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BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20201005T104000Z
DTEND:20201005T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/1
DESCRIPTION:Title: C
ommutative $d$-torsion $K$-theory and its applications\nby Cihan Okay
(Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held i
n SB-Z11.\n\nAbstract\nCommutative $K$-theory is introduced by Adem-Gomez-
Lind-Tillmann as a generalized cohomology theory obtained from topological
$K$-theory. The construction uses classifying spaces for commutativity\,
first introduced by Adem-Cohen-Torres Giese. In this talk we are intereste
d in a $d$-torsion version of this construction: Let $G$ be a topological
group. The aforementioned classifying space $B(\\mathbb{Z}/d\,G)$ is assem
bled from tuples of pairwise commuting elements in $G$ whose order divides
$d$. We will describe the homotopy type of this space when $G$ is the sta
ble unitary group\, following the ideas of Gritschacher-Hausmann. The corr
esponding generalized cohomology theory will be called the commutative $d$
-torsion $K$-theory\, and will be denoted by $k\\mu_d$. Our motivation for
studying this cohomology theory comes from applications to operator-theor
etic problems that arise in quantum information theory. For this we introd
uce another spectrum obtained from $k\\mu_d$ and show that a famous constr
uction from the study of quantum contextuality\, known as Mermin's square\
, corresponds to a non-trivial class in this generalized cohomology theory
. This refines the topological approach to quantum contextuality developed
earlier jointly with Raussendorf.\n\nFor a related talk see https://www.y
outube.com/watch?v=XCTHaASjurg\n
LOCATION:https://researchseminars.org/talk/BilTop/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Surojit Ghosh (University of Haifa)
DTSTART:20201019T104000Z
DTEND:20201019T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/2
DESCRIPTION:Title: H
igher differentials in Adams spectral sequence\nby Surojit Ghosh (Univ
ersity of Haifa) as part of Bilkent Topology Seminar\n\nLecture held in SB
-Z11.\n\nAbstract\nThe $E_2$-term of the Adams spectral sequence may be id
entified with certain derived functors\, and this also holds for other Bou
sfield-Kan types spectral sequence.\n\nIn this talk\, I'll explain how the
higher terms of such spectral sequences are determined by truncations of
functors\, defined in terms of certain (spectrally) enriched functor calle
d mapping algebras.\n\nThis is joint work with David Blanc.\n
LOCATION:https://researchseminars.org/talk/BilTop/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Díaz Ramos (Universidad de Málaga)
DTSTART:20201026T104000Z
DTEND:20201026T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/3
DESCRIPTION:Title: O
n Quillen’s conjecture\nby Antonio Díaz Ramos (Universidad de Mála
ga) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbst
ract\nQuillen’s conjecture relates an algebraic invariant and a homotopy
invariant of a finite group. The conjecture is known to hold for several
families of groups since the work of Quillen\, Aschbacher\, Smith and Alpe
rin in the 80’s and 90’s. Here we present a new geometric approach to
the subject.\n
LOCATION:https://researchseminars.org/talk/BilTop/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Gritschacher (University of Copenhagen)
DTSTART:20201102T104000Z
DTEND:20201102T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/4
DESCRIPTION:Title: O
n the space of commuting $n$-tuples in a Lie group\nby Simon Gritschac
her (University of Copenhagen) as part of Bilkent Topology Seminar\n\nLect
ure held in SB-Z11.\n\nAbstract\nThe space of $n$-tuples of pairwise commu
ting elements in a compact Lie group $G$ can be identified with a moduli s
pace of flat $G$-bundles over the $n$-torus. Borel\, Friedman\, and Morgan
studied spaces of commuting pairs and triples to answer questions arising
in mathematical physics. Often the focus lies on the enumeration of conne
cted components\, but little is known about their higher homotopy and homo
logy groups. In this talk I will describe the second homology group of the
space of commuting pairs in any connected Lie group. Some results about a
bout $n$-tuples for $n>2$ in groups of type A or C are also obtained. This
is joint work with Alejandro Adem and Jose Manuel Gomez.\n
LOCATION:https://researchseminars.org/talk/BilTop/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Adem (University of British Columbia)
DTSTART:20201116T150000Z
DTEND:20201116T155000Z
DTSTAMP:20260422T102822Z
UID:BilTop/5
DESCRIPTION:Title: F
ree Finite Group Actions on Rational Homology Spheres\nby Alejandro Ad
em (University of British Columbia) as part of Bilkent Topology Seminar\n\
nLecture held in SB-Z11.\n\nAbstract\nIn this talk we will describe joint
work with Ian Hambleton on finite group actions on rational homology 3-sph
eres\, focusing on the case of untwisted actions. Applications to hyperbol
ic manifolds and possible extensions to higher dimensional manifolds will
also be discussed. Several examples will be provided.\n
LOCATION:https://researchseminars.org/talk/BilTop/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Williams (University of British Columbia)
DTSTART:20201207T154000Z
DTEND:20201207T163000Z
DTSTAMP:20260422T102822Z
UID:BilTop/6
DESCRIPTION:Title: A
1 homotopy groups of GL_n and a problem of Suslin's\nby Ben Williams (
University of British Columbia) as part of Bilkent Topology Seminar\n\nLec
ture held in SB-Z11.\n\nAbstract\nLet $F$ be an infinite field. Andrei Sus
lin constructed a morphism from the (Quillen) K-theory of $F$ to the Milno
r K-theory of $F$: $s_n : K_n(F) \\to K_n^M(F)$. He proved that the image
of $s_n$ contains $(n-1)! K_n^M(F)$. He raised the question of whether thi
s accounted for the whole image—it was known to when $n$ is $1$\, $2$ or
$3$. In this talk I will explain how one can partially recover this morph
ism as a morphism of $A^1$-homotopy groups of down-to-earth objects\, and
I will show how this tells us some things about Suslin's question when $n$
is $4$ and settles it when $n$ is $5$. This talk represents joint work wi
th Aravind Asok and Jean Fasel.\n
LOCATION:https://researchseminars.org/talk/BilTop/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aslı Güçlükan (Dokuz Eylul University)
DTSTART:20201012T104000Z
DTEND:20201012T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/7
DESCRIPTION:Title: S
mall covers over a product of simplices\nby Aslı Güçlükan (Dokuz E
ylul University) as part of Bilkent Topology Seminar\n\nLecture held in SB
-Z11.\n\nAbstract\nChoi shows that there is a bijection between Davis–Ja
nuszkiewicz equivalence classes of small covers over an $n$-cube and the s
et of acyclic digraphs with $n$-labeled vertices. Using this\, one can obt
ain a bijection between weakly $(\\mathbb{Z}/2)^n$-equivariant homeomorphi
sm classes of small covers over an $n$-cube and the isomorphism classes of
acyclic digraphs on labeled $n$ vertices up to local complementation and
reordering vertices. To generalize these results to small covers over a p
roduct of simplices we introduce the notion of $\\omega$-weighted digraphs
for a given dimension function $\\omega$. It turns out that there is a bi
jection between Davis–Januszkiewicz equivalence classes of small covers
over a product of simplices and the set of acyclic $\\omega$-weighted digr
aphs. After introducing the notion of an $\\omega$-equivalence\, we also s
how that there is a bijection between the weakly $(\\mathbb{Z}/2)^n$-equiv
ariant homeomorphism classes of small covers over $\\Delta^{n_1}\\times\\
cdots \\times \\Delta^{n_k}$ and the set of $\\omega$-equivalence classes
of $\\omega$-weighted digraphs with $k$-labeled vertices $\\{v_1\, \\cdots
\, v_k\\}$ where $\\omega$ is defined by $\\omega(v_i)=n_i$ and $n=n_1+\\c
dots+n_k$. As an example\, we obtain a formula for the number of weakly $(
\\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over
a product of three simplices.\n
LOCATION:https://researchseminars.org/talk/BilTop/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20201214T154000Z
DTEND:20201214T163000Z
DTSTAMP:20260422T102822Z
UID:BilTop/8
DESCRIPTION:Title: D
escent and vanishing in algebraic K-theory via group actions\nby Akhil
Mathew (University of Chicago) as part of Bilkent Topology Seminar\n\nLec
ture held in SB-Z11.\n\nAbstract\nI will explain some descent and vanishin
g results in the\nalgebraic K-theory of ring spectra\, motivated by the re
dshift\nphilosophy of Ausoni-Rognes. These results are all proved by\ncons
idering group actions on stable $\\infty$-categories and their\nK-theory\,
as well as some tools coming from chromatic homotopy theory.\nJoint work
with Dustin Clausen\, Niko Naumann\, and Justin Noel.\n
LOCATION:https://researchseminars.org/talk/BilTop/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernardo Villarreal (National Autonomous University of Mexico)
DTSTART:20201130T140000Z
DTEND:20201130T145000Z
DTSTAMP:20260422T102822Z
UID:BilTop/9
DESCRIPTION:Title: A
Lie group analogue of the coset poset of abelian subgroups\nby Bernar
do Villarreal (National Autonomous University of Mexico) as part of Bilken
t Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTo a group G an
d a family of subgroups F\, one can associate a simplicial complex C(F\,G)
\, whose simplices are in correspondence with the chains of cosets of G\,
with respect to F. Abels and Holz studied some homotopy properties of C(F\
,G)\, and their relationship with G. For example\, C(F\,G) is simply-conne
cted if and only if G is the amalgamated product of subgroups in F along i
ts intersections. C. Okay noted that for an arbitrary group G\, specializi
ng the simple-connectivity of C(F\,G) to the family of abelian subgroups\,
forces G to be abelian.\n\nIn this talk I will discuss a Lie group analog
ue of C(F\,G) with respect to the family of abelian subgroups\, arising fr
om the work of Adem\, Cohen and Torres-Giese. The main result I will descr
ibe is recent work with O. Antolín-Camarena and S. Gritschacher which dea
ls with the analogue of Okay’s result for compact Lie groups.\n
LOCATION:https://researchseminars.org/talk/BilTop/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sumeyra Sakalli (Max Planck Institute for Mathematics)
DTSTART:20201221T104000Z
DTEND:20201221T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/10
DESCRIPTION:Title:
Exotic 4-Manifold Constructions via Pencils of Curves of Small Genus and
Surgeries\nby Sumeyra Sakalli (Max Planck Institute for Mathematics) a
s part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\
nExotic manifolds are smooth manifolds which are homeomorphic but not\ndif
feomorphic to each other. Constructing exotic manifolds in dimension\nfour
has been an active research area in low dimensional and symplectic\ntopol
ogy over the last 30 years. In this talk\, we will first discuss major\nop
en problems and some recent progress in 4-manifolds theory. Then we\nwill
discuss our constructions of exotic 4-manifolds via pencils of complex\ncu
rves of small genus and via symplectic and smooth surgeries. Some of\nour
results that will be presented are joint with A. Akhmedov.\n
LOCATION:https://researchseminars.org/talk/BilTop/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgur Bayindir (University of Paris 13)
DTSTART:20201123T104000Z
DTEND:20201123T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/11
DESCRIPTION:Title:
Algebraic $K$-theory of $THH(\\mathbb{F}_p)$\nby Ozgur Bayindir (Unive
rsity of Paris 13) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nIn this work\, we study $THH(\\mathbb{F}_p)$ from var
ious perspectives. We\nstart with a new identification of $THH(\\mathbb{F}
_p)$ as an $E_2$-algebra.\nFollowing this\, we compute the $K$-theory of $
THH(\\mathbb{F}_p)$.\n\nThe first part of my talk is going to consist of a
n introduction to\nalgebraic $K$-theory and the Nikolaus Scholze approach
to trace methods.\nIn the second part\, I will introduce our results and t
he tools we\ndevelop to study the topological Hochschild homology of grade
d ring\nspectra and formal differential graded algebras.\n\nThis is a join
t work with Tasos Moulinos.\n
LOCATION:https://researchseminars.org/talk/BilTop/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20210208T103000Z
DTEND:20210208T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/12
DESCRIPTION:Title:
The Dade group of a finite group and dimension functions\nby Ergun Yal
cin (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture he
ld in SB-Z11.\n\nAbstract\nIf $G$ is a $p$-group and $k$ is a field of cha
racteristic $p$\, then the Dade group $D(G)$ of $G$ \nis the group whose e
lements are the equivalence classes of capped endo-permutation $kG$-module
s\, \nwhere the group operation is given by the tensor product over $k$. T
he Dade groups of p-groups have been \nstudied intensively in the last 20
years\, and a complete description of the group $D(G)$ has been \ngiven by
Bouc in terms of the genetic sections of $G$.\n\nFor finite groups the si
tuation is more complicated. There are two definitions of a Dade group of
a finite\ngroup given by Urfer and Lassueur\, however both definitions hav
e some shortcomings. In a recent work \nwith Gelvin\, we give a new defini
tion for the Dade group $D(G)$ of a finite group $G$ by introducing a noti
on \nof Dade $kG$-module as a generalization of endo-permutation modules.\
n \n\nWe show that there is a well-defined surjective group homomorphism $
\\Psi$ from the group of super class \nfunctions $C(G\, p)$ to the Dade gr
oup $D^{\\Omega} (G)$ generated by relative syzygies. Our main theorem \ni
s the verification that the subgroup of $C(G\,p)$ consisting of the dimens
ion functions of k-orientable real representations \nof $G$ lies in the ke
rnel of $\\Psi_G$. In the proof we consider Moore $G$-spaces which are the
equivariant versions \nof spaces which have nonzero reduced homology in o
nly one dimension\, and use the techniques \nfrom homological algebra over
the orbit category.\n \n\nThis is a joint work with Matthew Gelvin.\n
LOCATION:https://researchseminars.org/talk/BilTop/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen)
DTSTART:20210215T103000Z
DTEND:20210215T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/13
DESCRIPTION:Title:
An application of neighbourhoods in directed graphs in the classification
of binary dynamics\nby Ran Levi (University of Aberdeen) as part of Bi
lkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nA binary st
ate on a graph means an assignment of binary values to its vertices. For e
xample\, if one encodes a network of spiking neurons as a directed graph\,
then the spikes produced by the neurons at an instant of time is a binary
state on the encoding graph. Allowing time to vary and recording the spi
king patterns of the neurons in the network produces an example of a bina
ry dynamics on the encoding graph\, namely a one-parameter family of bina
ry states on it. The central object of study in this talk is the neighbour
hood of a vertex $v$ in a graph $\\mathcal{G}$\, namely the subgraph of $\
\mathcal{G}$ that is generated by $v$ and all its direct neighbours in $\\
mathcal{G}$. We present a topological/graph theoretic method for extracti
ng information out of binary dynamics on a graph\, based on a selection of
a relatively small number of vertices and their neighbourhoods. As a test
case we demonstrate an application of the method to binary dynamics that
arises from sample activity on the Blue Brain Project reconstruction of co
rtical tissue of a rat.\n
LOCATION:https://researchseminars.org/talk/BilTop/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calista Bernard (Stanford University)
DTSTART:20210308T103000Z
DTEND:20210308T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/14
DESCRIPTION:Title:
Twisted homology operations\nby Calista Bernard (Stanford University)
as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract
\nIn the 70s\, Fred Cohen and Peter May gave a description of the mod $p$
homology of a free $E_n$-algebra in terms of certain homology operations\,
known as Dyer--Lashof operations\, and the Browder bracket. These operati
ons capture the failure of the $E_n$ multiplication to be strictly commuta
tive\, and they prove useful for computations. After reviewing the main id
eas from May and Cohen's work\, I will discuss a framework to generalize t
hese operations to homology with certain twisted coefficient systems and g
ive a complete classification of twisted operations for $E_{\\infty}$-alge
bras. I will also explain computational results that show the existence of
new operations for $E_2$-algebras.\n
LOCATION:https://researchseminars.org/talk/BilTop/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (University of Southampton)
DTSTART:20210315T103000Z
DTEND:20210315T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/15
DESCRIPTION:Title:
Bieberbach group and decomposing flat manifolds\nby Ho Yiu Chung (Univ
ersity of Southampton) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nAn n-dimensional Bieberbach group is a discrete\,
cocompact torsion-free subgroup of the group of isometries of Euclidean n
-space. In this talk\, we will introduce the three Bieberbach theorems in
order to understand the algebraic structure of Bieberbach groups. Such gro
ups are interesting because they arise as fundamental group of compact fla
t Riemannian manifolds. In the second half of the talk\, we will discuss t
he Vasquez invariant of finite groups which was introduced by A. T. Vasque
z in 1970. This invariant is related to a decomposition theorem of sorts f
or compact flat Riemannian manifolds. We will discuss several results abou
t such invariant.\n
LOCATION:https://researchseminars.org/talk/BilTop/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20210322T103000Z
DTEND:20210322T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/16
DESCRIPTION:Title:
Higher order Toda brackets\nby Aziz Kharoof (University of Haifa) as p
art of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTo
da brackets are a type of higher homotopy operation. Like Massey products\
, they are not always defined\, and their value is indeterminate. Neverthe
less\, they play an important role in algebraic topology and related field
s:
Toda originally constructed them as a tool for comput
ing homotopy groups of spheres. Adams later showed that they can be used t
o calculate differentials in spectral sequences.\n\nAfter reviewing the co
nstruction and properties of the classical Toda bracket\, we shall describ
e a higher order version\, there are two ways to do that. We will provide
a diagrammatic description for the system we need to define the higher ord
er Toda brackets\, then we will use that to give alternative definition us
ing the homotopy cofiber.\n
LOCATION:https://researchseminars.org/talk/BilTop/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Sanchez Ocal (Texas A&M University)
DTSTART:20210329T103000Z
DTEND:20210329T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/17
DESCRIPTION:Title:
Hochschild cohomology of general twisted tensor products\nby Pablo San
chez Ocal (Texas A&M University) as part of Bilkent Topology Seminar\n\nLe
cture held in SB-Z11.\n\nAbstract\nThe Hochschild cohomology is a tool for
studying associative algebras that has a lot of structure: it is a Gerste
nhaber algebra. This structure is useful because of its applications in de
formation and representation theory\, and recently in quantum symmetries.
