymmetric operads in the same way that quasicategor
ies generalize ordinary categories when embedded in the category of simpli
cial sets. Therefore\, it is natural to refer to these infinity operads as
quasioperads. Next\, we will discuss a homotopy coherent nerve functor fr
om the category of simplicial operads to the category of simplicial lists\
, which sends Kan complex enriched operads to quasioperads\, analogous to
the homotopy coherent nerve functor from the category of simplicial catego
ries to the category of simplicial sets. Finally\, we will discuss the hom
ology of simplicial lists\, and hence quasioperads\, and perform some homo
logy computations.\nThis is joint work with Redi Haderi.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Caviglia (University of Leichester)
DTSTART:20240423T150000Z
DTEND:20240423T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/45
DESCRIPTION:Title: 2-stacks and quotient 2-stacks\nby Elena Caviglia (Un
iversity of Leichester) as part of Feza Gursey Center Higher Structures Se
minars\n\n\nAbstract\nStacks generalize one dimension higher the fundament
al concept of sheaf. They are pseudofunctors that are able to glue togethe
r weakly compatible local data into global data. Stacks are a very importa
nt concept in geometry\, due to their ability to take into account automor
phisms of objects. While many classification problems do not have a moduli
space as solution because of the presence of automorphisms\, it is often
nonetheless possible to construct a moduli stack. In recent years\, the re
search community has begun generalizing the notion of stack one dimension
higher. Lurie studied a notion of (∞\, 1)-stack\, that yields a notion o
f (2\, 1)- stack for a trihomomorphism that takes values in (2\, 1)-catego
ries\, when truncated to dimension 3. And Campbell introduced a notion of
2-stack that involves a trihomomorphism from a one-dimensional category in
to the tricategory of bicategories. In this talk\, we will introduce a not
ion of 2-stack that is suitable for a trihomomorphism from a 2-category en
dowed with a bitopology into the tricategory of bicategories. The notion o
f bitopology that we consider is the one introduced by Street for bicatego
ries. We achieve our definition of 2-stack by generalizing a characterizat
ion of stack due to Street. Since our definition of 2-stack is quite abstr
act\, we will also present a useful characterization in terms of explicit
gluing conditions that can be checked more easily in practice. These expli
cit conditions generalize to one dimension higher the usual stacky gluing
conditions. A key idea behind our characterization is to use the tricatego
rical Yoneda Lemma to translate the biequivalences required by the definit
ion of 2-stack into effectiveness conditions of appropriate data of descen
t. As a biequivalence is equivalently a pseudofunctor which is surjective
on equivalence classes of objects\, essentially surjective on morphisms an
d fully faithful on 2-cells\, we obtain effectiveness conditions for data
of descent on objects\, morphisms and 2-cells. It would have been hard to
give the definition of 2-stack in these explicit terms from the beginning\
, as we would not have known the correct coherences to ask in the various
gluing conditions. Our natural implicit definition is instead able to guid
e us in finding the right coherence conditions. Finally\, we will present
the motivating example for our notion of 2-stack\, which is the one of quo
tient 2-stack. After having generalized principal bundles and quotient sta
cks to the categorical context of sites\, we aimed at a generalization of
our theory one dimension higher\, to the context of bisites\, motivated by
promising applications of principal 2- bundles to higher gauge theory. Bu
t there was no notion of higher dimensional stack suitable for the produce
d analogues of quotient prestacks in the two-categorical context. Our noti
on of 2-stack is able to fill this gap. Indeed\, we have proven that\, if
the bisite satisfies some mild conditions\, our analogues of quotient stac
ks one dimension higher are 2-stacks.\n\nMeeting ID: 832 8539 1847\nPassco
de: 167146\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doğancan Karabaş (Kavli Institute for the Physics and Mathematic
s of the Universe - University of Tokyo)
DTSTART:20241001T120000Z
DTEND:20241001T130000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/46
DESCRIPTION:Title: A computational approach to the homotopy theory of dg-cat
egories\nby Doğancan Karabaş (Kavli Institute for the Physics and Ma
thematics of the Universe - University of Tokyo) as part of Feza Gursey Ce
nter Higher Structures Seminars\n\n\nAbstract\nThe homotopy theory of diff
erential graded (dg) categories plays a significant role in\nvarious field
s\, including algebraic geometry\, representation theory\, higher categori
es\, and\nsymplectic geometry. In particular\, understanding dg-categories
is crucial for formulating and\ninterpreting homological mirror symmetry.
