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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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
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:20211209T073705Z
UID:BilTop/35
DESCRIPTION:by Natalia Castellana (Universitat Autònoma de Barcelona) as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\nAbstract: TBA
\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:20211209T073705Z
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
END:VCALENDAR