Unfortunately\, computing it remains a notoriously difficult task. In this
talk we will present techniques that give explicit formulas of the Gerste
nhaber algebra structure for general twisted tensor product algebras. This
will include an unpretentious introduction to this cohomology and to our
objects of interest\, as well as the unexpected generality of the techniqu
es. This is joint work with Tekin Karadag\, Dustin McPhate\, Tolulope Oke\
, and Sarah Witherspoon.\n
LOCATION:https://researchseminars.org/talk/BilTop/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (Istanbul Technical University)
DTSTART:20210405T103000Z
DTEND:20210405T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/18
DESCRIPTION:Title:
From filtered complexes to matroids to cobordisms: an unlikely story in th
ree parts\nby Atabey Kaygun (Istanbul Technical University) as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nOur stor
y starts with a question in data analysis and computational topology/geome
try. Given a finite sample of points from an unknown manifold embedded in
an affine space\, how can we extract information about topological invaria
nts of the said manifold? Even though the answer is known for a long time\
, the connections of the question with computational geometry and data ana
lysis have only recently been made. We will review these connections\, and
then move on to the "representation problem" of homology of filtered comp
lexes. Specifically\, we will explain why "bar-codes" are enough for filte
red complexes over reals\, but why there is no such hope for other seeming
ly nice posets. Then we will talk about why matroids and cobordisms (of sp
heres) might naturally provide us the necessary tools for devising a solut
ion for this problem.\n
LOCATION:https://researchseminars.org/talk/BilTop/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rune Haugseng (Norwegien University of Science and Technology)
DTSTART:20210412T103000Z
DTEND:20210412T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/19
DESCRIPTION:Title:
Higher Morita categories\nby Rune Haugseng (Norwegien University of Sc
ience and Technology) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nClassical Morita theory for associative algebras c
an be described in terms of a 2-category with associative algebras as obje
cts\, bimodules as morphisms\, and bimodule homomorphisms as 2-morphisms\;
this can be further enhanced to a double category that also includes alge
bra homomorphisms. More generally\, we can consider 2-categories and doubl
e categories of enriched categories and bimodules between them. I will dis
cuss homotopical versions of these structures and their higher-dimensional
generalizations to $E_n$-algebras and enriched n-categories\, which are o
f interest as targets for fully extended TQFTs.\n
LOCATION:https://researchseminars.org/talk/BilTop/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Scoccola (Michigan State University)
DTSTART:20210419T123000Z
DTEND:20210419T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/20
DESCRIPTION:Title:
Approximate and discrete vector bundles in theory and applications\nby
Luis Scoccola (Michigan State University) as part of Bilkent Topology Sem
inar\n\nLecture held in SB-Z11.\n\nAbstract\nSynchronization problems\, su
ch as the problem of reconstructing a 3D shape from a set of 2D projection
s\, can often be modeled by principal bundles. Similarly\, the application
of local PCA to a point cloud concentrated around a manifold approximates
the tangent bundle of the manifold. In the first case\, the characteristi
c classes of the bundle provide obstructions to global synchronization\, w
hile\, in the second case\, they provide topological information of the ma
nifold beyond its homology\, and give obstructions to dimensionality reduc
tion. I will describe joint work with Jose Perea in which we propose notio
ns of approximate and discrete vector bundle\, study the extent to which t
hey determine true vector bundles\, and give algorithms for the stable and
consistent computation of low-dimensional characteristic classes directly
from these combinatorial representations.\n
LOCATION:https://researchseminars.org/talk/BilTop/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Romero (Universidad de la Rioja)
DTSTART:20210503T103000Z
DTEND:20210503T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/21
DESCRIPTION:Title:
Effective homology and perturbation theory for computations in algebraic t
opology\nby Ana Romero (Universidad de la Rioja) as part of Bilkent To
pology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk we wil
l present the theory of effective homology\, a technique which can be used
for computing homology and homotopy groups of complicated spaces. We will
also present some perturbation lemmas\, which are the main ingredient to
determine the effective homology of many spaces. Both techniques are imple
mented in the computer algebra system Kenzo\, which has made it possible t
o determine homology and homotopy groups of spaces of infinite type. We wi
ll finish the talk with some examples of calculations.\n
LOCATION:https://researchseminars.org/talk/BilTop/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20210301T133000Z
DTEND:20210301T143000Z
DTSTAMP:20260422T102822Z
UID:BilTop/22
DESCRIPTION:Title:
Variants of the Waldhausen S-construction\nby Julie Bergner (Universit
y of Virginia) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z
11.\n\nAbstract\nThe S-construction\, first defined in the setting of cofi
bration categories by Waldhausen\, gives a way to define the algebraic K-t
heory associated to certain kinds of categorical input. It was proved by
Galvez-Carrillo\, Kock\, and Tonks that the result of applying this constr
uction to an exact category is a decomposition space\, also called a 2-Seg
al space\, and Dyckerhoff and Kapranov independently proved the same resul
t for the slightly more general input of proto-exact categories. In joint
work with Osorno\, Ozornova\, Rovelli\, and Scheimbauer\, we proved that
these results can be maximally generalized to the input of augmented stabl
e double Segal spaces\, so that the S-construction defines an equivalence
of homotopy theories. In this talk\, we'll review the S-construction and
the reasoning behind these stages of generalization. Time permitting\, we
'll discuss attempts to characterize those augmented stable double Segal s
paces that correspond to cyclic spaces\, which is work in progress with Wa
lker Stern.\n
LOCATION:https://researchseminars.org/talk/BilTop/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgun Unlu (Bilkent University)
DTSTART:20210222T103000Z
DTEND:20210222T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/23
DESCRIPTION:Title:
Free Group Actions on Products of Two Equidimensional Spheres\nby Ozgu
n Unlu (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nWe will first review some known restrictions
on finite groups that can act freely on products of two equidimensional s
pheres. Then we will discuss some constructions of free actions of finite
p-groups on products of two equidimensional spheres. Finally\, we will di
scuss some open problems about free $p$-group actions on two equidimension
al spheres.\n
LOCATION:https://researchseminars.org/talk/BilTop/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Baker (University of Glasgow)
DTSTART:20210426T103000Z
DTEND:20210426T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/24
DESCRIPTION:Title:
Duals of P-algebras and their comodules\nby Andrew Baker (University o
f Glasgow) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\
n\nAbstract\nP-algebras are connected graded cocommutative Hopf algebras w
hich are unions of finite dimensional Hopf algebras (which are also Poinca
re duality algebras). These are quasi-Frobenius algebras and have some rem
arkable homological properties. The motivating examples for which the theo
ry was produced are the Steenrod algebra at a prime and large sub and quot
ient \nHopf algebras. \n\nThe dual of a P-algebra is a commutative Hopf al
gebra and I will discuss some homological properties of its comodules. In
particular there is a large class of coherent comodules which admit finite
ly generated projective resolutions\, but finite dimensional comodules hav
e no non-trivial maps from these. \n\nUsing some Cartan-Eilenberg spectral
sequences this can be applied to show that certain Bousfield classes of s
pectra are distinct\, thus extending results of Ravenel.\n
LOCATION:https://researchseminars.org/talk/BilTop/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (University of Warwick)
DTSTART:20211004T103000Z
DTEND:20211004T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/25
DESCRIPTION:Title:
$RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra\nby I
gor Sikora (University of Warwick) as part of Bilkent Topology Seminar\n\n
Lecture held in SB-Z11.\n\nAbstract\nIn non-equivariant topology the ordin
ary homology of a point is described by the dimension axiom and is quite s
imple - namely\, it is concentrated in degree zero. The situation in $G$-e
quivariant topology is different. This is due to the fact that Bredon homo
logy - the equivariant counterpart of the ordinary homology - is naturally
graded over $RO(G)$\, the ring of $G$-representations. Whereas the equiva
riant dimension axiom describes the part of the Bredon homology of a point
which is graded over trivial representations\, it does not put any requir
ements on the rest of the grading - in which the homology may be quite com
plicated.\n\nThe $RO(G)$-graded Bredon homology theories are represented b
y $G$-Eilenberg-MacLane spectra\, and thus the Bredon homology of a point
is the same thing as coefficients of these spectra. During the talk I will
present the method of computing the $RO(C_2)$-graded coefficients of $C_2
$-Eilenberg-MacLane spectra based on the Tate square. As demonstrated by G
reenlees\, the Tate square gives an algorithmic approach to computing the
coefficients of equivariant spectra. In the talk we will discuss how to us
e this method to obtain the $RO(C_2)$-graded coefficients of a $C_2$-Eilen
berg-MacLane spectrum as a $RO(C_2)$-graded abelian group. We will also pr
esent the multiplicative structure of the $C_2$-Eilenberg-MacLane spectrum
associated to the Burnside Mackey functor. This allows us to further desc
ribe the $RO(C_2)$-graded coefficients of any $C_2$-Eilenberg-MacLane spec
trum as a module over the coefficients of the $C_2$-Eilenberg-MacLane spec
trum of the Burnside Mackey functor. Finally\, we will discuss the $RO(C_2
)$-graded ring structure of coefficients of spectra associated to ring Mac
key functors.\n
LOCATION:https://researchseminars.org/talk/BilTop/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tane Vergili (Karadeniz Technical University)
DTSTART:20211011T123000Z
DTEND:20211011T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/26
DESCRIPTION:Title:
Persistence modules and the interleaving distance\nby Tane Vergili (Ka
radeniz Technical University) as part of Bilkent Topology Seminar\n\nLectu
re held in SB-Z11.\n\nAbstract\nIn topological data analysis\, a persisten
ce module is obtained with applying homology with coefficients in some fix
ed field to the increasing family of topological spaces or complexes. The
distance between two persistence modules can be measured with the interlea
ving metric. The collection of persistence modules with the interleaving m
etric fails to be a topological space since it is not a set but a class. F
or this\, one can restrict oneself to the identified sets together with th
e topology induced by the interleaving distance in order to study their ba
sic topological properties. In this talk we are going to discuss persisten
ce modules\, the interleaving distance and the topological properties of t
he considered sets of persistence modules induced by the interleaving dist
ance.\n
LOCATION:https://researchseminars.org/talk/BilTop/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Wu (Hebei Normal University)
DTSTART:20211018T103000Z
DTEND:20211018T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/27
DESCRIPTION:Title:
Hypergraph homology and its applications\nby Jie Wu (Hebei Normal Univ
ersity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\n
Abstract\nIn practical applications\, hypergraph is considered as the most
general mathematical model for network beyond pairwise interactions. From
topological views\, the notion of hypergraph is a generalization of simpl
icial complex. In this talk\, we will explain how to naturally extend simp
licial homology theory to a homology theory on hypergraphs so that algebra
ic topology admits broader applications in practice. As applications in da
ta science\, we will present hypergraph-based persistent cohomology (HPC)
for molecular representations in drug design.\n
LOCATION:https://researchseminars.org/talk/BilTop/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osman Berat Okutan (Florida State University)
DTSTART:20211025T123000Z
DTEND:20211025T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/28
DESCRIPTION:Title:
Persistent Homology and Injectivity\nby Osman Berat Okutan (Florida St
ate University) as part of Bilkent Topology Seminar\n\nLecture held in SB-
Z11.\n\nAbstract\nPersistent homology induced by the simplicial Vietoris-R
ips filtration is a standard method for capturing topological information
from metric spaces. In this talk\, I will describe a more geometric filtra
tion\, obtained through injective metric spaces\, which is equivalent to t
he Vietoris-Rips filtration up to homotopy. Injective metric spaces are th
e injective objects in the category of metric spaces. This new filtration
allows one to see new connections between the geometry and topology of the
underlying space. This is a joint work with Sunhyuk Lim and Facundo Memol
i.\n
LOCATION:https://researchseminars.org/talk/BilTop/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (Norwegian University of Science and Technology)
DTSTART:20211115T103000Z
DTEND:20211115T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/29
DESCRIPTION:Title:
Trigraded spectral sequences for principal fibrations\nby Markus Szymi
k (Norwegian University of Science and Technology) as part of Bilkent Topo
logy Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe Leray--Serre and
the Eilenberg--Moore spectral sequence are fundamental tools for computing
the cohomology of a group or\, more generally\, of a space. In joint work
with Frank Neumann\, we describe the relationship between these two spect
ral sequences in the situation when both of them share the same abutment.