\nIn this talk\, I will present our approach to the homotopy theory of dg-
categories by establishing a\ncofibration structure\, which can be viewed
as a half-model structure. This structure enables a\ncombinatorial descrip
tion of derived constructions and offers computational advantages. This is
\njoint work with Sangjin Lee (arXiv:2109.03411 and arXiv:2405.03258). Som
e key applications of\nour approach\, particularly in symplectic and conta
ct geometry\, include:\n\n$\\bullet$ Combinatorial description of homotopy
colimits of dg categories\, which gives a local-to-\nglobal formula compu
ting wrapped Fukaya categories of symplectic manifolds\,\n\n$\\bullet$ Loc
al-to-global construction of functors between wrapped Fukaya categories th
at are\ninduced by symplectomorphisms\,\n\n$\\bullet$ A simple description
of internal Hom and Hochschild cohomology of dg-categories. This\nongoing
work aims to provide useful tools for addressing the Weinstein conjecture
\, which\nconcerns the existence of periodic orbits of Reeb vector fields.
\n\nI plan to cover as much of this content as time permits\, and accordin
g to the audience's interest.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent University)
DTSTART:20241015T150000Z
DTEND:20241015T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/47
DESCRIPTION:Title: Constructions of contact derived stacks\nby Kadri İl
ker Berktav (Bilkent University) as part of Feza Gursey Center Higher Stru
ctures Seminars\n\n\nAbstract\nThis talk presents several examples of deri
ved Artin stacks with shifted contact\nstructures. We start by reviewing d
erived symplectic/contact geometry. Next\, we outline our\nconstructions:
the first one extends classical 1-jet bundles\, and the second set of cons
tructions arises from shifted geometric quantization.\n\nMeeting ID: 867 4
914 7487\nPassword: 038987\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ayala (Montana State University)
DTSTART:20241112T130000Z
DTEND:20241112T140000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/48
DESCRIPTION:Title: Factorization homology of higher categories\nby David
Ayala (Montana State University) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nThe "alpha" version of factorization homol
ogy pairs (framed) n-manifolds with En-algebras. This construction genera
lizes classical homology of a manifold\, yields novel results concerning c
onfiguration spaces of points in a manifold\, and supplies a sort of state
-sum model for sigma-models (ie\, mapping spaces) to\n(n−1)-connected ta
rgets. This "alpha" version of factorization homology novelly extends Poi
ncaré duality\, shedding light on deformation theory and dualities among
field theories. Being defined using homotopical mathematical foundations
\, "alpha" factorization homology is manifestly functorial and continuous
in all arguments\, notably in moduli of manifolds and embeddings between t
hem\, and it satisfies a local-to-global expression that is inherently hom
otopical in nature. \nNow\, En-algebras can be characterized as (∞\,n)-
categories equipped with an (n−1)-connected functor from a point. The (
full) "beta" version of factorization homology pairs (framed) n-manifolds
with pointed (∞\,n)-categories (with adjoints). Applying 0th homology\,
or π0\, recovers a version of the String Net construction of surfaces\,
as well as of Skein modules of 3-manifolds. In some sense\, the inherentl
y homotopical nature of (full) "beta" factorization homology affords other
wise unforeseen continuity in all arguments\, and local-to-global expressi
ons. \nIn this talk\, I will outline a definition of "beta" factorization
homology\, focusing on low-dimensions and on suitably\nreduced (∞\,n)-c
ategories (specifically\, braided monoidal categories). I will outline so
me examples\, and demonstrate some operational practice of factorization h
omology. Some of this material is established in literature\, some a work
in progress\, and some conjectural — the status of each assertion will
be made clear. I will be especially interested in targeting this talk wot
those present\, and so will welcome comments and questions. \nAll of thi
