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BEGIN:VEVENT
SUMMARY:Urs Schreiber (Czech Academy of Sciences)
DTSTART:20220208T113000Z
DTEND:20220208T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/1
DESCRIPTION:Title: Higher and Equivariant Bundles\nby Urs Schreiber (Czech Acade
my of Sciences) as part of Feza Gursey Center Higher Structures Seminars\n
\n\nAbstract\nThe natural promotion of the classical concept of (principal
) fiber\nbundles to "higher structures"\, namely to equivariant principal
infinity-bundles\ninternal to a singular-cohesive infinity-topos\, turns o
ut to be a natural foundation\nfor generalized cohomology theory in the fu
ll beauty of "twisted\nequivariant differential non-abelian cohomology of
orbifolds"\, and as such for much of the higher homotopical mathematics ne
eded at the interface of algebraic topology\, geometry and mathematical qu
antum physics. This talk gives some introduction and overview\, based on j
oint work with H. Sati (arXiv:2008.01101\, arXiv:2112.13654).\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masanori Morishita (Kyushu University)
DTSTART:20220125T113000Z
DTEND:20220125T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/2
DESCRIPTION:Title: Arithmetic topology and arithmetic TQFT\nby Masanori Morishit
a (Kyushu University) as part of Feza Gursey Center Higher Structures Semi
nars\n\n\nAbstract\nI will talk about some topics in arithmetic topology\,
related withclass field theory\,\n and then an arithmetic analog of Dijkg
raaf-Witten topological quantum field theory.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri Ilker Berktav (Middle East Technical University)
DTSTART:20220222T113000Z
DTEND:20220222T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/3
DESCRIPTION:Title: Symplectic Structures on Derived Schemes\nby Kadri Ilker Berk
tav (Middle East Technical University) as part of Feza Gursey Center Highe
r Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berkan Üze (Boğaziçi University)
DTSTART:20220308T113000Z
DTEND:20220308T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/4
DESCRIPTION:Title: A Glimpse of Noncommutative Motives\nby Berkan Üze (Boğazi
çi University) as part of Feza Gursey Center Higher Structures Seminars\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe University)
DTSTART:20220412T113000Z
DTEND:20220412T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/5
DESCRIPTION:Title: Homotopy theory of monoid actions via group actions and an Elmend
orf style theorem\nby Mehmet Akif Erdal (Yeditepe University) as part
of Feza Gursey Center Higher Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haldun Özgür Bayındır (City University of London)
DTSTART:20220426T113000Z
DTEND:20220426T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/6
DESCRIPTION:Title: Adjoining roots to ring spectra and algebraic K-theory\nby Ha
ldun Özgür Bayındır (City University of London) as part of Feza Gursey
Center Higher Structures Seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Orendain (Universidad Nacional Autónoma de México)
DTSTART:20220510T160000Z
DTEND:20220510T170000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/7
DESCRIPTION:Title: Higher lattice gauge fields and cubical $\\omega$-groupoids\n
by Juan Orendain (Universidad Nacional Autónoma de México) as part of Fe
za Gursey Center Higher Structures Seminars\n\n\nAbstract\nGauge fields de
scribe parallel transport of point particles\nalong curves\, with respect
to connections on principal bundles. This\ndata is captured as a smooth fu
nctor from the smooth path groupoid of\nthe base manifold into the deloopi
ng groupoid of the structure group\,\nplus gluing data. Lattice gauge fiel
ds do this for discretized versions\nof a base manifold. A lattice gauge f
ield is thus a functor from a\ndiscrete version of the path groupoid to a
delooping groupoid. Lattice\ngauge fields are meant to serve as discrete a
pproximations of regular\ngauge fields.\n\nHigher gauge fields describe pa
rallel transport of curves along\nsurfaces\, of surfaces along volumes\, e
tc. Several versions of\n2-dimensional gauge field have appeared in the li
terature. I will\nexplain how to extend these ideas to lattice gauge field
s on all\ndimensions\, using Brown's cubical homotopy \\omega-groupoid con
struction\nassociated to filtered spaces\, implementing a discrete notion
of thin\nhomotopy along the way.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatsuki Kuwagaki (Kyoto University)
DTSTART:20220524T113000Z
DTEND:20220524T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/8
DESCRIPTION:Title: An introduction to perverse schober\nby Tatsuki Kuwagaki (Kyo
to University) as part of Feza Gursey Center Higher Structures Seminars\n\
n\nAbstract\nA perverse sheaf is the topological counterpart of a differen
tial equation with (regular) singularities. A perverse schober is "a categ
ory-valued perverse sheaf". It consists of monodromy of categories and the
ir behaviors around singularities. The notion of perverse schober quite na
turally appears in many contexts e.g.\, mirror symmetry. In this talk\, I'
ll give an introduction to a very elementary part of perverse schober and
related topics.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Mazel-Gee (California Institute of Technology)
DTSTART:20221108T150000Z
DTEND:20221108T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/10
DESCRIPTION:Title: Towards knot homology for 3-manifolds\nby Aaron Mazel-Gee (C
alifornia Institute of Technology) as part of Feza Gursey Center Higher St
ructures Seminars\n\n\nAbstract\nThe Jones polynomial is an invariant of k
nots in $\\mathbb R^3$. Following a proposal of Witten\, it was extended t
o knots in 3-manifolds by Reshetikhin-Turaev using quantum groups.\nKhovan
ov homology is a categorification of the Jones polynomial of a knot in $\\
mathbb R^3$\, analogously to how ordinary homology is a categorification o
f the Euler characteristic of a space. It is a major open problem to exten
d Khovanov homology to knots in 3-manifolds.\nIn this talk\, I will explai
n forthcoming work towards solving this problem\, joint with Leon Liu\,\nD
avid Reutter\, Catharina Stroppel\, and Paul Wedrich. Roughly speaking\, o
ur contribution amounts\nto the first instance of a braiding on 2-represen
tations of a categorified quantum group. More\nprecisely\, we construct a
braided (∞\,2)-category that simultaneously incorporates all of Rouquier
's\nbraid group actions on Hecke categories in type A\, articulating a nov
el compatibility among them.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Can Yaylalı (Technische Universität Darmstadt)
DTSTART:20221122T140000Z
DTEND:20221122T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/11
DESCRIPTION:Title: Derived F-zips\nby Can Yaylalı (Technische Universität Dar
mstadt) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbst
ract\nThe theory of F-zips is a positive characteristic analog of the theo
ry of integral Hodge-structures. As shown by Moonen and Wedhorn\, one can
associate to any proper smooth scheme with degenerating Hodge-de Rham spec
tral sequence and finite locally free Hodge cohomologies an F-zips\, via
its n-th de Rham cohomology.\nUsing the theory of derived algebraic geomet
ry\, we can work with the de Rham hypercohomology and show that it has a d
erived analog of an F-zip structure. We call these structures derived F-zi
ps. We can attach to any proper smooth morphism a derived F-zip and analyz
e families of proper smooth morphisms via their underlying derived F-zip.\
n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kürşat Sözer (McMaster University)
DTSTART:20221206T140000Z
DTEND:20221206T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/12
DESCRIPTION:Title: Crossed module graded categories and state-sum homotopy invarian
ts of maps\nby Kürşat Sözer (McMaster University) as part of Feza G
ursey Center Higher Structures Seminars\n\n\nAbstract\nA well-known fact i
s that groups are algebraic models for 1-types. Generalizing groups\, cros
sed modules model 2-types. In this talk\, I will introduce the notion of a
crossed module graded fusion category which generalizes that of a fusion
category graded by a group. Then\,using such categories\, I will construct
a 3-dimensional state-sum homotopy quantum field theory (HQFT) with a 2-t
ype target. Such an HQFT associates a scalar to a map from a closed orient
ed 3-manifold to the fixed 2-type. Moreover\, this scalar is invariant und
er homotopies. This HQFT generalizes the state-sum Turaev-Virelizier HQFT
with an aspherical target. This is joint work with Alexis Virelizier.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ödül Tetik (University of Zurich)
DTSTART:20221220T140000Z
DTEND:20221220T150000Z
DTSTAMP:20260422T230719Z
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 Higher S
tructures Seminars\n\n\nAbstract\nI will introduce the notion of the 'Poin
caré' or 'Koszul' dual of a stratified space with tangential structure (T
S)\, 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 the fra
med case\, which was proposed by Lurie (later picked up by Calaque and Sch
eimbauer): duals of stably-framed bordisms are euclidean spaces with flag-
like stratifications. In particular\, this notion explains the 'shape' of
the higher Morita category of En-algebras when expressed in terms of facto
rization algebras\, and gives a natural definition of Morita categories of