This talk will be an introduction to the topic and our results with many e
xamples.\n
LOCATION:https://researchseminars.org/talk/BilTop/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (EPFL)
DTSTART:20211206T103000Z
DTEND:20211206T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/30
DESCRIPTION:Title:
A topological approach to signatures\nby Darrick Lee (EPFL) as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe path
signature is a characterization of paths initially developed by Chen to s
tudy the topology of loop spaces\, and has recently been used to form the
foundations of rough paths in stochastic analysis\, and provides a powerfu
l feature map for sequential data in machine learning. In this talk\, we r
eturn to the topological foundations in Chen's iterated integral cochain m
odels to develop generalizations of the signature.\n
LOCATION:https://researchseminars.org/talk/BilTop/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayse Borat (Bursa Technical University)
DTSTART:20211220T143000Z
DTEND:20211220T153000Z
DTSTAMP:20260422T102822Z
UID:BilTop/31
DESCRIPTION:Title:
Simplicial analogues of homotopic distance\nby Ayse Borat (Bursa Techn
ical University) as part of Bilkent Topology Seminar\n\nLecture held in SB
-Z11.\n\nAbstract\nHomotopic distance as introduced by Macias-Virgos and M
osquera-Lois in [2]\ncan be realised as a generalisation of topological co
mplexity (TC) and Lusternik\nSchnirelmann category (cat). In this talk\, w
e will introduce a simplicial analogue of\nhomotopic distance (in the sens
e of Ortiz\, Lara\, Gonzalez and Borat as in [3]) and\nshow that it has a
relation with simplicial complexity (as defined in [1]). We will\nalso tak
e a glance at contiguity distance - another simplicial analogue of homotop
ic\ndistance - as introduced in [2] and improved in [4].\nReferences\n\n[1
] J. Gonzalez\, Simplicial Complexity: Piecewise Linear Motion Planning in
Robotics\, New\nYork Journal of Mathematics 24 (2018)\, 279-292.\n[2] E.
Macias-Virgos\, D. Mosquera-Lois\, Homotopic Distance between Maps\, Mathe
matical\nProceedings of the Cambridge Philosophical Society (2021)\, 1-21.
\n[3] C. Ortiz\, A. Lara\, J. Gonzalez\, A. Borat\, A randomized greedy al
gorithm for piecewise linear\nmotion planning\, Mathematics\, Vol 9\, Issu
e 19 (2021).\n[4] A. Borat\, M. Pamuk\, T. Vergili\, Contiguity Distance b
etween Simplicial Maps\, submitted\,\n2020. ArXiv: 2012.10627.\n
LOCATION:https://researchseminars.org/talk/BilTop/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe Universitesi)
DTSTART:20211101T133000Z
DTEND:20211101T143000Z
DTSTAMP:20260422T102822Z
UID:BilTop/32
DESCRIPTION:Title:
An Elmendorf-Piacenza type Theorem for Actions of Monoids\nby Mehmet A
kif Erdal (Yeditepe Universitesi) as part of Bilkent Topology Seminar\n\nL
ecture held in SB-Z11.\n\nAbstract\nIn this talk I will describe a homotop
y theory for actions of monoids that is built by analyzing their ``reversi
ble parts". Let $M$ be a monoid and $G(M)$ be its group completion. I will
show that the category of $M$-spaces and $M$-equivariant maps admits a mo
del structure in which weak equivalences and fibrations are determined by
the standard equivariant homotopy theory of $G(N)$-spaces for each $N\\leq
M$. Then\, I will show that under certain conditions on $M$ this model st
ructure is Quillen equivalent to the projective model structure on the cat
egory of contravariant $\\mathbf{O}(M)$-diagrams of spaces\, where $\\math
bf{O}(M)$ is the category whose objects are induced orbits $M\\times_N G(N
)/H$ for each $N\\leq M$ and $H\\leq G(N)$ and morphisms are $M$-equivaria
nt maps. Finally\, if time permits\, I will state some applications.\n
LOCATION:https://researchseminars.org/talk/BilTop/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART:20211108T143000Z
DTEND:20211108T153000Z
DTSTAMP:20260422T102822Z
UID:BilTop/33
DESCRIPTION:Title:
Geometric Approaches on Persistent Homology\nby Baris Coskunuzer (UT D
allas) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nA
bstract\nPersistent Homology is one of the most important techniques used
in Topological Data Analysis. In the first half of the talk\, we give an i
ntroduction to the subject. In the second half\, we study the persistent h
omology output via geometric topology tools. In particular\, we give a geo
metric description of the term “persistence”. The talk will be non-tec
hnical\, and accessible to graduate students.\n
LOCATION:https://researchseminars.org/talk/BilTop/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Korkmaz (METU)
DTSTART:20211129T103000Z
DTEND:20211129T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/34
DESCRIPTION:Title:
Involution generators of mapping class groups\nby Mustafa Korkmaz (MET
U) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstr
act\nThe mapping class group of a surface plays an important role in low \
ndimensional topology.\nIts various generating sets are known. Since it is
not a quotient of a \ndihedral group\,\nit cannot be generated by two inv
olutions. A generating set consisting \nof 4-5 involutions\nhas been known
for more than 15 years. In this talk I will show how it \nis generated by
3 involutions.\n
LOCATION:https://researchseminars.org/talk/BilTop/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Castellana (Universitat Autònoma de Barcelona)
DTSTART:20211213T103000Z
DTEND:20211213T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/35
DESCRIPTION:Title:
The normalizer decomposition for p-local compact groups\nby Natalia Ca
stellana (Universitat Autònoma de Barcelona) as part of Bilkent Topology
Seminar\n\nLecture held in SB-Z11.\n\nAbstract\n(with Eva Belmont\, Jelena
Grbic\, Kathryn Lesh\, Michelle Strumila) In this project we study the no
rmalizer decomposition of a p-local compact group in a general setting.\nW
hen G is a compact Lie group\, using the information of the fusion system
of G on a maximal\ndiscrete p-toral subgroup\, we recover known decomposit
ions in terms of p-centric p-stubborn p-toral\nsubgroups up to p-completio
n. But this methods allow to also describe some exotic p-compact groups\ni
n terms of a pushout.\n
LOCATION:https://researchseminars.org/talk/BilTop/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nima Rasekh (EPFL)
DTSTART:20211122T103000Z
DTEND:20211122T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/36
DESCRIPTION:Title:
THH and Shadows of Bicategories\nby Nima Rasekh (EPFL) as part of Bilk
ent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTopological H
ochschild homology (THH)\, first defined for ring spectra and then later d
g-categories and spectrally enriched categories\, is an important invarian
t with connections to algebraic K-theory and fixed point methods. The exis
tence of THH in such diverse contexts motivated Ponto to introduce a notio
n that can encompass the various perspectives: a shadow of bicategories. O
n the other side\, many versions of THH have been generalized to the homot
opy coherent setting providing us with motivation to develop an analogous
homotopy coherent notion of shadows.\n\nThe goal of this talk is to use an
appropriate bicategorical notion of THH to prove that a shadow on a bicat
egory is equivalent to a functor out of THH of that bicategory. We then us
e this result to give an alternative conceptual understanding of shadows a
s well as an appropriate definition of a homotopy coherent shadow.\n\nThis
is joint work with Kathryn Hess.\n
LOCATION:https://researchseminars.org/talk/BilTop/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Viruel (Universidad de Málaga)
DTSTART:20220221T103000Z
DTEND:20220221T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/37
DESCRIPTION:Title:
Path Partial Groups\nby Antonio Viruel (Universidad de Málaga) as par
t of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn t
his lecture we shall show how path concatenation in a simple graph G gives
rise to a partial group P(G) that we call the path partial group associat
ed to the graph G. The construction of path partial groups is indeed funct
orial and allows us to embed the category of simple graphs into the catego
ry of partial groups. This embedding is full on automorphism so it shows t
hat any group can be realised as the full group of automorphisms of a part
ial group\, while not every group is the full group of automorphisms of an
honest group. Finally\, thinking of partial grops as simplicial complexes
\, we show that every group is the group of self homotopy equivalences of
a simplicial complex. This is a joint work with Antonio Díaz-Ramos (U. Ma
laga) and Rémi Molinier (U. Grenoble).\n
LOCATION:https://researchseminars.org/talk/BilTop/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20220228T103000Z
DTEND:20220228T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/38
DESCRIPTION:Title:
Higher limits over the fusion orbit category\nby Ergun Yalcin (Bilkent
University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11
.\n\nAbstract\nOne of the open problems related to the homotopy theory of
fusion\nsystems asks whether or not the subgroup decomposition for a p-loc
al finite\ngroup is sharp. The sharpness of the subgroup decomposition is
known to be true\nfor finite group fusion systems\, but in general this pr
oblem is still open except\nfor some special cases. I will describe some n
ew methods for calculating higher\nlimits over the fusion orbit category o
f a discrete group and show how these new\nmethods can be applied to the s
harpness problem. In particular\, we show that\nthe subgroup decomposition
for p-local finite groups is sharp\, if it is sharp\nfor every p-local fi
nite group with nontrivial center.\n
LOCATION:https://researchseminars.org/talk/BilTop/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART:20220314T103000Z
DTEND:20220314T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/39
DESCRIPTION:Title:
An introduction to Vietoris-Rips complexes\nby Henry Adams (Colorado S
tate University) as part of Bilkent Topology Seminar\n\nLecture held in SB
-Z11.\n\nAbstract\nI will give an introduction to Vietoris-Rips complexes
and their uses in applied and computational topology. If a dataset is samp
led from some unknown underlying space (say a manifold)\, then as more and
more samples are drawn\, the Vietoris-Rips persistent homology of the dat
aset converges to the Vietoris-Rips persistent homology of the manifold. B
ut little is known about Vietoris-Rips complexes of manifolds. An exceptio
n is the case of the circle: I will describe how as the scale parameter in
creases\, the Vietoris-Rips complexes of the circle obtain the homotopy ty
pes of the circle\, the 3-sphere\, the 5-sphere\, ...\, until finally they
are contractible. Much less is known about Vietoris-Rips complexes of sph
eres. I will also briefly explain how Vietoris-Rips complexes relate to ge
neralizations of the Borsuk-Ulam theorem and to Gromov-Hausdorff distances
between spheres.\n
LOCATION:https://researchseminars.org/talk/BilTop/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Jardine (Western University)
DTSTART:20220321T133000Z
DTEND:20220321T143000Z
DTSTAMP:20260422T102822Z
UID:BilTop/40
DESCRIPTION:Title:
UMAP for the working mathematician\nby Rick Jardine (Western Universit
y) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstr
act\nThe Healy-McInnes UMAP algorithm is a highly successful clustering to
ol that involves interesting ideas from mathematics and data science:\n\n1
) Spivak's theory of extended pseudo metric spaces (ep-metric spaces)\n2)
TDA constructions in ep-metric spaces\n3) weighted graphs\n4) classical di
mension reduction\n5) graph optimization: fuzzy sets\, cross entropy\n\nI
will explain the algorithm from a mathematical point of view.\n
LOCATION:https://researchseminars.org/talk/BilTop/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toni Annala (University of British Columbia)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260422T102822Z
UID:BilTop/41
DESCRIPTION:Title:
Topologically protected vortex knots and links\nby Toni Annala (Univer
sity of British Columbia) as part of Bilkent Topology Seminar\n\n\nAbstrac
t\nThe physical properties of condensed-matter systems can often be approx
imated by a "mean field" which\, outside a small singular locus of the sys
tem (defects)\, takes values in a topological space M called the order par
ameter space. A topological vortex is a codimension two defect\, about whi
ch the order parameter field winds in a way that corresponds to a non-cont
ractible loop in M. If the fundamental group of the order parameter space
is non-Abelian\, then these vortices exhibit a remarkable behavior: not al
l pairs of topological vortices are free to pass through each other.\n\nIt
is then a natural to wonder if such vortices could be employed in tying r
obust linked structures in physical fields. As a minimum\, such a structur
e should not untie via strand crossings and local reconnections\, which ar
e the usual means of decay for knotted and linked vortex loops. In this ta
lk\, we will present several examples of such structures. Our approach is
based on the fact that if the second homotopy group of M is trivial\, then
the order parameter field admits a combinatorial description\, which\, de
pending on the fundamental group of M\, can be expressed graphically. Henc
e\, finding topologically stable tangled structures reduces to constructin
g nontrivial invariants for "colored" links\, which remain unchanged in st
rand crossings and local reconnections.\n
LOCATION:https://researchseminars.org/talk/BilTop/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université PARIS 13)
DTSTART:20220404T103000Z
DTEND:20220404T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/42
DESCRIPTION:Title:
A Krull-Remak-Schmidt theorem for fusion systems\nby Bob Oliver (Unive
rsité PARIS 13) as part of Bilkent Topology Seminar\n\nLecture held in SB
-Z11.\n\nAbstract\nThe Krull-Remak-Schmidt theorem\, when restricted to fi
nite groups\, implies \nthat every finite group factorizes as a product of
indecomposable subgroups \nwhich are unique up to isomorphism. But the th
eorem actually says much \nmore. For example\, as a special case\, it impl
ies that this factorization is \nunique (not only up to isomorphism) whene
ver the group is perfect or \nhas trivial center. This is important\, for
example\, when describing the \nautomorphisms of the group in terms of the
automorphisms of its \nindecomposable factors.\n\nA similar factorization
theorem is true for fusion systems over finite \n$p$-groups (in fact\, fo
r fusion systems over discrete $p$-toral groups). In \nthis talk\, I plan
to begin by discussing the original theorem for groups \nand sketching its
proof\, and then\, after a brief introduction to fusion \nsystems\, descr
ibe how these ideas can be carried over \nto prove the corresponding resul
t in that setting.\n
LOCATION:https://researchseminars.org/talk/BilTop/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Torres (Trinity Western University)
DTSTART:20220418T140000Z
DTEND:20220418T150000Z
DTSTAMP:20260422T102822Z
UID:BilTop/43
DESCRIPTION:Title:
Sequential Motion Planning assisted by Group Actions\nby Enrique Torre
s (Trinity Western University) as part of Bilkent Topology Seminar\n\nLect
ure held in SB-Z11.\n\nAbstract\nIn this talk I will revisit the concept o
f effectual and effective topological complexity (TC) in the context of se
quential motion planning. These invariants provide a natural context to in
corporate group actions into the study of the motion planning problem. Rel
ated to these invariants\, I will talk about a third version of TC that in
corporates the group action into its planners\, which we call orbital topo
logical complexity. I will discuss how they relate to each other and to th
e TC of the quotient space. I will also present some calculations for acti
ons of the group of order two on orientable surfaces and spheres.\n
LOCATION:https://researchseminars.org/talk/BilTop/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Henke (TU Dresden)
DTSTART:20220425T120000Z
DTEND:20220425T130000Z
DTSTAMP:20260422T102822Z
UID:BilTop/44
DESCRIPTION:Title:
Fusion systems\, linking systems and punctured groups\nby Ellen Henke
(TU Dresden) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11
.\n\nAbstract\nSaturated fusion systems and associated linking systems are
categories modelling the $p$-local structure of finite groups. In particu
lar\, linking systems contain the algebraic information that is needed to
study $p$-completed classifying spaces of fusion systems similarly to $p$
-completed classifying spaces of finite groups. If $G$ is a finite group a
nd $S$ is a Sylow $p$-subgroup of $G$\, then we can construct a saturated
fusion system $\\F_S(G)$ as follows: The objects are all subgroups of $S$\
, and the morphisms between two objects are the injective group homomorphi
sms induced by conjugation with elements of $G$. Saturated fusion systems
which do not arise in this way are called exotic.\n\n\n\nThe concept of a
linking system was generalized by Oliver and Ventura to transporter system
s. Andrew Chermak introduced moreover group-like structures\, called local
ities\, which correspond in a certain way to transporter systems. I will g
ive an introduction to the subject and outline how the theory of localitie
s can be used to prove new theorems on fusion systems. Moreover\, I will r
eport on a project with Assaf Libman and Justin Lynd\, where we study "pun
ctured groups''. Here a transporter system (or a locality) associated to f
usion system $\\F$ over $S$ is called a punctured group if the object set
is the collection of all non-identity subgroups. It should be noted in thi
s context that a fusion system $\\F$ over a $p$-group $S$ can be realized
as a category $\\F_S(G)$ as above if and only if there is a transporter sy
stem whose object set is the full collection of subgroups of $S$. In parti
cular\, to every group fusion system one can associate a punctured group.