s work is joint with John Francis.\n\nNote the unusual time: at 16:00 Ista
nbul time!\nMeeting ID: 815 1508 2956\nPasscode: 613918\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan (Koç University)
DTSTART:20241128T140000Z
DTEND:20241128T150000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/49
DESCRIPTION:Title: Some applications of toposes of measure-theoretic sheaves
\nby Asgar Jamneshan (Koç University) as part of Feza Gursey Center H
igher Structures Seminars\n\n\nAbstract\nWe construct toposes of sheaves o
n measure spaces and highlight the usefulness of interpreting certain stru
ctures from classical measure theory and functional analysis\, combined wi
th a Boolean internal logic\, in applications to ergodic structure theory
and vector duality.\n\nPlease note the unusual day.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranav Pandit (ICTS-TIFR)
DTSTART:20241210T120000Z
DTEND:20241210T130000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/50
DESCRIPTION:Title: Towards Categorical Kähler Geometry\nby Pranav Pandi
t (ICTS-TIFR) as part of Feza Gursey Center Higher Structures Seminars\n\n
\nAbstract\nThe Donaldson-Uhlenbeck-Yau theorem describes a deep relations
hip between holomorphic vector bundles on Kähler manifolds and solutions
to certain partial differential equations. I will report on progress\ntowa
rds formulating and proving an analogue of this theorem in categorical non
commutative geometry. This talk is based on joint work with Fabian Haiden\
, Ludmil Katzarkov\, and Maxim Kontsevich.\n\nMeeting ID: 847 8067 3908 Pa
sscode: 328020\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keremcan Doğan (Gebze Technical University)
DTSTART:20241224T150000Z
DTEND:20241224T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/51
DESCRIPTION:Title: Proto Bialgebroids for Exceptional Geometries\nby Ker
emcan Doğan (Gebze Technical University) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nRecent advancements in the mathema
tics of dualities seem to be in favor of certain generalizations of differ
ential geometric structures on algebroids. The success of the generalized
geometry program for T-duality motivates the construction of analogous exc
eptional geometries suitable for U-duality. In particular the Drinfeld dou
ble structure for Lie bialgebroids is a crucial concept for T-duality. In
this talk\, we will introduce the notion of bialgebroid extending these id
eas in the realm of U-duality. We will present a calculus framework on alg
ebroids\; both twistless and twistful cases. In order to focus on exceptio
nal geometries\, we extend T-duality notions in a more general class of al
gebroids\, where the setting allows us to work with non-dual vector bundle
s of arbitrary rank. We will conclude the talk with a specific constructio
n crucial for exceptional Drinfeld algebras in the context of higher Coura
nt algebroids and Nambu-Poisson structure.\n\nMeeting ID: 836 5961 7974 Pa
sscode: 694072\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simona Paoli (University Of Aberdeen)
DTSTART:20250121T150000Z
DTEND:20250121T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/52
DESCRIPTION:Title: The weakly globular approach to higher categories\nby
Simona Paoli (University Of Aberdeen) as part of Feza Gursey Center Highe
r Structures Seminars\n\n\nAbstract\nHigher categories are motivated by na
turally occurring examples in diverse areas of mathematics\, including hom
otopy theory\, mathematical physics\, logic and computer sciences. Several
different approaches exist to formalize the notion of a higher category.
In this talk I will give an overview of an approach to model 'truncated' h
igher categories: namely those having higher morphisms in dimensions 0 up
to n only. These arise naturally in homotopy theory\, in modelling the bui
lding blocks of topological spaces\, called n-types.\n\nClassically\, in a
higher category we have sets of objects and sets of higher morphisms. Thi
s is also called 'globularity condition' as it is the condition that gives
rise to the globular shape of the higher morphisms in a higher category.