disk-algebras with any TS. If time permits\, I will propose a simple Pois
son-structured version of this procedure which should construct\, using Po
isson additivity\, extended classical gauge theories given only the 1-shif
ted Poisson algebra of bulk observables.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (University of Zurich)
DTSTART:20221025T113000Z
DTEND:20221025T123000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/14
DESCRIPTION:Title: Geometric structures as stacks and geometric field theories\
nby Kadri İlker Berktav (University of Zurich) as part of Feza Gursey Cen
ter Higher Structures Seminars\n\n\nAbstract\nIn this talk\, we outline a
general framework for geometric field theories formulated by Ludewig and S
toffel. In brief\, functorial field theories (FFTs) can be formalized as c
ertain functors from an appropriate bordism category Bord to a suitable ta
rget category. Atiyah's topological field theories and Segal's conformal
field theories are the two important examples of such formulation. Given a
n FFT\, one can also require the source category to endow with a ''geometr
ic structure''. Of course\, the meaning of ''geometry'' must be clarified
in this new context. To introduce geometric field theories in an appropria
te way\, therefore\, we first explain how to define ''geometries'' using t
he language of stacks\, and then we provide the so-called geometric bordis
m category GBord. Finally\, we give the definition of a geometric field th
eory as a suitable functor on GBord.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neslihan Güğümcü (İzmir Institute of Technology)
DTSTART:20230117T140000Z
DTEND:20230117T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/15
DESCRIPTION:Title: On a quantum invariant of multi-knotoids\nby Neslihan Güğ
ümcü (İzmir Institute of Technology) as part of Feza Gursey Center High
er Structures Seminars\n\n\nAbstract\nKnotoids are immersed arcs in surfac
es\, introduced by Vladimir Turaev.\nKnotoids in the 2-sphere can be consi
dered as open knot diagrams with\ntwo endpoints that can lie anywhere in S
2. In this sense\, the theory of\nspherical knotoids extends the theory of
knots in the Euclidean 3-space\,\nand the classification problem of knots
generalizes to knotoids in an\ninteresting way with the existence of open
ends. In this talk we will\npresent multi-knotoids and an Alexander polyn
omial type invariant for\nthem by utilizing a partition function involving
a solution of the\nYang-Baxter equation. This talk is a joint work with L
ouis Kauffman.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Roberts (University of Adelaide)
DTSTART:20230131T070000Z
DTEND:20230131T080000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/16
DESCRIPTION:Title: Low-dimensional higher geometry: a case study\nby David Robe
rts (University of Adelaide) as part of Feza Gursey Center Higher Structur
es Seminars\n\n\nAbstract\nConsiderations from several different areas of
mathematics have prompted\nthe development of so- called higher geometry:
the study of categorified\nanalogues of geometric structures. Despite bein
g studied for nearly two\ndecades\, few examples that capture non-abelian
phenomena have been\nconstructed. And here by "constructed"\, we mean to t
he level that would\nsatisfy traditional differential geometers\, as oppos
ed to the kind of\nconstruction that category theorists are comfortable wi
th.\nTo this end\, I will describe a new framework to work with bundle\n2-
gerbes\, which from a higher- category point of view are certain types\nof
truncated descent data for $\\infty$-stacks on a manifold. The\ndescripti
on is sufficient to undertake concrete computations more\nsatisfying to tr
aditional differential geometers and mathematical\nphysicists. I also desc
ribe explicit geometric examples that can be\nconstructed using our framew
ork\, including infinite families of explicit\ngeometric string structures
.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Plavnik (Indiana University\, Bloomington)
DTSTART:20230228T140000Z
DTEND:20230228T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/17
DESCRIPTION:Title: On the classification of modular categories\nby Julia Plavni
k (Indiana University\, Bloomington) as part of Feza Gursey Center Higher
Structures Seminars\n\n\nAbstract\nModular categories are intricate organi
zing algebraic structures\nappearing in a variety of mathematical subjects
including topological\nquantum field theory\, conformal field theory\, re
presentation theory of\nquantum groups\, von Neumann algebras\, and vertex
operator algebras. They\nare fusion categories with additional braiding a
nd pivotal structures\nsatisfying a non- degeneracy condition. The problem
of classifying\nmodular categories is motivated by applications to topolo
gical quantum\ncomputation as algebraic models for topological phases of m
atter.\n\nIn this talk\, we will start by introducing some of the basic de
finitions\nand properties of fusion\, braided\, and modular categories\, a
nd we will\nalso give some concrete examples to have a better understandin
g of their\nstructures. I will give an overview of the current situation o
f the\nclassification program for modular categories\, with a particular f
ocus\non the results for odd-dimensional modular categories\, and we will\
nmention some open directions in this field.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivia Caramello (Institut des Hautes Études Scientifiques)
DTSTART:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/18
DESCRIPTION:Title: Gröthendieck toposes as unifying “bridges” in mathematics.<
/a>\nby Olivia Caramello (Institut des Hautes Études Scientifiques) as pa
rt of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nI will
explain the sense in which Gröthendieck toposes can act as unifying 'brid
ges' for relating different mathematical theories to each other and studyi
ng them from a multiplicity of points of view. I shall first present the g
eneral techniques underpinning this theory and then discuss a number of se
lected applications in different mathematical fields.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics)
DTSTART:20230411T150000Z
DTEND:20230411T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/19
DESCRIPTION:Title: Higher algebraic closure\nby Theo Johnson-Freyd (Perimeter I
nstitute for Theoretical Physics) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nDeligne's work on Tannakian duality identi
fies the category sVec of super vector spaces as the "algebraic closure" o
f the category Vec of vector spaces (over C). I will describe my construct
ion\, joint with David Reutter\, of the higher-categorical analog of sVec:
the algebraic closure of the n-category of "n-vector spaces". The constru
ction mixes ideas from Galois theory\, quantum physics\, homotopy theory\,
and fusion category theory. Time permitting\, I will describe the higher-
categorical\nGalois group\, which turns out to have a surgery-theoretic de
scription through which it is almost\, but not quite\, the group PL.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Scheimbauer (Technische Universität München)
DTSTART:20230509T150000Z
DTEND:20230509T160000Z
DTSTAMP:20260422T230719Z
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 (Technische Un
iversität München) as part of Feza Gursey Center Higher Structures Semin
ars\n\n\nAbstract\nI will explain how to generalize Harpaz’ universal pr
operty of the $(\\infty\,1)$-category of spans to the higher category ther
eof. The crucial property is “m-semiadditivity”\, which generalizes us
ual semiadditivity of categories. Combining this with the finite path inte
gral construction of Freed- Hopkins-Lurie-Teleman this yields finite gauge
theory as a fully extended TFT. This is joint work in progress with Tashi
Walde.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (İstanbul Technical University)
DTSTART:20230523T140000Z
DTEND:20230523T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/21
DESCRIPTION:Title: Dold-Kan equivalence and its extensions\nby Atabey Kaygun (
İstanbul Technical University) as part of Feza Gursey Center Higher Struc
tures Seminars\n\n\nAbstract\nThe Dold-Kan Correspondence is an equivalenc
e between the category of differential graded objects and the category of
simplicial objects on an abelian category. This equivalence is best unders
tood within the context of Quillen model categories. However\, a more stra
ightforward interpretation using the representation theory of small catego
ries is possible. We will demonstrate that the Dold-Kan equivalence can be
expressed through specific induction and restriction functors\, paving th
e way for similar equivalences for crossed-simplicial objects. There are e
xtensions to the Dold-Kan Correspondence in this context\, with the Dwyer-
Kan equivalence between the category of duplicial objects and the category
of cyclic objects over an abelian category being a notable example. We wi
ll also show that the Dwyer-Kan equivalence can be incorporated into the f
ramework we initially developed for the Dold-Kan Correspondence. Lastly\,
we will discuss further extensions.\n\nThis research is a joint work with
my PhD student\, Haydar Can Kaya.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20230328T140000Z
DTEND:20230328T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/23
DESCRIPTION:Title: A simplicial category for higher correspondences\nby Redi Ha