In the project with Libman and Lynd\, we determine for many of the known e
xotic fusion systems whether an associated punctured group exists.\n
LOCATION:https://researchseminars.org/talk/BilTop/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Facundo Mémoli (Ohio State University)
DTSTART:20220411T120000Z
DTEND:20220411T130000Z
DTSTAMP:20260422T102822Z
UID:BilTop/45
DESCRIPTION:Title:
The Gromov-Hausdorff distance between spheres\nby Facundo Mémoli (Ohi
o State University) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nThe Gromov-Hausdorff distance is a fundamental tool
in Riemanian geometry\, and also in applied geometry and topology. Whereas
it is often easy to estimate the value of the distance between two given
metric spaces\, its precise value is rarely easy to determine. Some of th
ese estimates follow from considerations related to the notion of 'persist
ent homology' and Gromov's filling radius. However\, these turn out to be
non-sharp.\n\n\nIn this talk I will describe results that we have obtained
which permit calculating the precise value to the Gromov-Hausdorff betwee
n certain pairs of spheres (endowed with their geodesic distance). These r
esults involve lower bounds\, which arise from certain versions of the Bor
suk-Ulam theorem which are applicable to discontinuous maps\, and from the
construction of specialized ``correspondences" between spheres which yie
ld matching upper bounds in some cases.\n
LOCATION:https://researchseminars.org/talk/BilTop/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Blanc (Haifa University)
DTSTART:20230206T103000Z
DTEND:20230206T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/46
DESCRIPTION:Title:
An introduction to infinity categories\nby David Blanc (Haifa Universi
ty) as part of Bilkent Topology Seminar\n\n\nAbstract\nIn studying the hom
otopy theory of topological spaces it soon becomes apparent that the homot
opy category itself is not sufficient\, since many homotopy invariants can
not be described or calculated in that category.\n\nSince there are other
settings\, such as the chain complexes of homological algebra\, in which t
his holds\, Quillen proposed an axiomatization of such situations in terms
of model categories. However\, these turn out\n\nto be too restrictive fo
r dealing with certain questions\, and in particular with homotopy commuta
tive diagrams and the invariants (such as Toda brackets) which they encode
. Dwyer and Kan suggested an\n\nalternative simplicial approach\, which la
ter devolved into several independent models for what we now call infinity
categories\, in terms of simplicially enriched categories\, simplicial sp
aces\, quasi-categories\, and others.\n\nIn the talk we will provide examp
les of questions best addressed in this setting\, and briefly describe the
form they take in the different models\, as time permits.\n
LOCATION:https://researchseminars.org/talk/BilTop/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230213T103000Z
DTEND:20230213T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/47
DESCRIPTION:Title:
Simplicial sets\nby Aziz Kharoof (Bilkent University) as part of Bilke
nt Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThis talk aims
to introduce and recall basic notions on simplicial sets. Apart from basi
c definitions\, we would like to discuss the following notions: weak equiv
alences\, Kan complexes\, Kan fibrations\, and geometric realization. Also
\, the adjunction between singular simplicial set and geometric realizatio
n should be covered.\n
LOCATION:https://researchseminars.org/talk/BilTop/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230220T103000Z
DTEND:20230220T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/48
DESCRIPTION:Title:
Quasicategories\nby Aziz Kharoof (Bilkent University) as part of Bilke
nt Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk w
e will introduce the first model of infinity categories\, namely quasicate
gories. We will discuss the construction of a nerve of a category and thus
embedding of the category of (small) categories in sSet. We will also see
how a topological space gives rise to a quasicategory – i.e.\, via the
fundamental infinity-groupoid construction.\n
LOCATION:https://researchseminars.org/talk/BilTop/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230227T103000Z
DTEND:20230227T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/49
DESCRIPTION:Title:
Basic constructions in quasicategories\nby Igor Sikora (Bilkent Univer
sity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAb
stract\nThe goal of this talk is the discussion of the basic notions and c
onstructions in the theory of infinity categories. We want to discuss the
following constructions: the product of quasicategries\, homotopy category
of a quasicategory\, join\, slices and\, most importantly\, colimits and
limits.\n
LOCATION:https://researchseminars.org/talk/BilTop/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Akkaya (Bilkent University)
DTSTART:20230313T103000Z
DTEND:20230313T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/50
DESCRIPTION:Title:
Model categories I - basic definitions\nby Mustafa Akkaya (Bilkent Uni
versity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\
nAbstract\nThe goal of this talk is to provide basic definitions of the th
eory model categories. We would like to introduce the definition of a mode
l category and its homotopy category. In particular\, this will require a
discussion of fibrations\, cofibrations and weak equivalences\, fibrant an
d cofibrant objects\, cylinder and path objects. Then we will proceed to t
he notion of left and right homotopy and define the homotopy category of a
model category. The whole theory will be shown using two examples: Quille
n model structure on topological spaces and Quillen model structure on sim
plicial sets.\n
LOCATION:https://researchseminars.org/talk/BilTop/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230320T103000Z
DTEND:20230320T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/51
DESCRIPTION:Title:
Model Categories II - Derived functors and Quillen adjunctions\nby Igo
r Sikora (Bilkent University) as part of Bilkent Topology Seminar\n\nLectu
re held in SB-Z11.\n\nAbstract\nHaving the notion of a homotopy category\,
we will define the notion of a derived functor. Further on\, we will proc
eed to the idea of comparing model structures and their homotopy categorie
s by Quillen functors. Therefore we will cover Quillen functors\, Quillen
adjunctions and Quillen equivalences. We will also prove that Quillen mode
l structures on simplicial sets and topological spaces are Quillen equival
ent. The talk will finish with a model structure on simplicial sets which
is relevant for the theory of quasicategories\, i.e.\, the Joyal model str
ucture.\n
LOCATION:https://researchseminars.org/talk/BilTop/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230327T103000Z
DTEND:20230327T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/52
DESCRIPTION:Title:
Simplicial Categories I\nby Igor Sikora (Bilkent University) as part o
f Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this
talk\, we will discuss the second model of infinity categories: categorie
s enriched over simplicial sets. We will start with a short overview of en
riched categories and follow to the simplicial categories. We will also in
troduce simplicial functors and the homotopy category of a simplicial cate
gory. Then we will proceed with the Bergner model structure and sketch the
proof of the fact that it is indeed a model structure.\n
LOCATION:https://researchseminars.org/talk/BilTop/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230403T103000Z
DTEND:20230403T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/53
DESCRIPTION:Title:
Simplicial categories II - Dwyer-Kan localizations\nby Aziz Kharoof (B
ilkent University) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nThe goal of this talk will be to understand the idea
of localization of a category with respect to the class of maps and see ho
w Dwyer-Kan localization is an example of such. Therefore we will start wi
th the notion of a localization of a category. Then we will proceed to sev
eral approaches to the Dwyer-Kan localization - as a derived functor with
specific resolution and the hammock version\, that gives a constructive de
scription of the homotopy category. We will discuss the relation of DK loc
alization of a simplicial model category and of its homotopy category.\n
LOCATION:https://researchseminars.org/talk/BilTop/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgün Ünlü (Bilkent University)
DTSTART:20230410T103000Z
DTEND:20230410T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/54
DESCRIPTION:Title:
Segal spaces I\nby Özgün Ünlü (Bilkent University) as part of Bilk
ent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThis talk wil
l prepare a background for the third model of infinity categories: complet
e Segal spaces. Therefore the following topics should be discussed: bisimp
licial sets\, model structures on functor categories\, Reedy model structu
re as an example of the injective model structure and Rezk nerve of a cate
gory.\n
LOCATION:https://researchseminars.org/talk/BilTop/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université PARIS 13)
DTSTART:20230417T103000Z
DTEND:20230417T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/55
DESCRIPTION:by Bob Oliver (Université PARIS 13) as part of Bilkent Topolo
gy Seminar\n\nLecture held in SB-Z11.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilTop/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230424T103000Z
DTEND:20230424T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/56
DESCRIPTION:Title:
Segal spaces II\nby Igor Sikora (Bilkent University) as part of Bilken
t Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\,
we will continue introducing the third model of infinity categories: compl
ete Segal spaces. The following notions will be covered: Segal spaces\, ho
motopy category of Segal spaces\, completeness of Segal spaces and CSS mod
el structure.\n
LOCATION:https://researchseminars.org/talk/BilTop/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20230502T103000Z
DTEND:20230502T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/57
DESCRIPTION:Title:
Homotopy Coherent Nerve\nby Redi Haderi (Bilkent University) as part o
f Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this
talk\, we aim to understand the equivalences between two different models
of infinity-categories: Simplicial categories and quasi-categories. We wi
ll define the homotopy coherent nerve as a functor from simplicial categor
ies to simplicial sets\, construct its left adjoint\, and we will show how
this gives us a Quillen equivalence between the described model categorie
s.\n
LOCATION:https://researchseminars.org/talk/BilTop/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260422T102822Z
UID:BilTop/58
DESCRIPTION:Title:
Complete Segal spaces and generalizations to higher $(\\infty\,n)$-categor
ies\nby Julie Bergner (University of Virginia) as part of Bilkent Topo
logy Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nComplete Segal spaces
provide one of the nicest models for $(\\infty\,1)$-categories from the p
erspective of homotopy theory\, since the model structure can be obtained
as a localization of the Reedy model structure on simplicial spaces. In t
his talk\, we'll recall complete Segal spaces and their model structure\,
and then compare them with other models. We will then look at some of the
ways these comparisons can be generalized higher $(\\infty\,n)$-categorie
s.\n
LOCATION:https://researchseminars.org/talk/BilTop/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Antonio Torres Castillo (CIMAT)
DTSTART:20230522T153000Z
DTEND:20230522T170000Z
DTSTAMP:20260422T102822Z
UID:BilTop/59
DESCRIPTION:Title:
Stable homotopy type of p-local finite groups via biset functors\nby V
ictor Antonio Torres Castillo (CIMAT) as part of Bilkent Topology Seminar\
n\nLecture held in SB-Z11.\n\nAbstract\nThe Martino-Priddy conjecture (now
a theorem) says that the p-fusion of G can be recovered (up to isomorphis
m) from the unstable homotopy type of BG^p. By making strong use of the Se
gal conjecture\, the same authors approached a stable analogous of that re
sult. In this talk\, we will explore some consequences of the (so-called)
stable Martino-Priddy conjecture and their generalizations for p-local fin
ite groups.\n
LOCATION:https://researchseminars.org/talk/BilTop/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (The University of Virginia)
DTSTART:20230523T133000Z
DTEND:20230523T150000Z
DTSTAMP:20260422T102822Z
UID:BilTop/60
DESCRIPTION:Title:
A story about spans\nby Walker Stern (The University of Virginia) as p
art of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nSp
ans in a category C arise in a variety of disparate contexts\, from the st
udy partially defined functions between sets to Lagrangian correspondences
in symplectic geometry. In this talk\, I will give an overview of some of
these connections and tell a story which leads from algebras in categorie
s of spans to operads. Along the way\, I will discuss past and ongoing wor
k (part of the latter joint with Ivan Contreras and Rajan Mehta) analyzing
and classifying various algebraic structures in spans.\n
LOCATION:https://researchseminars.org/talk/BilTop/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haihan Wu (The University of California\, Davis)
DTSTART:20230524T153000Z
DTEND:20230524T170000Z
DTSTAMP:20260422T102822Z
UID:BilTop/61
DESCRIPTION:Title:
Webs and Clasps\nby Haihan Wu (The University of California\, Davis) a
s part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\
nThe discovery of the Jones polynomial triggered mathematical\ndevelopment
s in areas including knot theory and quantum algebra. One way\nto define t
he Jones polynomial is by using the braiding in the Temperley-Lieb\ncatego
ry\, which can be defined with planar matching. We can use diagrams\nand g
raphical calculations in the Temperley-Lieb category to study the rep-\nre
sentation theory of quantum sl2. The irreducible representations can be\n
“visualized” as the Jones-Wenzl projectors\, which can be used to comp
ute\ncolored Jones polynomial and quantum sl2 3-manifold invariant.\n\nThe
sl2 case is generalized to other simple Lie algebras by introducing triva
-\nlent vertices\, and the generalized graphical categories are called spi
ders or web\ncategories. Clasps are defined as analogues of the Jones-Wenz
l projectors\, and\nwe can use clasps to compute colored quantum link inva
riants\, quantum 3-\nmanifold invariants\, 3-j symbols\, and 6-j symbols o
f different quantum groups.\n\nIn this talk\, I will review the background
material\, and talk about re-\ncent developments on definition of web cat
egories and clasp expansions for\ndifferent Lie types.\n
LOCATION:https://researchseminars.org/talk/BilTop/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230925T103000Z
DTEND:20230925T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/62
DESCRIPTION:Title:
Homotopical characterization of strong contextuality (part I)\nby Aziz
Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nLectu
re held in SB-Z11.\n\nAbstract\nSimplicial distributions introduced in the
paper “Simplicial quantum contextuality” provide a topological approa
ch to the study of contextuality for collections of probability distributi
ons. The space of measurements and the space of outcomes are represented b
y simplicial sets\, so one can ask what is the role of the homotopy theory
of simplicial sets here. In this talk\, we will give a homotopical charac
terization of strongly contextual simplicial distributions with binary out
comes\, specifically those defined on the cone of a 1-dimensional space. T
o prove this\, we introduce the corresponding category for simplicial dist
ribution on the cone of a 1-dimensional space and give the characterizatio
n of strong contextuality in terms of this category.\n
LOCATION:https://researchseminars.org/talk/BilTop/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20231002T103000Z
DTEND:20231002T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/63
DESCRIPTION:Title:
Homotopical characterization of strong contextuality (part II)\nby Azi
z Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nLect
ure held in SB-Z11.\n\nAbstract\nSimplicial distributions introduced in th
e paper “Simplicial quantum contextuality” provide a topological appro
ach to the study of contextuality for collections of probability distribut
ions. The space of measurements and the space of outcomes are represented
by simplicial sets\, so one can ask what is the role of the homotopy theor
y of simplicial sets here. In this talk\, we will give a homotopical chara
cterization of strongly contextual simplicial distributions with binary ou
tcomes\, specifically those defined on the cone of a 1-dimensional space.