Instead\, in the so called weakly globular approach I have introduced\, th
e objects and the higher morphism do not form a set but a structure only e
quivalent (in a higher dimensional sense) to a set. We call this 'weak glo
bularity condition'.\n\nOne advantage of this approach is that it is possi
ble to model a weak n-category using a rather rigid structure\, namely an
n-fold category satisfying additional conditions. These are the weakly glo
bular n-fold categories. I will mention some applications of these structu
res to homological algebra\, as well as a link between weak globularity an
d the notion of weak units in the case n=2. I will conclude with some conj
ectures for general dimension n.\n\nGiven the highly technical nature of t
his work\, and in the interest of making the talk broadly accessible\, I w
ill concentrate on the main ideas and intuitions\, but more details can be
found in the references below:\n\nAbout weakly globular n-fold categories
:\n\n· S. Paoli\, Simplicial Methods for Higher Categories: Segal-t
ype Models of Weak n-Categories\, Algebra and Applications 26\, Springer (
2019).\n\n· S. Paoli\, D. Pronk\, A double categorical model of wea
k 2-categories\, _Theory and Application of categories_\, 28\, (2013)\, 93
3-980.\n\nAbout weak globularity and weak units:\n\n· S. Paoli\, We
akly globular double categories and weak units\, arXiv:2008.11180 (2024).\
n\nAn application of weakly globular n-fold categories to homological alge
bra:\n\n· D. Blanc\, S. Paoli\, A model for the Andre-Quillen cohom
ology of an (\\infty\,1)-category\, arXiv:2405.12674 (2024).\n\nMeeting ID
: 830 1320 7597\nPasscode: 389958\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe University)
DTSTART:20250107T150000Z
DTEND:20250107T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/53
DESCRIPTION:Title: Fibration category structures on monoidal and enriched ca
tegories\nby Mehmet Akif Erdal (Yeditepe University) as part of Feza G
ursey Center Higher Structures Seminars\n\n\nAbstract\nWe first discuss Br
own's category of fibrant objects structures on closed monoidal categories
by means of some specific arrows called pseudo-cofibrations. These arrows
are the ones whose pullback-power with (acyclic) fibrations are also (acy
clic) fibrations\; which can be defined whenever the underlying category i
s closed monoidal or enriched over a category of fibrant objects. Later we
discuss the category of fibrant objects structures on enriched categories
. If V is a closed monoidal category with a category of fibrant object str
ucture on it and C is enriched over V and powered over a colimit dense sub
category of V\, then under mild conditions C can also be made into a categ
ory of fibrant objects. We discuss constructions and properties of these s
tructures and their extension to the equivariant setting. Lastly\, we give
some already existing and some new examples of such categories of fibrant
objects and mention some applications.\n\nMeeting ID: 843 5555 9891\nPass
code: 084032\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Orendain (Case Western Reserve University)
DTSTART:20250306T150000Z
DTEND:20250306T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/54
DESCRIPTION:Title: Compact closed Gray monoids\nby Juan Orendain (Case W
estern Reserve University) as part of Feza Gursey Center Higher Structures
Seminars\n\n\nAbstract\nClosed and compact closed bicategories arise natu
rally in the context of topological quantum field theory\, where pseudofun
ctors between a compact closed bicategory of cobordisms with corners and t
he compact closed bicategory of dualizable locally presentable linear cate
gories are one way of defining once-extended TQFTs\, and where certain com
pact closed bicategories have been proposed as appropriate initial data fo
r four dimensional state-sum constructions.
\n\nIn this talk\, I will present an exposition of the stri
ctest reasonable version of a bicategorical analogue of compact closed cat
egories\, namely compact closed Gray monoids. Reasonable here means that t
here is a strictification theorem from the general setting of monoidal bic
ategories with dual objects to our compact closed Gray monoids.\n\nI will
introduce a pictorial calculus for categories enriched over Gray monoids\,
and I use this to show that transformations enriched over a closed or com
pact closed monoid\, between certain enriched functors can be reformulate
d in an adjoint fashion. This reformulation has the virtue of behaving com
putationally like corresponding unenriched 1-categorical notions. Moreover
\, I will provide coherence theorems allowing the strictification of close
d (resp. compact closed) bicategories to closed permutative Gray monoids.