deri (Bilkent University) as part of Feza Gursey Center Higher Structures
Seminars\n\n\nAbstract\nCorrespondences between simplicial sets (and oo-ca
tegories) are a generalization of the notion of profunctor between categor
ies. It is known that functors between categories are classified by lax\nd
iagram of profunctors. We will present this fact from the lens of double c
ategory theory.\nThen\, we will show how simplicial sets\, simplicial maps
and correspondences are organized in a simplicial category (this is a wea
k simplicial object in categories). A simplicial category may\nbe regarded
as a 2-fold version of a simplicially enriched category\, and hence some
ideas from double category theory apply. In particular we formulate the fa
ct that simplicial maps are classified by diagrams of correspondences. As
a corollary\, we obtain a formulation of Lurie's prediction that inner fib
rations are classified by diagrams of correspondences between oo-categorie
s.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuf Barış Kartal (University of Edinburgh)
DTSTART:20230221T140000Z
DTEND:20230221T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/24
DESCRIPTION:Title: Frobenius operators in symplectic topology\nby Yusuf Barış
Kartal (University of Edinburgh) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nOne can define the Frobenius operator on a
commutative ring of characteristic p as the p th power operation\, and th
is has generalizations to a larger class of commutative rings\, and even t
o topological spaces and spectra. Spectra with circle actions and Frobeniu
s operators are called cyclotomic spectra. The simplest example is the fre
e loop space\, and important examples arise in algebraic and arithmetic ge
ometry as topological Hochschild homology of rings and categories. By topo
logical reasons and mirror symmetry\, it is natural to expect such a struc
ture to arise in symplectic topology-- more precisely in ``closed string F
loer theory''. In this talk\, we will explain how to construct such spectr
a using Hamiltonian Floer theory\, i.e. by using holomorphic cylinders in
symplectic manifolds. Joint work in progress with Laurent Cote.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erdal Ulualan (Kütahya Dumlupınar Üniversitesi)
DTSTART:20230425T133000Z
DTEND:20230425T143000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/26
DESCRIPTION:Title: Simplisel gruplardan yüksek boyutlu cebirsel modellere funktor
lar\nby Erdal Ulualan (Kütahya Dumlupınar Üniversitesi) as part of
Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nBu çalış
mada bir simplisel grubun Moore kompleksinde tanımlı olan hiper çapraz
lanmış kompleks çiftleri kullanılarak parçalanmış simplisel gru
plar ile cebirsel modeller arasındaki ilişkiler verilecektir. 1-parça
lanmış simplisel grubun bir çaprazlanmış modülü nasıl modelle
diği ve 1- parçalanmış bisimplisel grubun bir çaprazlanmış kar
eyi nasıl modellediği gösterilecektir. Sonuç olarak\, bu ilişkile
ri genelleştirerek 1-parçalanmış n-boyutlu multisimplisel grubun bi
r çaprazlanmış n-küpü nasıl modellediğini göstereceğiz.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lakshya Bhardwaj (University of Oxford)
DTSTART:20230926T120000Z
DTEND:20230926T130000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/27
DESCRIPTION:Title: TQFTs and Gapped Phases with Non-Invertible Symmetries\nby L
akshya Bhardwaj (University of Oxford) as part of Feza Gursey Center Highe
r Structures Seminars\n\n\nAbstract\nI will discuss classification of topo
logical quantum field theories (TQFTs) with non-invertible generalized/cat
egorical symmetries. From a condensed matter point of view\, this is relat
ed to the classification of gapped phases of systems with non-invertible s
ymmetries. Although the general formalism will be applicable to any spacet
ime dimension\, I will provide concrete details in spacetime dimension $d=
2$. As main examples\, I will describe the only $(1+1)d$ gapped phase with
Ising symmetry which carries 3 vacua along with relative Euler terms\, an
d four possible $(1+1)d$ gapped phases with $Rep(S_3)$ symmetry. Along the
way\, I will also discuss the order parameters for such gapped phases\, w
hich carry generalized charges under non-invertible symmetries.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Rumynin (University of Warwick)
DTSTART:20231010T150000Z
DTEND:20231010T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/28
DESCRIPTION:Title: C_2-Graded groups\, their Real representations and Dyson's tenfo
ld way\nby Dmitriy Rumynin (University of Warwick) as part of Feza Gur
sey 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 represent
ation is a complex representation of $H$ with an action of the other coset
$G\\H$ of odd elements in another way that needs to be chosen. Different
choices lead to different theories.\nSuch representations appeared indepen
dently in three different disciplines: Algebra\, Physics and Topology.\n\n
The goal of the talk is to review the formalism and various choices\, incl
uding resulting theories.\nThe talk is based on my recent works with James
Taylor (Oxford) and Matthew B. Young (Utah State).\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Street (Macquarie University)
DTSTART:20231024T090000Z
DTEND:20231024T100000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/29
DESCRIPTION:Title: Could representations of your category be those of a groupoid?\nby Ross Street (Macquarie University) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nBy a representation of a category
ℱ here is meant a functor from ℱ to a category V of modules over a com
mutative ring R. The question is whether there is a groupoid G whose categ
ory [G\,V] of representations is equivalent to the category [ℱ\,V] of re
presentations of the given category ℱ. That is to say\, is there a group
oid G such that the free V - category RG on G is Morita V - equivalent to
the free V - category Rℱ on ℱ? The groupoid G could be the core groupo
id ℱinv of ℱ\; that is\, the subcategory of ℱ with the same objects
but with only the invertible morphisms. Motivating examples come from Dold
-Kan-type theorems and a theorem of Nicholas Kuhn [see “Generic represen
tation theory of finite fields in nondescribing characteristic”\, Advanc
es 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 examples.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Gurski (Case Western Reserve University)
DTSTART:20231107T120000Z
DTEND:20231107T130000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/30
DESCRIPTION:Title: Computing with symmetric monoidal functors\nby Nick Gurski (
Case Western Reserve University) as part of Feza Gursey Center Higher Stru
ctures Seminars\n\n\nAbstract\nCoherence theorems\, while often technicall
y complicated\, serve a simple role: to make computations easier on the us
er. Abstract forms of coherence theorems often take one of two forms\, eit
her a strictification form or a diagrammatic form. The general\, abstract
kinds of coherence theorems that would apply to symmetric or braided monoi
dal functors are of the strictification variety\, but in practice the diag
rammatic versions are often what one might need. I will present a general
form of\na diagrammatic coherence theorem applicable to monoidal functors
(of any variety) or any other structure governed by a reasonably nice 2-mo
nad. This is joint work with Niles Johnson.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Donovan (Yau Mathematical Sciences Center\, Tsinghua Unive
rsity)
DTSTART:20231128T110000Z
DTEND:20231128T120000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/31
DESCRIPTION:Title: Homological comparison of resolution and smoothing\nby Willi
am Donovan (Yau Mathematical Sciences Center\, Tsinghua University) as par
t of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nA singul
ar space often comes equipped with (1) a resolution\, given by a morphism
from a smooth space\, and (2) a smoothing\, namely a deformation with smoo
th generic fibre. I will discuss work in progress on how these may be rela
ted homologically.\n
LOCATION:https://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:20260422T230719Z
UID:FezaGurseyHigher/32
DESCRIPTION:Title: Complexes of stable infinity-categories\nby Merlin Christ (I
nstitut de Mathématiques de Jussieu – Paris Rive Gauche) as part of Fe
za Gursey Center Higher Structures Seminars\n\n\nAbstract\nA complex of st
able infinity-categories is a categorification of a chain complex\, meanin
g a sequence of stable infinity-categories together with a differential th
at squares to the zero functor. We refer to such categorified complexes as
categorical complexes. We give a categorification of the totalization con
struction\, which associates a categorical complex with a categorical mult
i-complex. Special cases include the totalizations of commutative squares
or higher cubes of stable infinity categories. This can be used to constru
ct interesting examples of categorical complexes\, for instance coming fro
m normal crossing divisors.\nThe study of categorical complexes can be see
n as part of the conjectural/emerging subject of categorified homological
algebra. We will also indicate a partial formalisation of this\, based on
the notion of a lax additive (infinity\,2)-category\, categorifying the no
tion of an additive 1-category.\nThis talk is based on joint work with T.