To prove this\, we introduce the corresponding category for simplicial dis
tribution on the cone of a 1-dimensional space and give the characterizati
on of strong contextuality in terms of this category.\n
LOCATION:https://researchseminars.org/talk/BilTop/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20231009T103000Z
DTEND:20231009T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/64
DESCRIPTION:Title:
Colimits of categories\, zig-zags and necklaces\nby Redi Haderi (Bilke
nt University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z
11.\n\nAbstract\nColimits of simplicial categories are generally considere
d hard to understand in explicit terms. Important simplicial categories\,
such as those freely generated by simplicial sets\, arise as such colimits
. In fact\, the free simplicial category - coherent nerve adjunction has b
een demonstrated by Lurie to be a Quillen equivalence.\nWe discuss how the
problem of computing colimits of simplicial categories reduces to computi
ng colimits of categories. Then\, we present a theorem which describes the
latter in explicit terms (to the best of our knowledge\, not in the liter
ature). As an application\, we provide a computational proof of the Neckla
ce Theorem of Dugger and Spivak.\n
LOCATION:https://researchseminars.org/talk/BilTop/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora
DTSTART:20231023T103000Z
DTEND:20231023T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/65
DESCRIPTION:Title:
Equivariant contextuality\nby Igor Sikora as part of Bilkent Topology
Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nSimplicial quantum context
uality\, introduced by Okay\, Kharoof and Ipek\, is a framework for using
topological methods based on simplicial sets to study quantum contextualit
y. It subsumes earlier approaches - topological (Okay\, Roberts\, Bartlett
\, Raussendorf) and sheaf-theoretic (Abramsky\, Brandenburger).\n\nIn this
talk we will discuss how group action can be composed into this framework
. To this end\, we will use such tools as Borel construction and partial g
roups in the sense of Broto-Gonzalez. We will start with the notions of eq
uivariant simplicial distributions and equivariant contextuality and conne
ct them with the Borel construction. Then we will proceed with the cohomol
ogical aspects\, which are based on the extensions of partial groups and c
ofibre sequences of simplicial sets.\n\nThe talk is based on a joint work
with Cihan Okay\, to appear on arxiv soon.\n
LOCATION:https://researchseminars.org/talk/BilTop/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Cantarero
DTSTART:20231030T140000Z
DTEND:20231030T150000Z
DTSTAMP:20260422T102822Z
UID:BilTop/66
DESCRIPTION:Title:
Configuration spaces of commuting elements\nby Jose Cantarero as part
of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe ra
tional cohomology of the configuration space of commuting\nelements in a c
ompact Lie group is determined by the action of the Weyl group on the conf
iguration space of its maximal torus. This can be used to determine (co)ho
mological stability phenomena and other unstable computations. In this tal
k I will begin with some motivation for the study of these spaces and the
case of SU(2)\, where the homotopy type can be completely determined. Then
I will describe the stability results mentioned previously and other inte
resting cohomology computations. This is joint work with Ángel R. Jiméne
z.\n
LOCATION:https://researchseminars.org/talk/BilTop/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koray Karabina
DTSTART:20231106T103000Z
DTEND:20231106T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/67
DESCRIPTION:Title:
Secure Boundary Matrix Reduction Algorithm Using Homomorphic Encryption\nby Koray Karabina as part of Bilkent Topology Seminar\n\nLecture held i
n SB-Z11.\n\nAbstract\nTopological Data Analysis (TDA) offers a suite of c
omputational tools that provide quantified shape features in high-dimensio
nal data\, which can be utilized by modern statistical and predictive mach
ine learning models. In particular\, persistent homology (PH) takes in dat
a and derives compact representations of latent topological structures\, k
nown as persistence diagrams. PH has been widely adopted for model develop
ment on sensitive data\, motivating the computation of PH on encrypted dat
a. In this presentation\, I will provide brief introductions to TDA and se
cure computing and then demonstrate how to modify the boundary matrix redu
ction algorithm to compute PH on encrypted data using homomorphic encrypti
on.\n
LOCATION:https://researchseminars.org/talk/BilTop/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Torres Castillo
DTSTART:20231113T103000Z
DTEND:20231113T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/68
DESCRIPTION:Title:
Partial group cohomology\nby Victor Torres Castillo as part of Bilkent
Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nPartial groups w
ere introduced by Chermak as a tool to approach the issue of the existence
and uniqueness of a centric linking system for a saturated fusion system.
Roughly speaking\, a partial group is a set with a partially defined prod
uct (you can still multiply certain strings of elements together\, but not
always).\nIn this talk\, we will discuss the main similarities and differ
ences between the categories of partial groups and (actual) groups. Then\,
we will introduce the cohomology of a partial group inspired by the Gabri
el-Zisman cohomology\, as defined by Galvez-Neumann-Tonks.\nThe talk is ba
sed on a joint work in progress with Cihan Okay and Igor Sikora.\n
LOCATION:https://researchseminars.org/talk/BilTop/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Kirtisoglu
DTSTART:20231120T103000Z
DTEND:20231120T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/69
DESCRIPTION:Title:
Thomason's Homotopy Colimit Theorem\nby Mehmet Kirtisoglu as part of B
ilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this ta
lk\, we will discuss the proof of Thomason's homotopy colimit theorem. The
theorem states that given a functor from a small category to the category
of small categories\, the homotopy colimit construction on the nerves of
the categories in the diagram is naturally homotopy equivalent to the ner
ve space of the Grothendieck Construction.\n
LOCATION:https://researchseminars.org/talk/BilTop/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern
DTSTART:20231127T103000Z
DTEND:20231127T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/70
DESCRIPTION:Title:
$(\\infty\,2)$-categories and lax colimits\nby Walker Stern as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nMany hig
her-categorical structures\, most notably $(\\infty\,1)$-categories themse
lves\, form $(\\infty\,2)$-categories. It is thus highly desirable to char
acterize such structures in terms of $(\\infty\,2)$-categorical universal
properties. One recent framework allowing us to understand such $(\\infty\
,2)$-categorical universal properties is the theory of (co)limits in $(\\i
nfty\,2)$-categories. In this talk\, I will explain the developing theory
of (partially) lax colimits in $(\\infty\,2)$-categories\, and discuss how
it recovers a number of previous notions in the literature. I will then e
xplain how one can generalize from the $(\\infty\,1)$-categorical setting
to obtain a cofinality criterion for $(\\infty\,2)$-functors. This work wa
s joint with Fernando Abellán.\n
LOCATION:https://researchseminars.org/talk/BilTop/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ivan Piterman
DTSTART:20231204T103000Z
DTEND:20231204T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/71
DESCRIPTION:Title:
Advances on Quillen's conjecture\nby Kevin Ivan Piterman as part of Bi
lkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe study o
f the p-subgroup complexes began motivated by group cohomology and equivar
iant cohomology of topological spaces "modulo the prime p". For example\,
Kenneth Brown proved that the reduced Euler characteristic of this complex
is divisible by the size of a Sylow p-subgroup\, giving rise to a sort of
"Homological Sylow theorem". Later\, he showed that the mod-p equivariant
cohomology of the p-subgroup complex of a finite group coincides with the
mod-p cohomology of the group. Deeper relations with finite group theory\
, representation theory\, and finite geometries were also explored. For in
stance\, uniqueness of certain simple groups\, finite geometries for spora
dic groups\, Lefschetz modules\, and\, more recently\, endotrivial modules
.\n\nIn 1978\, Daniel Quillen conjectured that the poset of non-trivial p-
subgroups of a finite group G is contractible if and only if G has non-tri
vial p-core. Quillen established the conjecture for solvable groups and so
me families of groups of Lie type. The major step towards the resolution o
f the conjecture was done by Michael Aschbacher and Stephen D. Smith at th
e beginning of the nineties. They roughly proved that if p>5 and G is a gr
oup of minimal order failing the conjecture\, then G contains a simple com
ponent PSU(n\,q^2) failing a certain homological condition denoted by (QD)
(namely\, the top-degree homology group of its p-subgroup poset does not
vanish).\n\nIn this talk\, I will present recent advances in the conjectur
e\, with a particular focus on the prime p=2\, which was not covered by th
e methods developed by Aschbacher-Smith. In particular\, we show that the
study of the conjecture for the prime p=2 basically reduces to studying (Q
D) on the poset of p-subgroups of certain families of classical groups. Pa
rt of this work is in collaboration with S.D. Smith\n
LOCATION:https://researchseminars.org/talk/BilTop/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART:20231211T103000Z
DTEND:20231211T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/72
DESCRIPTION:Title:
Filling Radius and Persistent Homology\nby Baris Coskunuzer as part of
Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn this
talk\, we discuss interesting relations between notions from applied topol
ogy and metric geometry in point cloud setting. First\, we introduce sever
al notions in both fields to measure the size of a manifold. Then\, for a
point cloud X in R^n\, we relate the life spans of the topological feature
s to their extrinsic and Gromov’s filling radius in R^n\, and by using t
his relation\, we give bounds for them with Urysohn width. Next\, we discu
ss an interesting relationship between the life spans of the topological f
eatures in PD_k(X) in R^n and l^\\infty principal components (PCA_\\infty)
of the point cloud X.\n
LOCATION:https://researchseminars.org/talk/BilTop/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART:20231211T133000Z
DTEND:20231211T143000Z
DTSTAMP:20260422T102822Z
UID:BilTop/73
DESCRIPTION:Title:
Topological Machine Learning and Applications in Drug Discovery and Cancer
Detection\nby Baris Coskunuzer as part of Bilkent Topology Seminar\n\
nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we'll introduce funda
mental techniques in topological machine learning and showcase their appli
cation in two specific contexts. The first application is on computer-aide
d drug discovery\, utilizing Multiparameter Persistence for graph represen
tation learning. Our second application revolves around cancer detection f
rom histopathological images via cubical persistence. We apply our methodo
logies across five distinct cancer types\, demonstrating superior performa
nce compared to state-of-the-art deep learning methods. The talk is access
ible to graduate students in math\, science\, and engineering\, assuming n
o prior background in topology or machine learning.\n
LOCATION:https://researchseminars.org/talk/BilTop/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imma Gálvez Carrillo
DTSTART:20231218T103000Z
DTEND:20231218T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/74
DESCRIPTION:Title:
Cohomology of categories after Baues-Wirsching\nby Imma Gálvez Carril
lo as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstr
act\nIn this talk\, I will revise some aspects and generalizations of the
cohomology\nof small categories introduced by Baues and Wirsching in 1985
developed in more\nrecent work with Neumann and Tonks\, such as Thomason c
ohomology and\n Gabriel-Zisman cohomology for simplicial sets.\nAlso\, I w
ill report about work in progress with Neumann\, Paoli and\nTonks about th
e generalization of the above to the framework of 2-categories.\nThis has
applications for instance to higher Segal spaces.\n
LOCATION:https://researchseminars.org/talk/BilTop/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20240205T103000Z
DTEND:20240205T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/75
DESCRIPTION:Title:
TDA I: An Introduction to Topological Data Analysis\nby Ergun Yalcin (
Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nTopological Data Analysis is an emerging area of mat
hematics where topological\nmethods are used to analyze data. One of the m
ost important tools for TDA is Persistent\nHomology. The input of this pro
cess is a finite metric space (a data cloud) and the output\nis a barcode
or a persistent diagram. Given a finite metric space\, using closed balls\
nof changing radius\, we build a filtered simplicial complex. The homology
modules of these\nfiltered simplicial complexes are called persistent hom
ology modules and they are\nexpressed using barcodes or persistent diagram
s. What makes this method very useful\nis that the persistent homology cal
culations can be done using a simple matrix algorithm\,\ncalled the reduct
ion algorithm. I will introduce basic ideas behind persistent homology\nan
d show how the reduction algorithm works. Most of the talk should be acces
sible to\nan undergraduate student who has taken a linear algebra course.\
n\nPart I of a sequel on Topological Data Analysis (TDA).\n
LOCATION:https://researchseminars.org/talk/BilTop/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240212T103000Z
DTEND:20240212T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/76
DESCRIPTION:Title:
HC I: Quasi-categories and simplicially enriched categories\nby Walker
Stern (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nIn this talk\, we define quasi-categories as
simplicial sets satisfying a lifting condition related to both categories
and Kan complexes. We describe an adjunction that relates quasi-categorie
s and simplicially enriched categories and explain\nhow it allows us to de
fine some first categorical notions in quasi-categories.\n\nPart I of a se
quel on Higher Categories (HC).\n
LOCATION:https://researchseminars.org/talk/BilTop/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Praderio (Lancaster University)
DTSTART:20240219T103000Z
DTEND:20240219T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/77
DESCRIPTION:Title:
Sharpness for the Benson-Solomon fusion systems\nby Marco Praderio (La
ncaster University) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nSince their appearance fusion systems have received
much interest in both algebra and topology and in 2011 Asbacher\, Kessar a
nd Oliver published a list of problems involving fusion systems many of wh
ich remain nowadays open. One of such problems was rephrased in a more gen
eral way by Díaz and Park in 2013 and has since been known as the sharpne
ss for fusion systems conjecture. This conjecture has seen a lot of activi
ty in recent years. During this talk we will briefly go over the concepts
of fusion system and Mackey functor\, use those in order to properly state
the sharpness conjecture\, mention the results we know involving this con
jecture and finally sketch the proof that the Benson-Solomon fusion system
s (the only known family of exotic fusion systems over 2 groups) satisfy t
his conjecture.\n
LOCATION:https://researchseminars.org/talk/BilTop/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240226T103000Z
DTEND:20240226T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/78
DESCRIPTION:Title:
HC II: First constructions\nby Walker Stern (Bilkent University) as pa
rt of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nWe
explain how slice quasi-categories are defined\, and how they provide a ne
w notion of mapping spaces in a quasi-category. Using this new notion\, we
give an alternate\ncharacterization of equivalences of quasi-categories\,
and define initial and terminal objects in a quasi-\ncategory.\n\nPart II
of a sequel on Higher Categories (HC).\n
LOCATION:https://researchseminars.org/talk/BilTop/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uzay Cetin (Bilkent University)
DTSTART:20240304T103000Z
DTEND:20240304T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/79
DESCRIPTION:Title:
TDA II: Matrix Reduction Algorithm and Morozov's Worst Case Example\nb
y Uzay Cetin (Bilkent University) as part of Bilkent Topology Seminar\n\nL
ecture held in SB-Z11.\n\nAbstract\nMatrix reduction algorithm on a simpli
cial complex is a fairly new wave in persistent homology due to its implem
entations on programs like Ripser and many algorithms that have been built
upon that. Persistent algorithm dates back to 2002 with a pairing algorit
hm and its runtime has been shown to be O(N^3). Morozov in his 2005 articl
e gives an explicit example of the existence of this case. In my talk\, I
will talk about the matrix reduction and how it is done\, and explain why
the example runs at O(N^3) by combining the logic behind pairing and matri
x algorithms. After that\, I will also mention an alternative example and
in which ways it improves the original example.\n\nPart II of a sequence o
n Topological Data Analysis (TDA).\n
LOCATION:https://researchseminars.org/talk/BilTop/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent University)
DTSTART:20240311T103000Z
DTEND:20240311T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/80
DESCRIPTION:Title:
Homotopy theory of stacks and higher structures\nby Kadri İlker Berkt
av (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nIn this talk\, we outline Hollander's homotopy t
heory of stacks and give some examples. We also briefly discuss more gener
al stacks and certain higher structures on them in the context of derived
algebraic/symplectic geometry.\n
LOCATION:https://researchseminars.org/talk/BilTop/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240318T103000Z
DTEND:20240318T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/81
DESCRIPTION:Title:
HC III: $\\text{Cat}_\\infty$ and Grothendieck\nby Walker Stern (Bilke
nt University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z
11.\n\nAbstract\nWe describe how one may define the (large) $\\infty$-cate
gory of small\n$\\infty$-categories using simplicial sets and simplicially
enriched categories. We then sketch the idea of the Grothendieck-Lurie co
nstruction for quasi-categories\, and discuss applications.\n\nTalk III in
the sequence of Higher Categories (HC).\n
LOCATION:https://researchseminars.org/talk/BilTop/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240325T103000Z
DTEND:20240325T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/82
DESCRIPTION:Title:
HC IV: Limits and colimits\nby Walker Stern (Bilkent University) as pa
rt of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nWe
define limits and colimits in a quasi-category\, and describe how\nthey ge
neralize both 1-categorical limits\, and homotopy limits. We survey some t
heorems about the computation of limits and colimits — in particular\, c
ofinality.\n\n\nPart IV of a sequnce on Higher Categories (HC).\n
LOCATION:https://researchseminars.org/talk/BilTop/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgun Unlu (Bilkent University)
DTSTART:20240401T103000Z
DTEND:20240401T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/83
DESCRIPTION:Title:
Zigzag Persistence in Topological Data Analysis\nby Ozgun Unlu (Bilken
t University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z1
1.\n\nAbstract\nZigzag Persistence is a pivotal technique within the Topol
ogical Data Analysis (TDA) domain. This talk delves into the mathematical
underpinnings and algorithmic implementations of Zigzag Persistence\, eluc
idating its efficacy in capturing the dynamic evolution of topological str
uctures across varying resolutions. Through a rigorous examination of Zigz
ag Persistence diagrams and their interpretation\, we discuss its potentia
l to find subtle patterns and extract information from high-dimensional da
ta spaces.\n\nPart III of a sequence on Topological Data Analysis (TDA).\n
LOCATION:https://researchseminars.org/talk/BilTop/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Hackney (University of Louisiana at Lafayette)
DTSTART:20240422T130000Z
DTEND:20240422T140000Z
DTSTAMP:20260422T102822Z
UID:BilTop/84
DESCRIPTION:Title:
Partial groups and symmetric simplicial sets\nby Philip Hackney (Unive
rsity of Louisiana at Lafayette) as part of Bilkent Topology Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nPartial groups are a generalization of
groups which allow for the possibility that some n-fold products of elemen
ts may be undefined. They were introduced by Chermak to serve in the study
of the p-local structure of a finite group. These partial groups may be v
iewed as certain simplicial sets\, or better yet\, as certain symmetric si
mplicial sets. I'll explain this viewpoint\, as well as some implications.