Finally\, I will provide examples\, and a detailed exposition of one versi
on of the expected compact closed structure on the bicategory with manifol
ds as objects\, cobordisms as 1-arrows\, and cobordisms of cobordisms as 2
-arrows\, which occurs in the theory of once-extended TQFTs. This is joint
work with Nick Gurski and David Yetter.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov (Moscow Institute of Physics & Technology)
DTSTART:20250318T150000Z
DTEND:20250318T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/55
DESCRIPTION:Title: 10 years of Gkn: towards invariants of knots and links\nby Vassily O. Manturov (Moscow Institute of Physics & Technology) as pa
rt of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nIt has
been 10 years since the author introduced groups Gkn depending on two natu
ral numbers n>k and constructed invariants of many configuration spaces va
lued in such groups. https://www.arxiv.org/abs/1501.05208 . The first two
natural invariants dealt with braids on n strands\, n>3\, valued in G3n an
d G4n. We shall discuss how to construct similar invariants for n-componen
t links and describe various possible ways what to do with knots (single c
omponent). The approach uses closed braids and Markov moves. Many unsolve
d problems will be formulated.\n\nZoom details have been changed\, please
find the new ID and Password below:\nMeeting ID: 935 6390 4955 \nPasscode:
699568\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Raptis (Aristotle University of Thessaloniki)
DTSTART:20250401T150000Z
DTEND:20250401T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/56
DESCRIPTION:Title: From derivators and ∞-categories to ∞-derivators\
nby George Raptis (Aristotle University of Thessaloniki) as part of Feza G
ursey Center Higher Structures Seminars\n\n\nAbstract\nThe theory of deriv
ators is an approach to homotopical algebra that focuses on the idea of en
hancing the classical homotopy category ho(C) of a homotopy theory C by th
e collection of the homotopy categories of diagrams in C all at once. The
resulting objects turn out to be much richer than the homotopy category al
one and this viewpoint has been useful for expressing homotopical universa
l properties. At the same time\, this approach is different from (and less
strong than) the methods of higher category theory - which has been devel
oped and used in recent years for related purposes with great impact in va
rious areas of research. I will survey the basic theory\, applications and
examples of derivators\, and then I will discuss the general notion of an
∞-derivator\, as a natural higher categorical extension of ordinary der
ivators. This generalization is based on the use of the homotopy n-categor
y\, for 1≤n≤∞\, it bridges the gap between derivators and ∞-catego
ries\, and it provides a common framework of reference for both types of o
bjects/approaches.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Li (Tsinghua University)
DTSTART:20250415T100000Z
DTEND:20250415T110000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/57
DESCRIPTION:Title: Stochastic process and algebraic index\nby Si Li (Tsi
nghua University) as part of Feza Gursey Center Higher Structures Seminars
\n\n\nAbstract\nWe explain a stochastic approach to topological field theo
ry and present a case study of quantum mechanical model and its relation t
o non-commutative geometry and algebraic index.\n\nMeeting ID: 935 6390 49
55\nPasscode: 699568\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zimmermann (Université de Picardi)
DTSTART:20250429T150000Z
DTEND:20250429T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/58
DESCRIPTION:Title: On the ring theory of differential graded algebras\nb
y Alexander Zimmermann (Université de Picardi) as part of Feza Gursey Cen
ter Higher Structures Seminars\n\n\nAbstract\nLet R be a commutative ring.
