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BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART;VALUE=DATE-TIME:20201005T104000Z
DTEND;VALUE=DATE-TIME:20201005T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201019T104000Z
DTEND;VALUE=DATE-TIME:20201019T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201026T104000Z
DTEND;VALUE=DATE-TIME:20201026T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201102T104000Z
DTEND;VALUE=DATE-TIME:20201102T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201116T150000Z
DTEND;VALUE=DATE-TIME:20201116T155000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201207T154000Z
DTEND;VALUE=DATE-TIME:20201207T163000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201012T104000Z
DTEND;VALUE=DATE-TIME:20201012T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201214T154000Z
DTEND;VALUE=DATE-TIME:20201214T163000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201130T140000Z
DTEND;VALUE=DATE-TIME:20201130T145000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201221T104000Z
DTEND;VALUE=DATE-TIME:20201221T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20201123T104000Z
DTEND;VALUE=DATE-TIME:20201123T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210208T103000Z
DTEND;VALUE=DATE-TIME:20210208T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210215T103000Z
DTEND;VALUE=DATE-TIME:20210215T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210308T103000Z
DTEND;VALUE=DATE-TIME:20210308T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210315T103000Z
DTEND;VALUE=DATE-TIME:20210315T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210322T103000Z
DTEND;VALUE=DATE-TIME:20210322T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210329T103000Z
DTEND;VALUE=DATE-TIME:20210329T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210405T103000Z
DTEND;VALUE=DATE-TIME:20210405T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210412T103000Z
DTEND;VALUE=DATE-TIME:20210412T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210419T123000Z
DTEND;VALUE=DATE-TIME:20210419T133000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210503T103000Z
DTEND;VALUE=DATE-TIME:20210503T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210301T133000Z
DTEND;VALUE=DATE-TIME:20210301T143000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210222T103000Z
DTEND;VALUE=DATE-TIME:20210222T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20210426T103000Z
DTEND;VALUE=DATE-TIME:20210426T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211004T103000Z
DTEND;VALUE=DATE-TIME:20211004T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211011T123000Z
DTEND;VALUE=DATE-TIME:20211011T133000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211018T103000Z
DTEND;VALUE=DATE-TIME:20211018T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211025T123000Z
DTEND;VALUE=DATE-TIME:20211025T133000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211115T103000Z
DTEND;VALUE=DATE-TIME:20211115T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211206T103000Z
DTEND;VALUE=DATE-TIME:20211206T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211220T143000Z
DTEND;VALUE=DATE-TIME:20211220T153000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211101T133000Z
DTEND;VALUE=DATE-TIME:20211101T143000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211108T143000Z
DTEND;VALUE=DATE-TIME:20211108T153000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211129T103000Z
DTEND;VALUE=DATE-TIME:20211129T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211213T103000Z
DTEND;VALUE=DATE-TIME:20211213T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20211122T103000Z
DTEND;VALUE=DATE-TIME:20211122T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220221T103000Z
DTEND;VALUE=DATE-TIME:20220221T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220228T103000Z
DTEND;VALUE=DATE-TIME:20220228T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220314T103000Z
DTEND;VALUE=DATE-TIME:20220314T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220321T133000Z
DTEND;VALUE=DATE-TIME:20220321T143000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220328T160000Z
DTEND;VALUE=DATE-TIME:20220328T170000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220404T103000Z
DTEND;VALUE=DATE-TIME:20220404T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220418T140000Z
DTEND;VALUE=DATE-TIME:20220418T150000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220425T120000Z
DTEND;VALUE=DATE-TIME:20220425T130000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20220411T120000Z
DTEND;VALUE=DATE-TIME:20220411T130000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230206T103000Z
DTEND;VALUE=DATE-TIME:20230206T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230213T103000Z
DTEND;VALUE=DATE-TIME:20230213T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230220T103000Z
DTEND;VALUE=DATE-TIME:20230220T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230227T103000Z
DTEND;VALUE=DATE-TIME:20230227T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230313T103000Z
DTEND;VALUE=DATE-TIME:20230313T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230320T103000Z
DTEND;VALUE=DATE-TIME:20230320T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230327T103000Z
DTEND;VALUE=DATE-TIME:20230327T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230403T103000Z
DTEND;VALUE=DATE-TIME:20230403T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230410T103000Z
DTEND;VALUE=DATE-TIME:20230410T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230417T103000Z
DTEND;VALUE=DATE-TIME:20230417T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230424T103000Z
DTEND;VALUE=DATE-TIME:20230424T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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;VALUE=DATE-TIME:20230502T103000Z
DTEND;VALUE=DATE-TIME:20230502T113000Z
DTSTAMP;VALUE=DATE-TIME:20230331T094116Z
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
END:VCALENDAR