I will also touch on the question about which partial groups are higher S
egal spaces. This is joint work with Justin Lynd.\n
LOCATION:https://researchseminars.org/talk/BilTop/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université Sorbonne Paris Nord)
DTSTART:20240506T103000Z
DTEND:20240506T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/85
DESCRIPTION:by Bob Oliver (Université Sorbonne Paris Nord) as part of Bil
kent Topology Seminar\n\nLecture held in SB-Z11.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilTop/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240520T103000Z
DTEND:20240520T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/86
DESCRIPTION:Title:
What is an infinity operad? (part I)\nby Redi Haderi (Bilkent Universi
ty) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbst
ract\nWe propose a combinatorial model for non-symmetric infinity operads.
Our approach is simplicial\, except that the simplicial objects we study
take values in a category of sets in which morphisms assign lists of eleme
nts in the codomain to an element in the domain.\nWe briefly discuss ordin
ary operads and their algebras in order to motivate our constructions. Thi
s is joint work with Özgün Ünlü.\n
LOCATION:https://researchseminars.org/talk/BilTop/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Castillo (Bilkent University)
DTSTART:20240415T103000Z
DTEND:20240415T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/87
DESCRIPTION:Title:
Quantum nonlocal games and the d-torsion commutative space\nby Victor
Castillo (Bilkent University) as part of Bilkent Topology Seminar\n\nLectu
re held in SB-Z11.\n\nAbstract\nNonlocal games have played a prominent rol
e in quantum information theory by demonstrating the power of non-locality
. In particular\, the 'magic' examples due to Mermin and Peres belong to t
he class of linear system games. The Mermin-Peres games have no classical
solutions\, but they admit operator solutions.\n\nIn this talk\, we transl
ate the problem of finding operator solutions into a problem of extensions
for partial groups (in the sense of Broto-Gonzalez). In particular\, we d
efine the d-torsion commutative nerve for groups\, whose homotopy structur
e is crucial to identify a practical criterion (in terms of higher limits)
to test a conjecture due to Chung-Okay-Sikora regarding linear system gam
es over Z_d\, with d odd.\n\nThis is joint work with Ho Yiu Chung and Ciha
n Okay.\n
LOCATION:https://researchseminars.org/talk/BilTop/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Bauer (Technical University of Munich)
DTSTART:20240513T103000Z
DTEND:20240513T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/88
DESCRIPTION:Title:
Connect the dots: from data through complexes to persistent homology\n
by Ulrich Bauer (Technical University of Munich) as part of Bilkent Topolo
gy Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, I will s
urvey some recent results on theoretical and computational aspects of appl
ied topology. I will illustrate various aspects of persistent homology: it
s structure\, which serves as a topological descriptor\, its stability wit
h respect to perturbations of the data\, its computation on a large scale\
, and connections to Morse theory.\n\nThese aspects will be motivated and
illustrated by concrete examples and applications\, such as\n\n* reconstr
uction of a shape and its homology from a point cloud\,\n\n* faithful sim
plification of contours of a real-valued function\,\n\n* existence of uns
table minimal surfaces\, and\n\n* identification of recurrent mutations i
n the evolution of COVID-19.\n
LOCATION:https://researchseminars.org/talk/BilTop/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240527T103000Z
DTEND:20240527T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/91
DESCRIPTION:Title:
What is an infinity operad? (part 2)\nby Redi Haderi (Bilkent Universi
ty) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbst
ract\nWe will discuss some of the details of the nerve construction which
we presented in the previous talk. Then\, we will explain how the category
of simplicial lists has the structure of a presheaf category. We will als
o present a homotopy coherent nerve construction which\, among other thing
s\, outputs a quasi-operad for all operads enriched in Kan complexes. This
is joint work with Özgün Ünlü.\n
LOCATION:https://researchseminars.org/talk/BilTop/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20241028T103000Z
DTEND:20241028T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/92
DESCRIPTION:Title:
Introduction to simplicial distributions\nby Cihan Okay (Bilkent Unive
rsity) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nA
bstract\nSimplicial distributions [1] is a new approach to studying measur
ement statistics of experiments\, mainly quantum\, from a topological pers
pective. The topology that comes in is combinatorial in flavor and is base
d on the theory of simplicial sets. In this talk\, I will introduce the ba
sic notions of the theory and explain the origins connecting to earlier wo
rk on preserves of distributions by Abramsky--Brandenburger.\n\n[1] Simpli
cial quantum contextuality\, https://arxiv.org/abs/2204.06648\n\n(This tal
k is part of the reading seminar series on the theory and applications of
simplicial distributions.)\n
LOCATION:https://researchseminars.org/talk/BilTop/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241104T103000Z
DTEND:20241104T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/93
DESCRIPTION:Title:
Simplicial distributions\, convex categories\, and contextuality\nby A
ziz Kharoof (University of Haifa) as part of Bilkent Topology Seminar\n\nL
ecture held in SA 141.\n\nAbstract\nIn a quantum mechanical experiment\, t
he data describing outcome probabilities consists of a family of probabili
ty distributions indexed by subsets of jointly permissible measurements. T
he simplicial framework introduced in the first talk models this data as a
morphism in the Kleisli category associated with the distribution monad.
By studying certain properties of the distribution monad\, we gain insight
s into the enriched structure of this Kleisli category. These categories\,
referred to as convex categories\, have a one-object version known as con
vex monoids. In this talk\, we characterize contextuality as a monoid-theo
retic concept by introducing a weak notion of invertibility for convex mon
oids. Our main result is that a simplicial distribution is noncontextual i
f and only if it is weakly invertible.\n\n(This talk is part of the readin
g seminar series on the theory and applications of simplicial distribution
s.)\n
LOCATION:https://researchseminars.org/talk/BilTop/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241112T103000Z
DTEND:20241112T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/94
DESCRIPTION:Title:
The monoid of simplicial distributions\nby Aziz Kharoof (University of
Haifa) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\n
Abstract\nIn this talk\, we will discuss the monoid structure of simplicia
l distributions (when the outcome space is a simplicial group) and its app
lications. We give some important examples of subgroups and submonoids whe
n the outcome space is the nerve of a finite cyclic group. We then show th
e importance of the action of deterministic distributions on the simplicia
l distributions to understand their geometrical structure. Finally\, we wi
ll introduce the Bell inequalities for a simplicial scenario and describe
the action of the deterministic distributions on it.\n\n\n(This talk is pa
rt of the reading seminar series on the theory and applications of simplic
ial distributions.)\n
LOCATION:https://researchseminars.org/talk/BilTop/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20241118T103000Z
DTEND:20241118T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/95
DESCRIPTION:Title:
Simplicial distributions and polyhedral geometry\nby Selman Ipek (Bilk
ent University) as part of Bilkent Topology Seminar\n\nLecture held in SA
141.\n\nAbstract\nSimplicial distributions are collections of probability
distributions that satisfy certain compatibility conditions that can be en
coded topologically using simplicial sets. For a simplicial scenario where
the measurement space X and outcome space Y are finitely generated the sp
ace sDist(X\,Y) of allowed simplicial distributions is a convex set\, in f
act\, a convex polytope. By the Minskowski-Weyl theorem of polytope theory
it is well-known that there are two equivalent descriptions of a convex p
olytope as the intersection of finitely many half-space inequalities (H-re
presentation) or as the convex hull of finitely many extreme points (V-rep
resentation). In this talk we detail how one constructs the H-representati
on of sDist(X\,Y) and discuss the conversion to its V-representation\, kno
wn as the vertex enumeration problem. Time permitting\, we will also discu
ss the Bell polytope\, which delineates the boundary between contextual an
d noncontextual measurement statistics\, and is a subpolytope of sDist(X\,
Y).\n\n(This talk is part of the reading seminar series on the theory and
applications of simplicial distributions.)\n
LOCATION:https://researchseminars.org/talk/BilTop/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241126T103000Z
DTEND:20241126T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/96
DESCRIPTION:Title:
Gluing and extending simplicial distributions\nby Aziz Kharoof (Univer
sity of Haifa) as part of Bilkent Topology Seminar\n\nLecture held in SA 1
41.\n\nAbstract\nIn the theory of simplicial distributions\, contextuality
is determined by a natural map. As a result\, any diagram of measurement
spaces induces a diagram that can be used to compare contextuality. In thi
s talk\, we will focus on two cases: (1) an Inclusion map between measurem
ent spaces and (2) a pushout square of measurement spaces. These two cases
lead to the Extending Lemma and the Gluing Lemma\, respectively. The proo
f of the second Lemma is based on the fact that the distribution monad wea
kly preserves pullbacks: the natural map from the distribution of a pullba
ck to the pullback of the distributions has a section. We will show that t
his section behaves like a composition.\n\n(This talk is part of the readi
ng seminar series on the theory and applications of simplicial distributio
ns.)\n
LOCATION:https://researchseminars.org/talk/BilTop/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20241202T103000Z
DTEND:20241202T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/97
DESCRIPTION:Title:
Topological methods for studying contextuality and Bell inequalities\n
by Selman Ipek (Bilkent University) as part of Bilkent Topology Seminar\n\
nLecture held in SA 141.\n\nAbstract\nGoing back to the seminal work of J.
S. Bell [1]\, and later A. Fine [2] and M. Froissart [3]\, it is possible
to study the separation between noncontextual and contextual measurement s
tatistics using polyhedral geometry. From this geometric point of view a d
istribution is termed noncontextual if it lies within the convex hull of s
o-called deterministic distributions\, and contextual otherwise. The facet
defining inequalities of this convex set are called Bell inequalities. In
this talk we follow [4] and use the framework of simplicial distributions
to derive Bell inequalities for the well-known N-cycle scenarios and thei
r generalization\, the flower scenarios first introduced in [4]. We restri
ct our attention to outcomes in integers mod 2. Our proof techniques utili
ze topological notions\, such as gluing and extension\, together with a to
pological interpretation of Fourier-Motzkin elimination\, a common techniq
ue used in polytope theory.\nReferences:\n[1] J.S. Bell\, On the Einstein
Podolsky Rosen Paradox\n[2] A. Fine\, Hidden variables\, joint probability
\, and the Bell inequalities\n[3] M. Froissart\, Constructive generalizati
on of Bell's inequalities\n[4] Kharoof\, et al. Topological methods for st
udying contextuality: N-cycle scenarios and beyond\n\n(This talk is part o
f the reading seminar series on the theory and applications of simplicial
distributions.)\n
LOCATION:https://researchseminars.org/talk/BilTop/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20241209T103000Z
DTEND:20241209T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/98
DESCRIPTION:Title:
Homotopical characterization of strong contextuality\nby Aziz Kharoof
(Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held i
n SA 141.\n\nAbstract\nFor a simplicial scenario\, the space of measuremen
ts and the space of outcomes are represented by simplicial sets\, so one c
an ask what the role of the homotopy theory of simplicial sets is in the t
heory of simplicial distributions. In this talk\, we will give a homotopic
al characterization of strongly contextual simplicial distributions with b
inary outcomes\, specifically those defined in 1-dimensional space. To pro
ve this\, we introduce the corresponding category for simplicial distribut
ion on 1-dimensional space and characterize strong contextuality in terms
of this category.\n\n(This talk is part of the reading seminar series on t
he theory and applications of simplicial distributions.)\n
LOCATION:https://researchseminars.org/talk/BilTop/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20241224T103000Z
DTEND:20241224T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/100
DESCRIPTION:Title: The category of bundle scenarios of simplicial complexes\nby Aziz Kha
roof (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture h
eld in SA 141.\n\nAbstract\nIn this talk\, we begin by introducing the she
af-theoretic framework for contextuality. We then define the category of s
cenarios\, based on this framework. The definition of morphisms between sc
enarios allows us to deal with simulation between empirical models. Next\,
we extend this framework to define the category of bundle scenarios. A bu
ndle scenario is a map between simplicial complexes that satisfies specifi
c properties\, allowing it to behave analogously to a contextuality scenar
io. The transition from scenarios to bundle scenarios is facilitated by th
e nerve complex functor\, which operates as a monad on simplicial complexe
s. Finally\, we introduce the concept of an empirical model over a bundle
scenario.\n
LOCATION:https://researchseminars.org/talk/BilTop/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav
DTSTART:20250303T103000Z
DTEND:20250303T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/102
DESCRIPTION:Title: Derived geometry I: Basics of infinity-categories\nby Ilker Kadri Ber
ktav as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/BilTop/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250317T103000Z
DTEND:20250317T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/104
DESCRIPTION:Title: Derived geometry II: Basics of infinity-categories-2\nby Ilker Kadri
Berktav (Bilkent University) as part of Bilkent Topology Seminar\n\nLectur
e held in SA 141.\n\nAbstract\nIn this talk\, we will continue discussing
infinity-categories\, focusing on the simplicial categorical description.