Following Cartan (1954) a differential graded algebra (A\,d) over R is a
Z-graded R-algebra A with a homogeneous R-linear endomorphism d of degree
1 with d2=0 satisfying\n$$d(a⋅b)=d(a)⋅b+(−1)∣a∣a⋅d(b)$$\nfor a
ny homogeneous a\, b ∈ A of degree ∣a∣\, resp. ∣b∣. Similarly\,
a differential graded module is defined as a Z-graded A-module with an end
omorphism δ of degree 1 and square 0 satisfying\n$$δ(a⋅m)=d(a)⋅m+(
−1)∣a∣a⋅δ(m)$$\nfor all homogeneous a ∈ A and m ∈ M.\n\nUntil
very recently the ring theory of differential graded algebras and differe
ntial graded modules remained largely unexplored. The case of acyclic diff
erential graded algebras was completely classified by Aldrich and Garcia-R
ozas in 2002 and the case of R being a field and A being finite dimensiona
l was considered by Orlov in 2020\, basically with geometric motivations i
n mind. In a more systematic study I studied basic ring theoretical questi
ons\, such as a notion of dg-Jacobson radicals\, a dg- Nakayama lemma\, Or
e localisation of dg-algebras\, and dg-Goldie’s theorem. Most interestin
gly\, several standard properties in general ring theory do not generalise
\, but some do. We give examples\, and further classify dg-division rings
and dg-separable dg-field extensions\, and also a dg-version of the classi
cal Levitzki-Hopkins theorem on artinian respectively semiprimary algebras
.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (University of Groningen)
DTSTART:20250513T150000Z
DTEND:20250513T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/59
DESCRIPTION:Title: Zeta and K in F_1-geometry\nby Oliver Lorscheid (Univ
ersity of Groningen) as part of Feza Gursey Center Higher Structures Semin
ars\n\n\nAbstract\nIn this talk we give an overview of zeta functions and
K-theory in F_1-geometry. We begin with a short historical introduction be
fore we explain what the zeta functions of an F_1-scheme is. In the second
part on K-theory\, we begin with a reminder of Quillen's Q-construction b
efore we give an impression how it is applied to a specific approach to F_
1-geometry via monoid schemes. The talk is accessible without any preknowl
edge on F_1-geometry\, and focus lies on conveying the grand ideas.\n\nMee
ting ID: 935 6390 4955\nPasscode: 699568\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Utah State University)
DTSTART:20251002T120000Z
DTEND:20251002T130000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/60
DESCRIPTION:Title: Z invariants for Lie superalgebras\nby Matthew Young
(Utah State University) as part of Feza Gursey Center Higher Structures Se
minars\n\n\nAbstract\nZ invariants of 3-manifolds were introduced in the p
hysics literature by Gukov\, Pei\, Putrov and Vafa in the context of super
symmetric gauge theory with the goal of categorifying the Reshetikhin-Tura
ev invariants of 3-manifold. Z invariants depend on the input data of a Li
e superalgebra and some discrete geometric data on the 3-manifold\, such a
s a Spin-c structure. The goal of this talk is to explain a connection bet
ween Z invariants and 3-manifold invariants associated to non-semisimple c
ategories of representations of quantum supergroups. Based on work with Fr
ancesco Costantino\, Matthew Harper and Adam Robertson.\n\nPlease note the
unusual time and date.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (METU)
DTSTART:20251014T150000Z
DTEND:20251014T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/61
DESCRIPTION:Title: Legendrians in derived geometry\nby Kadri İlker Berk
tav (METU) as part of Feza Gursey Center Higher Structures Seminars\n\n\nA
bstract\nThis talk introduces Legendrian structures in derived contact geo
metry\,\ncovering key concepts and constructions that lead to a tubular\nn
eighborhood theorem and examples similar to the classical ones. We\nstart
by reviewing Lagrangians in derived symplectic geometry and then\nintroduc
e analogous structures in the derived contact setting using\ntechniques ad
apted from the symplectic case.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajan Mehta (Smith College)
DTSTART:20251028T150000Z
DTEND:20251028T160000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/62
DESCRIPTION:Title: Coherent 2D span-valued TQFTs\nby Rajan Mehta (Smith
College) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbs
tract\nIt is well-known that 2D TQFTs taking values in a category correspo
nd to commutative Frobenius objects in that category. If the target catego
ry is the category of spans\, it is reasonable to ask if there is a lift t
o a coherent structure (i.e. a Frobenius pseudomonoid) in the bicategory o
f spans. Such structures can be neatly described by simplicial sets\, equi
pped with some additional symmetric group actions\, and satisfying some co