Dyckerhoff and T. Walde\, see https://arxiv.org/abs/2301.02606.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Félix Loubaton (MPIM\, Bonn)
DTSTART:20231219T150000Z
DTEND:20231219T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/33
DESCRIPTION:Title: Lax univalence for $(\\infty\,\\omega)$-categories\nby Féli
x Loubaton (MPIM\, Bonn) as part of Feza Gursey Center Higher Structures S
eminars\n\n\nAbstract\nThe classical Grothendieck construction establishes
an isomorphism between the (pseudo)functor $F:C\\to Cat$ and the left Car
tesian fibration $E\\to C$. We can then show that $E$ is the lax colimit o
f the\nfunctor $F$.\n\nThis presentation is dedicated to the generalizatio
n of this result for $(\\infty\,\\omega)$-categories. After defining $(\\i
nfty\,\\omega)$-categories\, we will state the lax univalence for $(\\inft
y\,\\omega)$- categories. We'll then explain how this result allows us to
express a strong link between Grothendieck construction for $(\\infty\,\\o
mega)$-categories and the lax-colimits of $(\\infty\,\\omega)$-categories\
, similar to the classical case.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent Üniversitesi)
DTSTART:20240116T150000Z
DTEND:20240116T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/35
DESCRIPTION:Title: Shifted contact structures on derived stacks\nby Kadri İlke
r Berktav (Bilkent Üniversitesi) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nIn this talk\, we outline our program for
the development of shifted contact structures in the context of derived al
gebraic geometry. We start by recalling some key notions and results from
derived algebraic/symplectic geometry. Next\, we discuss shifted contact s
tructures on derived Artin stacks and report our results regarding their l
ocal theory\, together with some future directions.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nils Baas (Norwegian University of Science and Technology)
DTSTART:20240213T150000Z
DTEND:20240213T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/37
DESCRIPTION:Title: Beyond Categories\nby Nils Baas (Norwegian University of Sci
ence and Technology) as part of Feza Gursey Center Higher Structures Semin
ars\n\n\nAbstract\nMy talk will be philosophical. I will motivate the need
to go beyond higher categories in order to get a good framework for many
types of higher structures. This leads me to the notion of hyperstructures
which I will motivate and explain. Initially this is a very general conce
pt in order to cover both mathematical and applied aspects which I will ex
plain. I will also relate to extended Field Theories.\n\nMeeting ID: 828 0
129 1723\nPasscode: 530129\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meng-Chwan Tan (National University of Singapore)
DTSTART:20240227T090000Z
DTEND:20240227T100000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/38
DESCRIPTION:Title: Vafa-Witten Theory: Invariants\, Floer Homologies\, Higgs Bundle
s\, a Geometric Langlands Correspondence\, and Categorification\nby Me
ng-Chwan Tan (National University of Singapore) as part of Feza Gursey Cen
ter Higher Structures Seminars\n\n\nAbstract\nWe revisit Vafa-Witten theor
y in the more general setting whereby the underlying moduli space is not t
hat of instantons\, but of the full Vafa-Witten equations. We physically d
erive (i) a novel Vafa-Witten four-manifold invariant associated with this
moduli space\, (ii) their relation to Gromov-Witten invariants\, (iii) a
novel Vafa-Witten Floer homology assigned to three-manifold boundaries\, (
iv) a novel Vafa-Witten Atiyah-Floer correspondence\, (v) a proof and gene
ralization of a conjecture by Abouzaid-Manolescu in [1] about the hypercoh
omology 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 parameter
that specializes to the classical correspondence in the zero-coupling lim
it\, where Higgs bundles feature in (ii)\, (iv)\, (vi) and (vii). We also
explain how these invariants and homologies will be categorified in the pr
ocess\, and discuss their higher categorification. In essence\, we will re
late differential and enumerative geometry\, topology and geometric repres
entation theory in mathematics\, via a maximally-supersymmetric topologica
l quantum field theory with electric-magnetic duality in physics.\n\nMeeti
ng ID: 892 5026 2628\nPasscode: 521946\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Dimitriadis Bermejo (Paul Sabatier University)
DTSTART:20240312T150000Z
DTEND:20240312T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/39
DESCRIPTION:Title: A new model for dg-categories\nby Elena Dimitriadis Bermejo
(Paul Sabatier University) as part of Feza Gursey Center Higher Structures
Seminars\n\n\nAbstract\nDg-categories have been very important in Algebra
ic Geometry for a really long time\; but they are not without their issues
. In order to solve these\, current researchers have been turning to diffe
rent models of infinity-categories for inspiration. Enriched infinity cate
gories\, dg-Segal categories\, enriched quasi-categories... Following this
flourishing field\, in this talk we will define a new model for dg-catego
ries inspired in Rezk's complete Segal spaces model for infinity-categorie
s.\n\nDuring this talk we will define dg-Segal spaces\, give its relations
hip to classical Segal spaces\, use this to define complete dg-Segal space
s and its model structure and give a sketch of the proof of its equivalenc
e to Tabuada's model structure of dg-categories. If time allows\, we will
say a word about some possible refinements of the model\, and mention some
work in progress surrounding its relationship to Mertens and Borges Marqu
es' model of dg-Segal spaces.\n\nMeeting ID: 817 3634 5226\nPasscode: 4582
43\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240326T150000Z
DTEND:20240326T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/40
DESCRIPTION:Title: Commutative and Frobenius algebras in span categories\nby Wa
lker Stern (Bilkent University) as part of Feza Gursey Center Higher Struc
tures Seminars\n\n\nAbstract\nIn this talk\, I will discuss the relation o
f span categories to various versions of the symplectic category. I will t
hen expose the connection between simplicial objects and algebras in span
categories\, focusing on the 1- and 2-categorical cases to explicate the u
nderlying intuitions. Finally\, I will discuss recent work (joint with Iva
n Contreras and Rajan Mehta) generalizing this correspondence to algebras
with further structure\, that is\, to commutative and Frobenius algebras.\
n\nMeeting ID: 865 0047 9193\nPasscode: 850569\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Huerta (Instituto Superior Técnico)
DTSTART:20240409T150000Z
DTEND:20240409T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/41
DESCRIPTION:Title: Poincaré duality for families of supermanifolds\nby John Hu
erta (Instituto Superior Técnico) as part of Feza Gursey Center Higher St
ructures Seminars\n\n\nAbstract\nIt is well known to experts\, but seldom
discussed explicitly\, that smooth supergeometry is best done in families.