We will then study the infinity-category of commutative differential grade
d algebras\, which will lead to the introduction of derived affine schemes
.\n
LOCATION:https://researchseminars.org/talk/BilTop/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beckham Myers (Einstein Institute of Mathematics)
DTSTART:20250324T103000Z
DTEND:20250324T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/105
DESCRIPTION:Title: Categorification and chromatic homotopy theory\nby Beckham Myers (Ein
stein Institute of Mathematics) as part of Bilkent Topology Seminar\n\nLec
ture held in SA 141.\n\nAbstract\nI will explain the idea of categorificat
ion\, which is the process of replacing notions like "equality" with "equi
valence". We will see that this naturally leads us to consider spectra\, t
he central objects of study in stable homotopy theory. We will conclude by
introducing the chromatic picture of spectra\, and explaining what catego
rification has to say in this context. (No previous knowledge of homotopy
theory will be assumed.)\n
LOCATION:https://researchseminars.org/talk/BilTop/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20250407T103000Z
DTEND:20250407T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/107
DESCRIPTION:Title: Simplicial methods in the resource theory of contextuality\nby Aziz K
haroof (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SA 141.\n\nAbstract\nWe introduce the concept of a category of sc
enarios structured over a monad with a gluing operator. Our main examples
are the category of simplicial bundle scenarios and the category of stocha
stic bundle scenarios. Using a relative variant of the Grothendieck constr
uction\, we define the simplicial distribution functor\, which extends the
functor of empirical models. Finally\, we leverage contextuality to chara
cterize the convex maps between simplicial distributions\, which are conve
x combinations of maps induced by morphisms in the category of simplicial
bundle scenarios.\n
LOCATION:https://researchseminars.org/talk/BilTop/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250414T103000Z
DTEND:20250414T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/108
DESCRIPTION:Title: Derived geometry III: Introduction to higher spaces\nby Ilker Kadri B
erktav (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SA 141.\n\nAbstract\nThis talk introduces the infinity-category o
f commutative differential graded algebras\, along with key concepts and c
onstructions that lead to the description of derived schemes and\, more ge
nerally\, derived stacks.\n
LOCATION:https://researchseminars.org/talk/BilTop/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250421T103000Z
DTEND:20250421T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/109
DESCRIPTION:Title: Derived geometry IV: Introduction to derived symplectic geometry\nby
Ilker Kadri Berktav (Bilkent University) as part of Bilkent Topology Semin
ar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we will continue
our discussion on the formulation of higher spaces\, following sheaf-theo
retical approaches. We will then present the basics of shifted symplectic
structures and related results.\n
LOCATION:https://researchseminars.org/talk/BilTop/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kursat Sozer (McMaster University)
DTSTART:20250505T133000Z
DTEND:20250505T143000Z
DTSTAMP:20260422T102822Z
UID:BilTop/111
DESCRIPTION:Title: Survey of 3-Dimensional TQFTs and Quantum Invariants of 3-Manifolds\n
by Kursat Sozer (McMaster University) as part of Bilkent Topology Seminar\
n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, I will give a gentl
e overview of 3-dimensional topological quantum field theories (TQFTs) and
the corresponding quantum invariants of closed 3-manifolds. After briefly
recalling essential algebraic notions such as pivotal\, fusion\, and modu
lar categories\, I will describe the two main constructions of 3-dimension
al TQFTs: the surgery approach (Witten–Reshetikhin–Turaev invariants)
and the state-sum approach (Turaev–Viro–Barrett–Westbury invariants)
. I will then summarize the key comparison result involving the categorica
l center construction\, illustrating how these two approaches yield isomor
phic TQFTs. If time permits\, I will close by briefly mentioning extension
s to homotopy quantum field theories (HQFTs) and highlight some recent dev
elopments in this direction.\n
LOCATION:https://researchseminars.org/talk/BilTop/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eren Uyanik (Bilkent University)
DTSTART:20250512T103000Z
DTEND:20250512T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/112
DESCRIPTION:Title: Introduction to Bicategories and Extended Topological Field Theories\
nby Eren Uyanik (Bilkent University) as part of Bilkent Topology Seminar\n
\nLecture held in SA 141.\n\nAbstract\nIn this talk\, I will motivate and
introduce bicategories and extended Topological Field Theories (eTFTs). I
will start with recalling the basics of Topological Quantum Field Theories
(TQFTs) and the classification theorem in 2-dimensional case. I will then
give the definition of eTFT as a functor between particular bicategories\
, generalizing the case of ordinary TQFT. Lastly\, I will informally discu
ss one of the classification theorems for 2-dimensional eTFTs.\n
LOCATION:https://researchseminars.org/talk/BilTop/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safranov (University of Edinburgh)
DTSTART:20250519T103000Z
DTEND:20250519T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/113
DESCRIPTION:Title: Simple homotopy invariance of the loop coproduct\nby Pavel Safranov (
University of Edinburgh) as part of Bilkent Topology Seminar\n\nLecture he
ld in SA 141.\n\nAbstract\nString topology provides algebraic operations o
n the homology of a free loop space of a manifold introduced by Chas and S
ullivan. While the loop product was known to be homotopy-invariant for a l
ong time\, Sullivan conjectured that the loop coproduct is not homotopy-in
variant. I will explain a recent proof due to Naef and myself (with relate
d work by Kenigsberg and Porcelli) that the failure of the loop coproduct
to be homotopy-invariant is given by the trace of the Whitehead torsion fr
om simple homotopy theory.\n
LOCATION:https://researchseminars.org/talk/BilTop/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250526T103000Z
DTEND:20250526T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/114
DESCRIPTION:Title: Derived geometry V: Topics in derived symplectic geometry\nby Ilker K
adri Berktav (Bilkent University) as part of Bilkent Topology Seminar\n\nL
ecture held in SA 141.\n\nAbstract\nIn this talk\, we will continue our di
scussion on shifted symplectic structures. We will then present several ke
y results in DSG. If time permits\, we will briefly mention our work in th
at setting\, focusing on the development of shifted contact structures and
related results.\n
LOCATION:https://researchseminars.org/talk/BilTop/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Topos Institute)
DTSTART:20250502T103000Z
DTEND:20250502T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/115
DESCRIPTION:Title: Double categorical right modules as the algebra of coupled dynamical syst
ems\nby David Jaz Myers (Topos Institute) as part of Bilkent Topology
Seminar\n\nLecture held in SA 141.\n\nAbstract\nOpen dynamical systems who
se dynamics depend on free parameters and which expose some variables of t
heir state may be coupled by setting their parameters as functions of the
exposed variables of other systems. Together with their parallel (cartesia
n) product\, these systems constitute a lax symmetric monoidal functor fro
m a category of interfaces (consisting of parameter and exposed variable s
ets) and coupling laws (often expressed as wiring diagrams) to the categor
y of sets --- that is\, we have a symmetric monoidal right module of syste
ms over the symmetric monoidal category of interfaces and coupling laws. S
chultz\, Spivak and Vasilakopoulou show that the behavior of these systems
may be expressed as a morphism of lax symmetric monoidal functors from th
is module of systems to a module of time-varying sets --- sheaves on the i
nterval domain of the real line.\n\nIn this talk\, we'll see that the SSV
behavior functors --- and many others similar behavior functors --- are in
fact representable when seen not as concerning right modules of categorie
s\, but as concerning right modules over double categories. We will develo
p the theory of (loose) modules between double categories using an approac
h inspired by Joyal's "barrels" (joint work with Sophie Libkind)\, and des
cribe the cartesian pseudo-functoriality of restriction of loose right mod
ules which allows for the pseudo-functorial construction of symmetric mono
idal loose right modules of open dynamical systems from an abstract notion
of "tangent bundle category". By expanding the definition of "tangent bun
dle" in this way\, we include all sorts of generalized Moore machines (inc
luding not only systems of ordinary differential equations\, but also part
ially observable Markov processes and various sorts of non-deterministic a
utomata).\n\nWe'll then see a general result (joint work with Matteo Capuc
ci) giving conditions under which discrete opfibration classifiers in a 2-
category K can be lifted to the 2-category of algebras and lax morphisms f
or a 2-monad T on K. We will use this result to show that a certain symmet
ric monoidal loose right module of spans is a discrete opfibration classif
ier among symmetric monoidal loose right modules\, and conclude by showing
that a variety of behavior functors for open dynamical systems are covari
antly representable. Time permitting\, we will also see that system safety
and stability properties are often themselves contravariantly representab
le via the representability of Lyapunov and control barrier functions by f
unctions into simple systems.\n
LOCATION:https://researchseminars.org/talk/BilTop/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART:20250530T113000Z
DTEND:20250530T123000Z
DTSTAMP:20260422T102822Z
UID:BilTop/116
DESCRIPTION:Title: Topological Machine Learning\nby Baris Coskunuzer (UT Dallas) as part
of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn th
is talk\, we will explore key techniques in topological machine learning a
nd highlight their applications in two distinct areas. First\, we will dis
cuss computer-aided drug discovery\, where Multiparameter Persistence is l
everaged for graph representation learning. Second\, we will examine cance
r detection from histopathological images using cubical persistence. Our a
pproach is applied to five different cancer types\, achieving superior per
formance compared to state-of-the-art deep learning methods. The talk is d
esigned to be accessible for advanced undergraduate students in mathematic
s\, science\, and engineering\, requiring no prior knowledge of topology o
r machine learning.\n
LOCATION:https://researchseminars.org/talk/BilTop/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Jan Mikhail (University of Copenhagen)
DTSTART:20250707T103000Z
DTEND:20250707T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/117
DESCRIPTION:Title: Abacus bicomodule configurations and the Bergner–Osorno–Ozornova–Ro
velli–Scheimbauer equivalence\nby Thomas Jan Mikhail (University of
Copenhagen) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.
\n\nAbstract\nA theorem of Bergner\, Osorno\, Ozornova\, Rovelli\, and Sch
eimbauer states an equivalence between 2-Segal spaces and certain augmente
d stable double Segal spaces. In this talk\, after a preliminary section o
n 2-Segal spaces\, I will establish more general equivalences\, involving
simplicial maps of 2-Segal spaces and abacus bicomodule configurations\, e
xtending results of Carlier. This talk is based on joint work with Joachim
Kock\, and a preprint of this work is available on the arXiv (see arXiv:2
501.16491).\n
LOCATION:https://researchseminars.org/talk/BilTop/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Oregon State University)
DTSTART:20250709T103000Z
DTEND:20250709T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/118
DESCRIPTION:Title: Homology of Simplicial G-complexes and Group Rings\nby Chung-Ping Lai
(Oregon State University) as part of Bilkent Topology Seminar\n\nLecture
held in SA 141.\n\nAbstract\nThere has been a growing trend to use the hom
ology of simplicial complexes to study complex data structures because of
its resilience to deformation and noise. In this talk\, we investigate th
e question of how one can recover the homology of a simplicial complex X e
quipped with a regular action of a finite group G from the structure of it
s quotient space X/G. Specifically\, we describe a process for enriching t
he structure of the chain complex C*(X/G\; F) using the data of a complex
of groups\, a framework developed by Bridson and Corsen for encoding the l
ocal structure of a group action. We interpret this data through the lens
of matrix representations of the acting group\, and combine this structure
with the standard simplicial boundary matrices for X/G to construct a sur
rogate chain complex. In the case G = Zk\, the group ring FG is commutativ
e and matrices over FG admit a Smith normal form\, allowing us to recover
the homology of G from this surrogate complex. This algebraic approach com
plements the geometric compression algorithm for equivariant simplicial co
mplexes described by Carbone\, Nanda\, and Naqvi.\n
LOCATION:https://researchseminars.org/talk/BilTop/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Basak Kucuk (University of Göttingen)
DTSTART:20250711T103000Z
DTEND:20250711T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/119
DESCRIPTION:Title: The Conjecture of Klein and Williams for the Equivariant Fixed Point Prob
lem\nby Basak Kucuk (University of Göttingen) as part of Bilkent Topo
logy Seminar\n\nLecture held in SA 141.\n\nAbstract\nKlein and Williams de
veloped an obstruction theory for the homotopical equivariant fixed point
problem\, which asks whether an equivariant map can be deformed\, through
an equivariant homotopy\, to a map with no fixed points [KW\, Theorem H].
An alternative approach was given by Fadell and Wong [FW]\, using a collec
tion of Nielsen numbers. The Nielsen number is a finer invariant than the
Lefschetz number in the sense that it provides a converse to the Lefschetz
fixed point theorem. Klein and Williams [KW] conjectured that these Niels
en numbers could be computed from their invariant.\nIn this talk\, we pres
ent our findings on this conjecture by providing an explicit decomposition
of the Klein–Williams invariant under the tom Dieck splitting. We furth
er discuss the application of the equivariant fixed point problem to the p
eriodic point problem of period n. In this setting\, we show that the Klei
n–Williams invariant and the Nielsen numbers N(fk)\, for all k dividing
n\, carry the same amount of information. However\, they are not exactly t
he same invariants\, and if time permits\, we will conclude with an explic
it example illustrating this difference.\nReferences:\n[KW] J. R. Klein a
nd B. Williams\, Homotopical intersection theory II\, Math. Z. 264 (2010).
\n[FW] E. Fadell and P. Wong\, On deforming G-maps to be fixed point free
\, Pacific Journal of Mathematics 132 (1988).\n
LOCATION:https://researchseminars.org/talk/BilTop/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20251006T123000Z
DTEND:20251006T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/120
DESCRIPTION:Title: Free Actions on Products of Real Projective Spaces\nby Ergun Yalcin (
Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held in
SA 141.\n\nAbstract\nWe recently proved the homotopy-theoretical version
of a conjecture\nby Cusick from 1983 on free actions of elementary abelian
2-groups on products\nof real projective spaces. In this talk I will expl
ain the main ideas of the proof after\nintroducing the necessary backgroun
d.\n
LOCATION:https://researchseminars.org/talk/BilTop/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20251013T123000Z
DTEND:20251013T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/121
DESCRIPTION:Title: The geometry of simplicial distributions on suspension scenarios\nby
Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nL
ecture held in SA 141.\n\nAbstract\nQuantum measurements often exhibit non
-classical features\, such as contextuality\, which generalizes Bell's non
-locality and serves as a resource in various quantum computation models.