nditions known as the "2-Segal conditions". I'll describe this corresponde
nce as well as a construction that produces examples from any commutative
monoid. This is joint work with Sophia Marx\, building on earlier work wit
h Ivan Contreras and Walker Stern.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Geisser (Rikkyo University)
DTSTART:20251111T080000Z
DTEND:20251111T090000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/63
DESCRIPTION:Title: Motivic cohomology theories and applications\nby Thom
as Geisser (Rikkyo University) as part of Feza Gursey Center Higher Struct
ures Seminars\n\n\nAbstract\nI will define motivic cohomology\, and give a
n overview over its\nproperties. Then I will discuss applications to arith
metic and algebraic\ngeometry\, focusing on special values of zeta-functio
ns and class field\ntheory. The talk is aimed at non-experts.\n\nPlease no
te the unusual time.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Ankara Yıldırım Beyazıt University)
DTSTART:20251125T180000Z
DTEND:20251125T190000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/64
DESCRIPTION:Title: Two models for higher operads\nby Redi Haderi (Ankara
Yıldırım Beyazıt University) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nIn this talk we will describe two models f
or the theory of infinity-operads: Lurie's model and the simplicial lists
model (developed in joint work with Özgün Ünlü). We begin by briefly i
ntroducing operads as a categorical tool to control and study a variety of
algebraic structures. As it is known that higher dimensional categorical
structures are presentation-sensitive\, different ways of thinking about o
rdinary operads lead to different formulations of a higher variant. Lurie'
s model is based on the notion of operator category\, while the simplicial
lists model is based on a nerve theorem related to the monoidal envelope
associated to an operad. Time permitting\, we will discuss how the two can
be related to each other.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Özlem (Mudanya University)
DTSTART:20260203T160000Z
DTEND:20260203T170000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/65
DESCRIPTION:Title: Weakened Axioms\, Idempotent Splittings\, and the Structu
re of Learning: From Algebra to AI\nby Semih Özlem (Mudanya Universi
ty) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract
\nWe often think of mathematics as a tower of abstractions\, but it begins
\nwith something deeply human: the act of telling things apart. In this\nt
alk\, I’ll explore how this simple idea—splitting and\nfocusing—mani
fests across different fields\, from linear algebra to\nmotives to machine
learning.\n\nWe’ll start with a basic observation: if we relax the unit
axiom in a\nvector space\, the scalar multiplication by 1 becomes an idem
potent\,\nsplitting the space into what is preserved and what is annihilat
ed. This\nsplitting phenomenon appears in surprising places: in the theory
of\nmotives\, where projectors decompose varieties\; in knot theory\, whe
re\nJones–Wenzl projectors filter diagram algebras\; and in deep learnin
g\,\nwhere attention mechanisms focus on relevant features.\n\nI’ll intr
oduce the topos-theoretic model of neural networks\n(Belfiore–Bennequin)
and suggest that learning difficulties like\ncatastrophic forgetting and
generalization gaps can be viewed as\nhomotopical obstructions to achievin
g “nice” (fibrant) network\nstates. Architectural tools like residual
connections and attention can\nthen be seen as learned\, conditional idemp
otents—adaptable splitters\nthat help networks organize information.\n\n
This talk is an invitation to think structurally across disciplines. I\nwo
n’t present finished theorems\, but a framework of connections that\nlin
ks motivic philosophy\, categorical algebra\, and the practice of\nmachine
learning. The goal is to start a conversation: can tools from\npure mathe
matics—obstruction theory\, homotopy colimits\,\nderivators—help us de
sign more robust\, interpretable\, and composable\nlearning systems?\n\nNo
expertise in motives\, knots\, or AI is required—only curiosity about\n
how ideas weave together.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dogancan Karabaş (Temple University Japan)
DTSTART:20260217T100000Z
DTEND:20260217T110000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/66
DESCRIPTION:Title: Gluing Methods for DG Categories from Geometry\nby Do
gancan Karabaş (Temple University Japan) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nMany dg categories arising in geom
etry admit local descriptions that can be assembled via homotopy-theoretic
gluing. In this talk\, I will survey a categorical framework\, developed