This is also called the relative setting\, and it implies that we need re
lative versions of standard supergeometric constructions. Such constructio
ns include the de Rham complex familiar from ordinary differential geometr
y\, but in the supergeometric setting\, they also include more exotic obje
cts\, such as the Berezinian line bundle (whose sections are the correct o
bjects to integrate over supermanifolds) and the related complex of integr
al forms\, where the super version of Stokes' theorem lives. To work in fa
milies\, we introduce relative versions of the de Rham complex and the int
egral form complex\, and we prove that they satisfy a relative version of
Poincaré duality. No background in supergeometry will be assumed for this
talk.\n\nThis is joint work with Konstantin Eder and Simone Noja.\n\nMeet
ing ID: 859 9026 1915\nPasscode: 578799\n\n--\nSeminar time has been updat
ed.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tubbenhauer (University of Sydney)
DTSTART:20240507T080000Z
DTEND:20240507T090000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/42
DESCRIPTION:Title: Counting in tensor products\nby Daniel Tubbenhauer (Universi
ty of Sydney) as part of Feza Gursey Center Higher Structures Seminars\n\n
\nAbstract\nThis talk is an introduction to analytic methods in tensor cat
egories with the focus on quantifying the number of summands in tensor pro
ducts of representations and related structures. Along the way\, we'll thr
ow in plenty of examples to keep things interesting!\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shulman (University of California – San Diego)
DTSTART:20240521T170000Z
DTEND:20240521T180000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/43
DESCRIPTION:Title: Higher Observational type theory\nby Michael Shulman (Univer
sity of California – San Diego) as part of Feza Gursey Center Higher Str
uctures Seminars\n\n\nAbstract\nHomotopy Type Theory is a new approach to
the foundations of mathematics\, in which the basic objects of mathematics
are not sets but homotopy types. It is natively isomorphism-invariant and
well-adapted to computer formalization\, and can be interpreted in higher
toposes to give a synthetic language for internal constructions and proof
s. It can also be explained intuitively to students\, giving them access t
o higher structures while avoiding the complicated machinery of combinator
ial homotopy theory\; and it can be used as a programming language\, to co
mpute certain invariants of higher structures by simply running code deriv
ed from their definitions. However\, until recently it was not known how t
o 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 Observationa
l Type Theory\; this is a new formal system for Homotopy Type Theory that\
, we hope\, is both intuitively natural and computationally adequate. This
is joint work in progress with Thorsten Altenkirch and Ambrus Kaposi.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgün Ünlü (Bilkent University)
DTSTART:20240604T150000Z
DTEND:20240604T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/44
DESCRIPTION:Title: Infinity operads as simplicial lists\nby Özgün Ünlü (Bil
kent University) as part of Feza Gursey Center Higher Structures Seminars\
n\n\nAbstract\nIn this talk\, we will present a model for infinity operads
. We will start by discussing how the category of colored nonsymmetric ope
rads can be embedded in a category which we call the category of simplicia
l lists. Within this category\, our model for infinity operads will genera
lize colored nonsymmetric operads in the same way that quasicategories gen
eralize ordinary categories when embedded in the category of simplicial se
ts. Therefore\, it is natural to refer to these infinity operads as quasio
perads. Next\, we will discuss a homotopy coherent nerve functor from the
category of simplicial operads to the category of simplicial lists\, which
sends Kan complex enriched operads to quasioperads\, analogous to the hom
otopy coherent nerve functor from the category of simplicial categories to
the category of simplicial sets. Finally\, we will discuss the homology o
f simplicial lists\, and hence quasioperads\, and perform some homology co
mputations.\nThis is joint work with Redi Haderi.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Caviglia (University of Leichester)
DTSTART:20240423T150000Z
DTEND:20240423T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/45
DESCRIPTION:Title: 2-stacks and quotient 2-stacks\nby Elena Caviglia (Universit
y of Leichester) as part of Feza Gursey Center Higher Structures Seminars\
n\n\nAbstract\nStacks generalize one dimension higher the fundamental conc
ept of sheaf. They are pseudofunctors that are able to glue together weakl
y compatible local data into global data. Stacks are a very important conc
ept in geometry\, due to their ability to take into account automorphisms
of objects. While many classification problems do not have a moduli space
as solution because of the presence of automorphisms\, it is often nonethe
less possible to construct a moduli stack. In recent years\, the research
community has begun generalizing the notion of stack one dimension higher.
Lurie studied a notion of (∞\, 1)-stack\, that yields a notion of (2\,
1)- stack for a trihomomorphism that takes values in (2\, 1)-categories\,
when truncated to dimension 3. And Campbell introduced a notion of 2-stack
that involves a trihomomorphism from a one-dimensional category into the
tricategory of bicategories. In this talk\, we will introduce a notion of
2-stack that is suitable for a trihomomorphism from a 2-category endowed w
ith a bitopology into the tricategory of bicategories. The notion of bitop
ology that we consider is the one introduced by Street for bicategories. W
e achieve our definition of 2-stack by generalizing a characterization of
stack due to Street. Since our definition of 2-stack is quite abstract\, w
e will also present a useful characterization in terms of explicit gluing
conditions that can be checked more easily in practice. These explicit con
ditions generalize to one dimension higher the usual stacky gluing conditi
ons. A key idea behind our characterization is to use the tricategorical Y
oneda Lemma to translate the biequivalences required by the definition of
2-stack into effectiveness conditions of appropriate data of descent. As a
biequivalence is equivalently a pseudofunctor which is surjective on equi
valence classes of objects\, essentially surjective on morphisms and fully
faithful on 2-cells\, we obtain effectiveness conditions for data of desc
ent on objects\, morphisms and 2-cells. It would have been hard to give th
e 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 guide us in
finding the right coherence conditions. Finally\, we will present the mot
ivating example for our notion of 2-stack\, which is the one of quotient 2
-stack. After having generalized principal bundles and quotient stacks to
the categorical context of sites\, we aimed at a generalization of our the
ory one dimension higher\, to the context of bisites\, motivated by promis
ing applications of principal 2- bundles to higher gauge theory. But there
was no notion of higher dimensional stack suitable for the produced analo
gues of quotient prestacks in the two-categorical context. Our notion of 2
-stack is able to fill this gap. Indeed\, we have proven that\, if the bis
ite satisfies some mild conditions\, our analogues of quotient stacks one
dimension higher are 2-stacks.\n\nMeeting ID: 832 8539 1847\nPasscode: 167
146\n
LOCATION:https://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:20260422T230719Z
UID:FezaGurseyHigher/46
DESCRIPTION:Title: A computational approach to the homotopy theory of dg-categories
\nby Doğancan Karabaş (Kavli Institute for the Physics and Mathemati
cs of the Universe - University of Tokyo) as part of Feza Gursey Center Hi
gher Structures Seminars\n\n\nAbstract\nThe homotopy theory of differentia
l graded (dg) categories plays a significant role in\nvarious fields\, inc
luding algebraic geometry\, representation theory\, higher categories\, an
d\nsymplectic geometry. In particular\, understanding dg-categories is cru
cial for formulating and\ninterpreting homological mirror symmetry.\nIn th
is talk\, I will present our approach to the homotopy theory of dg-categor
ies by establishing a\ncofibration structure\, which can be viewed as a ha
lf-model structure. This structure enables a\ncombinatorial description of
derived constructions and offers computational advantages. This is\njoint
work with Sangjin Lee (arXiv:2109.03411 and arXiv:2405.03258). Some key a
pplications of\nour approach\, particularly in symplectic and contact geom
etry\, include:\n\n$\\bullet$ Combinatorial description of homotopy colimi
ts of dg categories\, which gives a local-to-\nglobal formula computing wr
apped Fukaya categories of symplectic manifolds\,\n\n$\\bullet$ Local-to-g
lobal construction of functors between wrapped Fukaya categories that are\
ninduced by symplectomorphisms\,\n\n$\\bullet$ A simple description of int
ernal Hom and Hochschild cohomology of dg-categories. This\nongoing work a
ims to provide useful tools for addressing the Weinstein conjecture\, whic
h\nconcerns the existence of periodic orbits of Reeb vector fields.\n\nI p
lan to cover as much of this content as time permits\, and according to th
e audience's interest.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent University)
DTSTART:20241015T150000Z
DTEND:20241015T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/47
DESCRIPTION:Title: Constructions of contact derived stacks\nby Kadri İlker Ber
ktav (Bilkent University) as part of Feza Gursey Center Higher Structures
Seminars\n\n\nAbstract\nThis talk presents several examples of derived Art
in stacks with shifted contact\nstructures. We start by reviewing derived
symplectic/contact geometry. Next\, we outline our\nconstructions: the fir
st one extends classical 1-jet bundles\, and the second set of constructio
ns arises from shifted geometric quantization.\n\nMeeting ID: 867 4914 748
7\nPassword: 038987\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ayala (Montana State University)
DTSTART:20241112T130000Z
DTEND:20241112T140000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/48
DESCRIPTION:Title: Factorization homology of higher categories\nby David Ayala
(Montana State University) as part of Feza Gursey Center Higher Structures
Seminars\n\n\nAbstract\nThe "alpha" version of factorization homology pai
rs (framed) n-manifolds with En-algebras. This construction generalizes c
lassical homology of a manifold\, yields novel results concerning configur
ation spaces of points in a manifold\, and supplies a sort of state-sum mo
del for sigma-models (ie\, mapping spaces) to\n(n−1)-connected targets.