Existing frameworks have rigorously captured these phenomena\, and recentl
y\, simplicial distributions have been introduced to deepen this understan
ding. The geometrical structure of simplicial distributions can be seen as
a resource for applications in quantum information theory. In this talk\,
we use topological foundations to study this geometrical structure\, leve
raging the fact that\, in this simplicial framework\, measurements and out
comes are represented as spaces. This allows us to depict contextuality as
a topological phenomenon. We show that applying the cone construction to
the measurement space makes the corresponding non-signaling polytope equal
to the join of m copies of the original polytope\, where m is the number
of possible outcomes per measurement. Then we glue two copies of cone meas
urement spaces to obtain a suspension measurement space. The decomposition
done for simplicial distributions on a cone measurement space provides de
eper insights into the geometry of simplicial distributions on a suspensio
n measurement space and aids in characterizing the contextuality there. Ad
ditionally\, we apply these results to derive a new type of Bell inequalit
ies (inequalities that determine the set of local joint probabilities/non-
contextual simplicial distributions) and to offer a mathematical explanati
on for certain contextual vertices from the literature.\n
LOCATION:https://researchseminars.org/talk/BilTop/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Bilkent University)
DTSTART:20251020T123000Z
DTEND:20251020T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/122
DESCRIPTION:Title: Reducing Complexes with Discrete Morse Theory\nby Chung-Ping Lai (Bil
kent University) as part of Bilkent Topology Seminar\n\nLecture held in SA
141.\n\nAbstract\nSimplicial decompositions of spaces often introduce lar
ge number of simplices which can become a nuisance especially in computati
onal settings. Inspired by smooth Morse theory\, Forman introduced discret
e Morse theory which\, among its many applications\, offers an approach to
reduce many kinds of cell complexes. In this talk we first introduce an a
bstract cell complex that unifies various combinatorial spaces—such as s
implicial and CW complexes. We then show how discrete Morse theory allows
us to reduce a finite cell complex to a Morse complex which contains less
cells while preserving the homology.\n
LOCATION:https://researchseminars.org/talk/BilTop/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Oregon State University)
DTSTART:20251027T123000Z
DTEND:20251027T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/123
DESCRIPTION:Title: Persistent Homology and Discrete Morse Theory\nby Chung-Ping Lai (Ore
gon State University) as part of Bilkent Topology Seminar\n\nLecture held
in SA 141.\n\nAbstract\nPersistent homology is a powerful tool in applied
topology\, yet its computation can be expensive. In this talk we will brie
fly introduce persistent homology. Then\, building on our previous discuss
ion of Discrete Morse Theory (DMT)\, we demonstrate how DMT can be used to
reduce the size of relevant complexes in persistent homology\, leading to
gains in computational efficiency.\n
LOCATION:https://researchseminars.org/talk/BilTop/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron David Fairbanks (Dalhousie University)
DTSTART:20251103T123000Z
DTEND:20251103T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/124
DESCRIPTION:Title: Comonads on Set\nby Aaron David Fairbanks (Dalhousie University) as p
art of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nIt
was noticed only within the last decade that polynomial comonads on Set a
re small categories. What then are general comonads on Set? Joint work wit
h Kevin Carlson and David Spivak.\n
LOCATION:https://researchseminars.org/talk/BilTop/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin M. Curry (University at Albany)
DTSTART:20251110T130000Z
DTEND:20251110T140000Z
DTSTAMP:20260422T102822Z
UID:BilTop/125
DESCRIPTION:Title: Stratification Theory for Reinforcement Learning\nby Justin M. Curry
(University at Albany) as part of Bilkent Topology Seminar\n\nLecture held
in SA 141.\n\nAbstract\nIn this talk I will use the framework of poset-st
ratified spaces to study games\, where reward can be both discrete and con
tinuous. Following work by Yuliy Baryshnikov\, I will show how certain vid
eo games naturally give rise to stratified spaces. Surprisingly\, when mod
ern neural nets are trained to play these same video games\, a similar str
atification structure can be observed in their latent representations. Our
methods follow recent work by Michael Robinson and others on using Volume
Growth Laws to detect non-manifold structure in the token space for LLMs.
We expand and strengthen Robinson’s analysis by considering non-textual
data and prove a realization result for volume growth in a stratified spa
ce. This is joint work with Brennan Lagasse\, Ngoc B. Lam\, Gregory Cox\,
David Rosenbluth\, and Alberto Speranzon.\n
LOCATION:https://researchseminars.org/talk/BilTop/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Moeller (Caltech)
DTSTART:20251124T160000Z
DTEND:20251124T170000Z
DTSTAMP:20260422T102822Z
UID:BilTop/127
DESCRIPTION:Title: Hybrid dynamical systems as coalgebras\nby Joe Moeller (Caltech) as p
art of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nLy
apunov theory provides a method for certifying the stability of a dynamica
l system without solving infeasible systems of differential equations. Thi
s theory has practical implications in the design of control algorithms fo
r many sorts of systems including robotics. We present a categorical frame
work for Lyapunov stability theory. This theory is developed in the langua
ge of coalgebras\, where a system is viewed as a coalgebra of an endofunct
or. Examples include continuous dynamical systems as coalgebras of the tan
gent bundle functor\, and discrete transition systems as coalgebras of the
powerset functor. We blend these two standard examples to give a coalgebr
aic encoding of hybrid dynamical systems\, which appear naturally in engin
eering contexts such as robotic bipedal locomotion. This enables us to app
ly the categorical Lyapunov theory to hybrid systems and find new conditio
ns for certifying the stability of Zeno equilibria.\n
LOCATION:https://researchseminars.org/talk/BilTop/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20251201T123000Z
DTEND:20251201T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/128
DESCRIPTION:Title: [cancelled] Simplicial methods in the resource theory of contextuality\nby Aziz Kharoof (Bilkent University) as part of Bilkent Topology Semina
r\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we introduce two
categories:\nThe category of event scenarios\, which extends the standard
scenarios known from the sheaf-theoretic approach.\nThe category of scenar
ios over a monad with a gluing operation\, which extends the category of s
implicial bundle scenarios.\nWe define the empirical model and simplicial
distribution functors for these categories using the relative Grothendieck
construction that presented in Behzat’s talk. We then introduce an inte
rnal hom structure for event scenarios and for simplicial bundle scenarios
\, which we call mapping scenarios.\nFinally\, we present our main result\
, which characterizes convex maps between simplicial distributions in term
s of non-contextual distributions on the corresponding mapping scenario\,
thereby enhancing and extending previous results in categorical quantum fo
undations.\n
LOCATION:https://researchseminars.org/talk/BilTop/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Tombari (KTH - Royal Institute of Technology)
DTSTART:20251208T123000Z
DTEND:20251208T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/129
DESCRIPTION:Title: Decompositions of tame parametrised chain complexes\nby Francesca Tom
bari (KTH - Royal Institute of Technology) as part of Bilkent Topology Sem
inar\n\nLecture held in SA 141.\n\nAbstract\nWe show a classification resu
lt for tame filtered chain complexes with indexing posets of dimension 1.
Filtered chain complexes\, on the one hand\, arise from filtrations of fin
ite point clouds. On the other hand\, they are the cofibrant replacements
of any tame parametrised chain complex\, once an appropriate model categor
y structure is defined. Posets of dimension 1 form the other fundamental p
iece of this presentation. Examples of these are given by natural\, intege
r\, real numbers with the usual order\, trees and zigzags. \n\nOur classif
ication result states that there are only two types of cofibrant (filtered
) indecomposables in the category tame(Q\, ch(C))\, where Q is a poset of
dimension 1\, and C is an appropriate category. They are either disks (tri
vial homology) of indecomposable projectives in tame(Q\, C) or spheres (no
n-trivial homology) on the minimal projective resolution of the homology o
f the chain complex. Both of them are nonzero in only two consecutive degr
ees. If time allows\, we will also show a technique\, based on “glueing
”\, to construct indecomposables in a functor category by “smaller”
indecomposables. Examples obtained in this way will also show that the res
ults presented above\, for functors indexed by posets of dimension 1\, are
not immediately generalisable. \n\nThis presentation is based on joint wo
rk with Wojciech Chachólski\, Barbara Giunti and Claudia Landi.\n
LOCATION:https://researchseminars.org/talk/BilTop/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urs Schreiber (NYU Abu Dhabi)
DTSTART:20251215T123000Z
DTEND:20251215T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/130
DESCRIPTION:Title: Fragile Topological Phases and Topological Order of 2D Crystalline Chern
Insulators\nby Urs Schreiber (NYU Abu Dhabi) as part of Bilkent Topolo
gy Seminar\n\nLecture held in SA 141.\n\nAbstract\nWe apply methods of equ
ivariant homotopy theory\, that may not previously have found due attentio
n in condensed matter physics\, to classify first the fragile topological
phases of 2D crystalline Chern insulator materials\, and second the potent
ial topological order of their fractional cousins. We highlight that the p
hases are given by the equivariant 2-Cohomotopy of the Brillouin torus of
crystal momenta (with respect to wallpaper point group actions) — which\
, despite the attention devoted to crystalline Chern insulators\, seems no
t to have been considered before. Arguing then that any topological order
must be reflected in the adiabatic monodromy of gapped quantum ground stat
es over the covariantized moduli space of these band topologies\, we compu
te the latter in various examples where this group is non-abelian\, should
that potential anyons must be localized in momentum space. We close with
an outlook on the relevance for the search for topological quantum computi
ng hardware.\n
LOCATION:https://researchseminars.org/talk/BilTop/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjørnar Gullikstad Hem (EPFL)
DTSTART:20251222T123000Z
DTEND:20251222T133000Z
DTSTAMP:20260422T102822Z
UID:BilTop/131
DESCRIPTION:Title: Decomposing multipersistence modules using functor calculus\nby Bjør
nar Gullikstad Hem (EPFL) as part of Bilkent Topology Seminar\n\nLecture h
eld in SA 141.\n\nAbstract\nMultiparameter persistent homology has attract
ed growing interest in the topological data analysis community\, in part d
ue to its ability to handle noisy data. However\, unlike the single-parame
ter case\, multipersistence modules do not generally admit an interval dec
omposition\, which makes the multiparameter setting considerably more comp
licated. Nevertheless\, there exist certain sufficient conditions that gua
rantee interval decomposability\, such as a locally defined condition call
ed middle exactness.\nIn this talk\, I introduce poset cocalculus\, which
is a variant of functor (co)calculus that is defined for functors from a p
oset to a model category. The motivation for this framework lies in the re
levance of functors from posets to the model category of chain complexes o
ver a field\, as any multipersistence module is the homology of such a fun
ctor. Poset cocalculus provides tools for relating local conditions on the
se functors to their global structure. I apply this to give a novel\, more
synthetic proof of the fact that middle exactness implies interval decomp
osability.\n
LOCATION:https://researchseminars.org/talk/BilTop/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shulman (University of San Diego)
DTSTART:20260323T160000Z
DTEND:20260323T170000Z
DTSTAMP:20260422T102822Z
UID:BilTop/132
DESCRIPTION:Title: Doubly weak double categories\nby Michael Shulman (University of San
Diego) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nA
bstract\nDouble categories are a two-dimensional categorical structure wit
h two different classes of 1-cells\, and 2-cells shaped like a square. It
is easy to define double categories with strict composition like 2-catego
ries\; but double categories with weak composition analogous to bicategori
es\, for both kinds of 1-cells\, are surprisingly difficult to define. We
give a simple definition of "doubly weak double categories" by using the
notion of "implicit" categorical structure\, in which composition is not a
n algebraic operation at all but is witnessed by isomorphisms. Then we di
scuss various ways in which this can be made algebraic. This is joint wor
k with Aaron David Fairbanks.\n
LOCATION:https://researchseminars.org/talk/BilTop/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20260330T103000Z
DTEND:20260330T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/133
DESCRIPTION:Title: Worst-case examples for the computation of persistent homology\nby Er
gun Yalcin (Bilkent University) as part of Bilkent Topology Seminar\n\nLec
ture held in SA 141.\n\nAbstract\nTopological Data Analysis via persistent
homology is a new emerging area of data analysis that uses methods from
simplicial topology. The persistent homology of a data set can be calculat
ed using a simple algorithm called reduction algorithm. In this talk\,
I will present a new construction of worst-case examples for this algorit
hm. Our constructions are similar to the worst-case examples introduced by
Morozov\, but replace the single-triangle arrangement with a strip forme
d by base and fin triangles. This structure allows us to give an explicit
algorithm for their construction and to perform experiments comparing the
runtime of different variants of the reduction algorithm. We further s
how that\, after suitable edge and triangle subdivisions\,\nthese strip ex
amples remain worst-case and can be realized as clique complexes of filter
ed graphs\, and hence as Vietoris--Rips complexes of finite point clouds
for a sequence of scale parameters.\n
LOCATION:https://researchseminars.org/talk/BilTop/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20260406T103000Z
DTEND:20260406T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/134
DESCRIPTION:Title: Extremal Simplicial Distributions on Glued Measurement Spaces\nby Azi
z Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nLect
ure held in SA 141.\n\nAbstract\nSimplicial distributions form the Kleisli
category of the distribution monad on simplicial sets. They were introduc
ed as a framework for studying non-signaling polytopes and contextuality a
rising from measurements in quantum physics\, with applications in quantum
information theory. The domain of a simplicial distribution is a simplici
al set that encodes the compatible measurements in a given scenario and is
called the measurement space.\n\nIn this talk\, we characterize extremal
simplicial distributions when the measurement space is a colimit of a diag
ram of simplicial sets. We apply this result to cases in which identical s
paces are glued together along a common subspace. In particular\, we obtai
n a characterization of extremal simplicial distributions on what we call
the rose and dipole graphs. Finally\, we show how this characterization ca
n be used to detect extremal simplicial distributions on one-dimensional m
easurement spaces.\n
LOCATION:https://researchseminars.org/talk/BilTop/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Frankland (University of Regina)
DTSTART:20260413T103000Z
DTEND:20260413T113000Z
DTSTAMP:20260422T102822Z
UID:BilTop/135
DESCRIPTION:Title: Enriched model categories and the Dold-Kan correspondence\nby Martin
Frankland (University of Regina) as part of Bilkent Topology Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nIf we start with a model category enric
hed in simplicial abelian groups and we normalize each hom complex\, what
kind of structure do we obtain? In joint work with Arnaud Ngopnang Ngompé
\, we show that changing the enrichment along a weak monoidal Quillen pair
results in a "weak" enriched model category. The main issue is that we lo
se the tensoring and cotensoring\, but we retain a weak form thereof.\n
LOCATION:https://researchseminars.org/talk/BilTop/135/
END:VEVENT
END:VCALENDAR