jointly with Sangjin Lee\, which provides a model-theoretic and combinator
ial description of such gluings\, namely homotopy colimits. This approach
leads to explicit computations of invariants in symplectic geometry and mi
crolocal sheaf theory. In particular\, I will describe our result proving
a conjecture of Kontsevich that wrapped Fukaya categories of Weinstein man
ifolds are Morita equivalent to dg algebras of finite type.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kürşat Sözer (Université de Lille)
DTSTART:20260303T160000Z
DTEND:20260303T170000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/67
DESCRIPTION:Title: Braiding self-equivalences with bordism\nby Kürşat
Sözer (Université de Lille) as part of Feza Gursey Center Higher Structu
res Seminars\n\n\nAbstract\nSpaces of homotopy self-equivalences capture s
ubtle geometric and\nhomotopy-theoretic information about manifolds\, but
are often difficult\nto analyze directly. In this talk\, I will present a
framework that\nrelates these spaces to bordism theories by organizing nor
mal bundle\ndata in a homotopy-theoretic way. For a closed smooth or topol
ogical\nmanifold M of dimension at least four\, we show that spaces of hom
otopy\nself-equivalences preserving prescribed normal information fit into
a\nhighly cartesian square involving infinite loop spaces representing\nc
ertain bordism theories. This leads to braids of interlocking exact\nseque
nces connecting homotopy groups of self-equivalence spaces with\nbordism g
roups\, providing a conceptual generalization of earlier work of\nHambleto
n–Kreck on 4-manifolds. This is joint work with Ian Hambleton\nand Robin
Sroka.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kensuke Arakawa (Kyoto University)
DTSTART:20260317T080000Z
DTEND:20260317T090000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/68
DESCRIPTION:Title: An operadic version of Mazel-Gee's localization theorem\nby Kensuke Arakawa (Kyoto University) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nA common phenomenon in higher cate
gory theory is that nontrivial\ninfinity categories often arise as localiz
ations of simpler (often\nordinary) categories. A natural question\, there
fore\, is: how can we\nrecognize when an infinity categoy is obtained in t
his way? Mazel-Gee's\nlocalization theorem provides a useful criterion for
this. In recent\nyears\, similar questions have begun to appear in the op
eradic setting\,\nmotivated by internal developements in higher operads an
d by examples\nfrom mathematical physics (such as factorization algebra an
d algebraic\nquantum field theory). This raises a basic problem: how can w
e detect\nwhen an infinity operad arises as a localization? In this talk\,
I will\npresent an operadic analog of Mazel-Gee's localization theorem\,
giving a\npractical criterion for recognizing localizations of infinity op
erads.\nAfter explaining the ideas behind the proof\, I will discuss sever
al\nexample applications to cyclic operads and factorization algebras.\n\n
Please note the unusual time.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shannon Rubin (Yau Mathematical Sciences Center - Tsinghua Univers
ity)
DTSTART:20260331T130000Z
DTEND:20260331T140000Z
DTSTAMP:20260404T111448Z
UID:FezaGurseyHigher/69
DESCRIPTION:Title: A hotomotopical invariant of Weinstein surfaces\nby S
hannon Rubin (Yau Mathematical Sciences Center - Tsinghua University) as p
art of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nIn sym
plectic geometry\, a Weinstein surface W can be understood by\ncombinatori
al data on its skeleton\, which is generically a finite\ntrivalent graph G
. Motivated by the microlocal theory of sheaves\, there\nis a naturally as
sociated diagram D of differential-graded categories\,\ndefined over the q
uiver which replaces each edge of G by a cospan. We\ncall such quivers 'gr
aphic'. After adding in appropriate homological\nshifts\, the homotopy lim
it of D yields an invariant of W\, so we are\nmotivated to find explicit p
resentations for these homotopy limits.\n\nAbstracting the story above\, w
e fix an arbitrary graphic quiver Q. Given\nany model category M (above we
had M = dg-categories) we consider\nM-valued diagrams over Q. In this tal
k I will present a combinatorial\ncharacterization of all such diagrams D
which are suitably 'fibrant\,'\nwhich in particular implies that the homot
opy limit of D is just its\nclassical limit. Analogous to the calculation
of derived functors in\nhomological algebra\, this yields an explicit form
ula for the homotopy\nlimit of any diagram.\n
LOCATION:https://stable.researchseminars.org/talk/FezaGurseyHigher/69/
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