This "alpha" version of factorization homology novelly extends Poincaré
duality\, shedding light on deformation theory and dualities among field t
heories. Being defined using homotopical mathematical foundations\, "alp
ha" factorization homology is manifestly functorial and continuous in all
arguments\, notably in moduli of manifolds and embeddings between them\, a
nd it satisfies a local-to-global expression that is inherently homotopica
l in nature. \nNow\, En-algebras can be characterized as (∞\,n)-categor
ies equipped with an (n−1)-connected functor from a point. The (full) "
beta" version of factorization homology pairs (framed) n-manifolds with po
inted (∞\,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 inherently homot
opical nature of (full) "beta" factorization homology affords otherwise un
foreseen continuity in all arguments\, and local-to-global expressions. \
nIn this talk\, I will outline a definition of "beta" factorization homolo
gy\, focusing on low-dimensions and on suitably\nreduced (∞\,n)-categori
es (specifically\, braided monoidal categories). I will outline some exam
ples\, and demonstrate some operational practice of factorization homology
. Some of this material is established in literature\, some a work in pro
gress\, 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 this work
is joint with John Francis.\n\nNote the unusual time: at 16:00 Istanbul ti
me!\nMeeting ID: 815 1508 2956\nPasscode: 613918\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan (Koç University)
DTSTART:20241128T140000Z
DTEND:20241128T150000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/49
DESCRIPTION:Title: Some applications of toposes of measure-theoretic sheaves\nb
y Asgar Jamneshan (Koç University) as part of Feza Gursey Center Higher S
tructures Seminars\n\n\nAbstract\nWe construct toposes of sheaves on measu
re spaces and highlight the usefulness of interpreting certain structures
from classical measure theory and functional analysis\, combined with a Bo
olean internal logic\, in applications to ergodic structure theory and vec
tor duality.\n\nPlease note the unusual day.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranav Pandit (ICTS-TIFR)
DTSTART:20241210T120000Z
DTEND:20241210T130000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/50
DESCRIPTION:Title: Towards Categorical Kähler Geometry\nby Pranav Pandit (ICTS
-TIFR) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstr
act\nThe Donaldson-Uhlenbeck-Yau theorem describes a deep relationship bet
ween holomorphic vector bundles on Kähler manifolds and solutions to cert
ain partial differential equations. I will report on progress\ntowards for
mulating and proving an analogue of this theorem in categorical noncommuta
tive geometry. This talk is based on joint work with Fabian Haiden\, Ludmi
l Katzarkov\, and Maxim Kontsevich.\n\nMeeting ID: 847 8067 3908 Passcode:
328020\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keremcan Doğan (Gebze Technical University)
DTSTART:20241224T150000Z
DTEND:20241224T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/51
DESCRIPTION:Title: Proto Bialgebroids for Exceptional Geometries\nby Keremcan D
oğan (Gebze Technical University) as part of Feza Gursey Center Higher St
ructures Seminars\n\n\nAbstract\nRecent advancements in the mathematics of
dualities seem to be in favor of certain generalizations of differential
geometric structures on algebroids. The success of the generalized geometr
y program for T-duality motivates the construction of analogous exceptiona
l geometries suitable for U-duality. In particular the Drinfeld double str
ucture for Lie bialgebroids is a crucial concept for T-duality. In this ta
lk\, we will introduce the notion of bialgebroid extending these ideas in
the realm of U-duality. We will present a calculus framework on algebroids
\; both twistless and twistful cases. In order to focus on exceptional geo
metries\, we extend T-duality notions in a more general class of algebroid
s\, where the setting allows us to work with non-dual vector bundles of ar
bitrary rank. We will conclude the talk with a specific construction cruci
al for exceptional Drinfeld algebras in the context of higher Courant alge
broids and Nambu-Poisson structure.\n\nMeeting ID: 836 5961 7974 Passcode:
694072\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simona Paoli (University Of Aberdeen)
DTSTART:20250121T150000Z
DTEND:20250121T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/52
DESCRIPTION:Title: The weakly globular approach to higher categories\nby Simona
Paoli (University Of Aberdeen) as part of Feza Gursey Center Higher Struc
tures Seminars\n\n\nAbstract\nHigher categories are motivated by naturally
occurring examples in diverse areas of mathematics\, including homotopy t
heory\, mathematical physics\, logic and computer sciences. Several differ
ent approaches exist to formalize the notion of a higher category. In this
talk I will give an overview of an approach to model 'truncated' higher c
ategories: namely those having higher morphisms in dimensions 0 up to n on
ly. These arise naturally in homotopy theory\, in modelling the building b
locks of topological spaces\, called n-types.\n\nClassically\, in a higher
category we have sets of objects and sets of higher morphisms. This is al
so called 'globularity condition' as it is the condition that gives rise t
o the globular shape of the higher morphisms in a higher category. Instead
\, in the so called weakly globular approach I have introduced\, the objec
ts and the higher morphism do not form a set but a structure only equivale
nt (in a higher dimensional sense) to a set. We call this 'weak globularit
y condition'.\n\nOne advantage of this approach is that it is possible to
model a weak n-category using a rather rigid structure\, namely an n-fold
category satisfying additional conditions. These are the weakly globular n
-fold categories. I will mention some applications of these structures to
homological algebra\, as well as a link between weak globularity and the n
otion of weak units in the case n=2. I will conclude with some conjectures
for general dimension n.\n\nGiven the highly technical nature of this wor
k\, and in the interest of making the talk broadly accessible\, I will con
centrate 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-type Mod
els of Weak n-Categories\, Algebra and Applications 26\, Springer (2019).\
n\n· S. Paoli\, D. Pronk\, A double categorical model of weak 2-cat
egories\, _Theory and Application of categories_\, 28\, (2013)\, 933-980.\
n\nAbout weak globularity and weak units:\n\n· S. Paoli\, Weakly gl
obular double categories and weak units\, arXiv:2008.11180 (2024).\n\nAn a
pplication of weakly globular n-fold categories to homological algebra:\n\
n· D. Blanc\, S. Paoli\, A model for the Andre-Quillen cohomology o
f an (\\infty\,1)-category\, arXiv:2405.12674 (2024).\n\nMeeting ID: 830 1
320 7597\nPasscode: 389958\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe University)
DTSTART:20250107T150000Z
DTEND:20250107T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/53
DESCRIPTION:Title: Fibration category structures on monoidal and enriched categorie
s\nby Mehmet Akif Erdal (Yeditepe University) as part of Feza Gursey C
enter Higher Structures Seminars\n\n\nAbstract\nWe first discuss Brown's c
ategory of fibrant objects structures on closed monoidal categories by mea
ns of some specific arrows called pseudo-cofibrations. These arrows are th
e ones whose pullback-power with (acyclic) fibrations are also (acyclic) f
ibrations\; which can be defined whenever the underlying category is close
d monoidal or enriched over a category of fibrant objects. Later we discus
s the category of fibrant objects structures on enriched categories. If V
is a closed monoidal category with a category of fibrant object structure
on it and C is enriched over V and powered over a colimit dense subcategor
y of V\, then under mild conditions C can also be made into a category of
fibrant objects. We discuss constructions and properties of these structur
es and their extension to the equivariant setting. Lastly\, we give some a
lready existing and some new examples of such categories of fibrant object
s and mention some applications.\n\nMeeting ID: 843 5555 9891\nPasscode: 0
84032\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Orendain (Case Western Reserve University)
DTSTART:20250306T150000Z
DTEND:20250306T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/54
DESCRIPTION:Title: Compact closed Gray monoids\nby Juan Orendain (Case Western
Reserve University) as part of Feza Gursey Center Higher Structures Semina
rs\n\n\nAbstract\nClosed and compact closed bicategories arise naturally i
n the context of topological quantum field theory\, where pseudofunctors b
etween a compact closed bicategory of cobordisms with corners and the comp
act closed bicategory of dualizable locally presentable linear categories
are one way of defining once-extended TQFTs\, and where certain compact cl
osed bicategories have been proposed as appropriate initial data for four
dimensional state-sum constructions.
\n\nIn this talk\, I will present an exposition of the strictest r
easonable version of a bicategorical analogue of compact closed categories
\, namely compact closed Gray monoids. Reasonable here means that there is
a strictification theorem from the general setting of monoidal bicategori
es with dual objects to our compact closed Gray monoids.\n\nI will introdu
ce a pictorial calculus for categories enriched over Gray monoids\, and I
use this to show that transformations enriched over a closed or compact cl
osed monoid\, between certain enriched functors can be reformulated in an
adjoint fashion. This reformulation has the virtue of behaving computatio
nally like corresponding unenriched 1-categorical notions. Moreover\, I wi
ll provide coherence theorems allowing the strictification of closed (resp
. compact closed) bicategories to closed permutative Gray monoids. Finally
\, I will provide examples\, and a detailed exposition of one version of t
he expected compact closed structure on the bicategory with manifolds as o
bjects\, cobordisms as 1-arrows\, and cobordisms of cobordisms as 2-arrows
\, which occurs in the theory of once-extended TQFTs. This is joint work w
ith Nick Gurski and David Yetter.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov (Moscow Institute of Physics & Technology)
DTSTART:20250318T150000Z
DTEND:20250318T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/55
DESCRIPTION:Title: 10 years of Gkn: towards invariants of knots and links\nby V
assily O. Manturov (Moscow Institute of Physics & Technology) as part of F
eza Gursey Center Higher Structures Seminars\n\n\nAbstract\nIt has been 10
years since the author introduced groups Gkn depending on two natural num
bers n>k and constructed invariants of many configuration spaces valued 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 and G4n.
We shall discuss how to construct similar invariants for n-component links
and describe various possible ways what to do with knots (single componen
t). The approach uses closed braids and Markov moves. Many unsolved probl
ems will be formulated.\n\nZoom details have been changed\, please find th
e new ID and Password below:\nMeeting ID: 935 6390 4955 \nPasscode: 699568
\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Raptis (Aristotle University of Thessaloniki)
DTSTART:20250401T150000Z
DTEND:20250401T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/56
DESCRIPTION:Title: From derivators and ∞-categories to ∞-derivators\nby Geo
rge Raptis (Aristotle University of Thessaloniki) as part of Feza Gursey C
enter Higher Structures Seminars\n\n\nAbstract\nThe theory of derivators i
s an approach to homotopical algebra that focuses on the idea of enhancing
the classical homotopy category ho(C) of a homotopy theory C by the colle
ction of the homotopy categories of diagrams in C all at once. The resulti
ng objects turn out to be much richer than the homotopy category alone and
this viewpoint has been useful for expressing homotopical universal prope
rties. At the same time\, this approach is different from (and less strong
than) the methods of higher category theory - which has been developed an
d used in recent years for related purposes with great impact in various a
reas of research. I will survey the basic theory\, applications and exampl
es of derivators\, and then I will discuss the general notion of an ∞-de
rivator\, as a natural higher categorical extension of ordinary derivators
. This generalization is based on the use of the homotopy n-category\, for
1≤n≤∞\, it bridges the gap between derivators and ∞-categories\,
and it provides a common framework of reference for both types of objects/
approaches.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Li (Tsinghua University)
DTSTART:20250415T100000Z
DTEND:20250415T110000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/57
DESCRIPTION:Title: Stochastic process and algebraic index\nby Si Li (Tsinghua U
niversity) as part of Feza Gursey Center Higher Structures Seminars\n\n\nA
bstract\nWe explain a stochastic approach to topological field theory and
present a case study of quantum mechanical model and its relation to non-c
ommutative geometry and algebraic index.\n\nMeeting ID: 935 6390 4955\nPas
scode: 699568\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zimmermann (Université de Picardi)
DTSTART:20250429T150000Z
DTEND:20250429T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/58
DESCRIPTION:Title: On the ring theory of differential graded algebras\nby Alexa
nder Zimmermann (Université de Picardi) as part of Feza Gursey Center Hig
her Structures Seminars\n\n\nAbstract\nLet R be a commutative ring. Follow
ing Cartan (1954) a differential graded algebra (A\,d) over R is a Z-grade
d 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 any homo
geneous a\, b ∈ A of degree ∣a∣\, resp. ∣b∣. Similarly\, a diffe
rential graded module is defined as a Z-graded A-module with an endomorphi
sm 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 rec
ently the ring theory of differential graded algebras and differential gra
ded modules remained largely unexplored. The case of acyclic differential
graded algebras was completely classified by Aldrich and Garcia-Rozas in 2
002 and the case of R being a field and A being finite dimensional was con
sidered by Orlov in 2020\, basically with geometric motivations in mind. I
n a more systematic study I studied basic ring theoretical questions\, suc
h as a notion of dg-Jacobson radicals\, a dg- Nakayama lemma\, Ore localis
ation of dg-algebras\, and dg-Goldie’s theorem. Most interestingly\, sev
eral standard properties in general ring theory do not generalise\, but so
me do. We give examples\, and further classify dg-division rings and dg-se
parable dg-field extensions\, and also a dg-version of the classical Levit
zki-Hopkins theorem on artinian respectively semiprimary algebras.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (University of Groningen)
DTSTART:20250513T150000Z
DTEND:20250513T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/59
DESCRIPTION:Title: Zeta and K in F_1-geometry\nby Oliver Lorscheid (University
of Groningen) as part of Feza Gursey Center Higher Structures Seminars\n\n
\nAbstract\nIn this talk we give an overview of zeta functions and K-theor
y in F_1-geometry. We begin with a short historical introduction before we
explain what the zeta functions of an F_1-scheme is. In the second part o
n K-theory\, we begin with a reminder of Quillen's Q-construction before w
e give an impression how it is applied to a specific approach to F_1-geome
try via monoid schemes. The talk is accessible without any preknowledge on
F_1-geometry\, and focus lies on conveying the grand ideas.\n\nMeeting ID
: 935 6390 4955\nPasscode: 699568\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Young (Utah State University)
DTSTART:20251002T120000Z
DTEND:20251002T130000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/60
DESCRIPTION:Title: Z invariants for Lie superalgebras\nby Matthew Young (Utah S
tate University) as part of Feza Gursey Center Higher Structures Seminars\
n\n\nAbstract\nZ invariants of 3-manifolds were introduced in the physics
literature by Gukov\, Pei\, Putrov and Vafa in the context of supersymmetr
ic gauge theory with the goal of categorifying the Reshetikhin-Turaev inva
riants of 3-manifold. Z invariants depend on the input data of a Lie super
algebra and some discrete geometric data on the 3-manifold\, such as a Spi
n-c structure. The goal of this talk is to explain a connection between Z
invariants and 3-manifold invariants associated to non-semisimple categori
es of representations of quantum supergroups. Based on work with Francesco
Costantino\, Matthew Harper and Adam Robertson.\n\nPlease note the unusua
l time and date.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (METU)
DTSTART:20251014T150000Z
DTEND:20251014T160000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/61
DESCRIPTION:Title: Legendrians in derived geometry\nby Kadri İlker Berktav (ME
TU) as part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract
\nThis talk introduces Legendrian structures in derived contact geometry\,
\ncovering key concepts and constructions that lead to a tubular\nneighbor
hood theorem and examples similar to the classical ones. We\nstart by revi
ewing Lagrangians in derived symplectic geometry and then\nintroduce analo
gous structures in the derived contact setting using\ntechniques adapted f
rom the symplectic case.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajan Mehta (Smith College)
DTSTART:20251028T150000Z
DTEND:20251028T160000Z
DTSTAMP:20260422T230719Z
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\nAbstract\n
It is well-known that 2D TQFTs taking values in a category correspond to c
ommutative Frobenius objects in that category. If the target category is t
he category of spans\, it is reasonable to ask if there is a lift to a coh
erent structure (i.e. a Frobenius pseudomonoid) in the bicategory of spans
. Such structures can be neatly described by simplicial sets\, equipped wi
th some additional symmetric group actions\, and satisfying some condition
s known as the "2-Segal conditions". I'll describe this correspondence as
well as a construction that produces examples from any commutative monoid.
This is joint work with Sophia Marx\, building on earlier work with Ivan
Contreras and Walker Stern.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Geisser (Rikkyo University)
DTSTART:20251111T080000Z
DTEND:20251111T090000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/63
DESCRIPTION:Title: Motivic cohomology theories and applications\nby Thomas Geis
ser (Rikkyo University) as part of Feza Gursey Center Higher Structures Se
minars\n\n\nAbstract\nI will define motivic cohomology\, and give an overv
iew over its\nproperties. Then I will discuss applications to arithmetic a
nd algebraic\ngeometry\, focusing on special values of zeta-functions and
class field\ntheory. The talk is aimed at non-experts.\n\nPlease note the
unusual time.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Ankara Yıldırım Beyazıt University)
DTSTART:20251125T180000Z
DTEND:20251125T190000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/64
DESCRIPTION:Title: Two models for higher operads\nby Redi Haderi (Ankara Yıld
ırım Beyazıt University) as part of Feza Gursey Center Higher Structure
s Seminars\n\n\nAbstract\nIn this talk we will describe two models for the
theory of infinity-operads: Lurie's model and the simplicial lists model
(developed in joint work with Özgün Ünlü). We begin by briefly introdu
cing operads as a categorical tool to control and study a variety of algeb
raic structures. As it is known that higher dimensional categorical struct
ures are presentation-sensitive\, different ways of thinking about ordinar
y operads lead to different formulations of a higher variant. Lurie's mode
l is based on the notion of operator category\, while the simplicial lists
model is based on a nerve theorem related to the monoidal envelope associ
ated to an operad. Time permitting\, we will discuss how the two can be re
lated to each other.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Özlem (Mudanya University)
DTSTART:20260203T160000Z
DTEND:20260203T170000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/65
DESCRIPTION:Title: Weakened Axioms\, Idempotent Splittings\, and the Structure of L
earning: From Algebra to AI\nby Semih Özlem (Mudanya University) as
part of Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nWe of
ten think of mathematics as a tower of abstractions\, but it begins\nwith
something deeply human: the act of telling things apart. In this\ntalk\, I
’ll explore how this simple idea—splitting and\nfocusing—manifests a
cross different fields\, from linear algebra to\nmotives to machine learni
ng.\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 idempotent\
,\nsplitting the space into what is preserved and what is annihilated. Thi
s\nsplitting phenomenon appears in surprising places: in the theory of\nmo
tives\, where projectors decompose varieties\; in knot theory\, where\nJon
es–Wenzl projectors filter diagram algebras\; and in deep learning\,\nwh
ere attention mechanisms focus on relevant features.\n\nI’ll introduce t
he topos-theoretic model of neural networks\n(Belfiore–Bennequin) and su
ggest that learning difficulties like\ncatastrophic forgetting and general
ization gaps can be viewed as\nhomotopical obstructions to achieving “ni
ce” (fibrant) network\nstates. Architectural tools like residual connect
ions and attention can\nthen be seen as learned\, conditional idempotents
—adaptable splitters\nthat help networks organize information.\n\nThis t
alk is an invitation to think structurally across disciplines. I\nwon’t
present finished theorems\, but a framework of connections that\nlinks mot
ivic philosophy\, categorical algebra\, and the practice of\nmachine learn
ing. The goal is to start a conversation: can tools from\npure mathematics
—obstruction theory\, homotopy colimits\,\nderivators—help us design m
ore robust\, interpretable\, and composable\nlearning systems?\n\nNo exper
tise in motives\, knots\, or AI is required—only curiosity about\nhow id
eas weave together.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dogancan Karabaş (Temple University Japan)
DTSTART:20260217T100000Z
DTEND:20260217T110000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/66
DESCRIPTION:Title: Gluing Methods for DG Categories from Geometry\nby Dogancan
Karabaş (Temple University Japan) as part of Feza Gursey Center Higher St
ructures Seminars\n\n\nAbstract\nMany dg categories arising in geometry ad
mit 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 combinatorial des
cription of such gluings\, namely homotopy colimits. This approach leads t
o explicit computations of invariants in symplectic geometry and microloca
l sheaf theory. In particular\, I will describe our result proving a conje
cture of Kontsevich that wrapped Fukaya categories of Weinstein manifolds
are Morita equivalent to dg algebras of finite type.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kürşat Sözer (Université de Lille)
DTSTART:20260303T160000Z
DTEND:20260303T170000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/67
DESCRIPTION:Title: Braiding self-equivalences with bordism\nby Kürşat Sözer
(Université de Lille) as part of Feza Gursey Center Higher Structures Sem
inars\n\n\nAbstract\nSpaces of homotopy self-equivalences capture subtle g
eometric and\nhomotopy-theoretic information about manifolds\, but are oft
en difficult\nto analyze directly. In this talk\, I will present a framewo
rk that\nrelates these spaces to bordism theories by organizing normal bun
dle\ndata in a homotopy-theoretic way. For a closed smooth or topological\
nmanifold M of dimension at least four\, we show that spaces of homotopy\n
self-equivalences preserving prescribed normal information fit into a\nhig
hly cartesian square involving infinite loop spaces representing\ncertain
bordism theories. This leads to braids of interlocking exact\nsequences co
nnecting homotopy groups of self-equivalence spaces with\nbordism groups\,
providing a conceptual generalization of earlier work of\nHambleton–Kre
ck on 4-manifolds. This is joint work with Ian Hambleton\nand Robin Sroka.
\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kensuke Arakawa (Kyoto University)
DTSTART:20260317T080000Z
DTEND:20260317T090000Z
DTSTAMP:20260422T230719Z
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 Higher St
ructures Seminars\n\n\nAbstract\nA common phenomenon in higher category th
eory is that nontrivial\ninfinity categories often arise as localizations
of simpler (often\nordinary) categories. A natural question\, therefore\,
is: how can we\nrecognize when an infinity categoy is obtained in this way
? Mazel-Gee's\nlocalization theorem provides a useful criterion for this.
In recent\nyears\, similar questions have begun to appear in the operadic
setting\,\nmotivated by internal developements in higher operads and by ex
amples\nfrom mathematical physics (such as factorization algebra and algeb
raic\nquantum field theory). This raises a basic problem: how can we detec
t\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 operads.\
nAfter explaining the ideas behind the proof\, I will discuss several\nexa
mple applications to cyclic operads and factorization algebras.\n\nPlease
note the unusual time.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shannon Rubin (Yau Mathematical Sciences Center - Tsinghua Univers
ity)
DTSTART:20260331T130000Z
DTEND:20260331T140000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/69
DESCRIPTION:Title: A hotomotopical invariant of Weinstein surfaces\nby Shannon
Rubin (Yau Mathematical Sciences Center - Tsinghua University) as part of
Feza Gursey Center Higher Structures Seminars\n\n\nAbstract\nIn symplectic
geometry\, a Weinstein surface W can be understood by\ncombinatorial data
on its skeleton\, which is generically a finite\ntrivalent graph G. Motiv
ated by the microlocal theory of sheaves\, there\nis a naturally associate
d diagram D of differential-graded categories\,\ndefined over the quiver w
hich replaces each edge of G by a cospan. We\ncall such quivers 'graphic'.
After adding in appropriate homological\nshifts\, the homotopy limit of D
yields an invariant of W\, so we are\nmotivated to find explicit presenta
tions for these homotopy limits.\n\nAbstracting the story above\, we fix a
n arbitrary graphic quiver Q. Given\nany model category M (above we had M
= dg-categories) we consider\nM-valued diagrams over Q. In this talk I wil
l present a combinatorial\ncharacterization of all such diagrams D which a
re suitably 'fibrant\,'\nwhich in particular implies that the homotopy lim
it of D is just its\nclassical limit. Analogous to the calculation of deri
ved functors in\nhomological algebra\, this yields an explicit formula for
the homotopy\nlimit of any diagram.\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Willerton (University of Sheffield)
DTSTART:20260414T160000Z
DTEND:20260414T170000Z
DTSTAMP:20260422T230719Z
UID:FezaGurseyHigher/70
DESCRIPTION:Title: The projection formula\, extranatural transformations and surfac
e diagrams in a monoidal double category\nby Simon Willerton (Universi
ty of Sheffield) as part of Feza Gursey Center Higher Structures Seminars\
n\n\nAbstract\nThis talk is motivated by trying to understand how closed m
onoidal\ncategories fit into higher categorical frameworks\, in particular
to\nunderstand why\, in abstract terms\, the projection formula -- f_!(a
x\nf^*b) = f_!(a) x b -- holds for an adjunction f_! -| f^* when f^* stron
g\nclosed monoidal. The circle of ideas involves the notion of\nextranatu
ral transformation\, which is key to a formal definition of\nclosed monoid
al category. These can be represented graphically using\n'surface diagram
s' and it transpires that these actually have a natural\ninterpretation in
terms of the double category of categories\, functors\nand profunctors.
Along the way we will see the notion of conjugation\nfor adjunctions of tw
o variables which will help formalize the\nprojection formula result.\n[Se
e also https://arxiv.org/abs/2501.01881]\n
LOCATION:https://researchseminars.org/talk/FezaGurseyHigher/70/
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