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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:20231201T001458Z
UID:BilTop/1
DESCRIPTION:Title: C
ommutative $d$-torsion $K$-theory and its applications\nby Cihan Okay
(Bilkent University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nA
bstract\nCommutative $K$-theory is introduced by Adem-Gomez-Lind-Tillmann
as a generalized cohomology theory obtained from topological $K$-theory. T
he construction uses classifying spaces for commutativity\, first introduc
ed by Adem-Cohen-Torres Giese. In this talk we are interested in a $d$-tor
sion version of this construction: Let $G$ be a topological group. The afo
rementioned classifying space $B(\\mathbb{Z}/d\,G)$ is assembled from tupl
es of pairwise commuting elements in $G$ whose order divides $d$. We will
describe the homotopy type of this space when $G$ is the stable unitary gr
oup\, following the ideas of Gritschacher-Hausmann. The corresponding gene
ralized cohomology theory will be called the commutative $d$-torsion $K$-t
heory\, and will be denoted by $k\\mu_d$. Our motivation for studying this
cohomology theory comes from applications to operator-theoretic problems
that arise in quantum information theory. For this we introduce another sp
ectrum obtained from $k\\mu_d$ and show that a famous construction from th
e 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 joint
ly with Raussendorf.\n\nFor a related talk see https://www.youtube.com/wat
ch?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:20231201T001458Z
UID:BilTop/2
DESCRIPTION:Title: H
igher differentials in Adams spectral sequence\nby Surojit Ghosh (Univ
ersity of Haifa) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstr
act\nThe $E_2$-term of the Adams spectral sequence may be identified with
certain derived functors\, and this also holds for other Bousfield-Kan typ
es spectral sequence.\n\nIn this talk\, I'll explain how the higher terms
of such spectral sequences are determined by truncations of functors\, def
ined in terms of certain (spectrally) enriched functor called mapping alge
bras.\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:20231201T001458Z
UID:BilTop/3
DESCRIPTION:Title: O
n Quillen’s conjecture\nby Antonio Díaz Ramos (Universidad de Mála
ga) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\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 g
roups since the work of Quillen\, Aschbacher\, Smith and Alperin 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:20231201T001458Z
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 Cihan Okay\n\nLecture held in SB
-Z11.\n\nAbstract\nThe space of $n$-tuples of pairwise commuting elements
in a compact Lie group $G$ can be identified with a moduli space of flat $
G$-bundles over the $n$-torus. Borel\, Friedman\, and Morgan studied space
s of commuting pairs and triples to answer questions arising in mathematic
al physics. Often the focus lies on the enumeration of connected component
s\, but little is known about their higher homotopy and homology groups. I
n this talk I will describe the second homology group of the space of comm
uting pairs in any connected Lie group. Some results about about $n$-tuple
s 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:20231201T001458Z
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 Cihan Okay\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-spheres\, focusin
g on the case of untwisted actions. Applications to hyperbolic manifolds a
nd possible extensions to higher dimensional manifolds will also be discus
sed. 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:20231201T001458Z
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 Cihan Okay\n\nLecture held in S
B-Z11.\n\nAbstract\nLet $F$ be an infinite field. Andrei Suslin constructe
d a morphism from the (Quillen) K-theory of $F$ to the Milnor K-theory of
$F$: $s_n : K_n(F) \\to K_n^M(F)$. He proved that the image of $s_n$ conta
ins $(n-1)! K_n^M(F)$. He raised the question of whether this accounted fo
r 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 morphism as a morph
ism of $A^1$-homotopy groups of down-to-earth objects\, and I will show ho
w this tells us some things about Suslin's question when $n$ is $4$ and se
ttles it when $n$ is $5$. This talk represents joint work with Aravind Aso
k 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:20231201T001458Z
UID:BilTop/7
DESCRIPTION:Title: S
mall covers over a product of simplices\nby Aslı Güçlükan (Dokuz E
ylul University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstr
act\nChoi shows that there is a bijection between Davis–Januszkiewicz eq
uivalence classes of small covers over an $n$-cube and the set of acyclic
digraphs with $n$-labeled vertices. Using this\, one can obtain a bijectio
n between weakly $(\\mathbb{Z}/2)^n$-equivariant homeomorphism classes of
small covers over an $n$-cube and the isomorphism classes of acyclic digra
phs on labeled $n$ vertices up to local complementation and reordering ver
tices. To generalize these results to small covers over a product of simp
lices we introduce the notion of $\\omega$-weighted digraphs for a given d
imension function $\\omega$. It turns out that there is a bijection betwee
n Davis–Januszkiewicz equivalence classes of small covers over a product
of simplices and the set of acyclic $\\omega$-weighted digraphs. After in
troducing the notion of an $\\omega$-equivalence\, we also show that there
is a bijection between the weakly $(\\mathbb{Z}/2)^n$-equivariant homeomo
rphism classes of small covers over $\\Delta^{n_1}\\times\\cdots \\times
\\Delta^{n_k}$ and the set of $\\omega$-equivalence classes of $\\omega$-w
eighted digraphs with $k$-labeled vertices $\\{v_1\, \\cdots\, v_k\\}$ whe
re $\\omega$ is defined by $\\omega(v_i)=n_i$ and $n=n_1+\\cdots+n_k$. 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 t
hree 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:20231201T001458Z
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 Cihan Okay\n\nLecture held in S
B-Z11.\n\nAbstract\nI will explain some descent and vanishing results in t
he\nalgebraic K-theory of ring spectra\, motivated by the redshift\nphilos
ophy of Ausoni-Rognes. These results are all proved by\nconsidering group
actions on stable $\\infty$-categories and their\nK-theory\, as well as so
me tools coming from chromatic homotopy theory.\nJoint work with Dustin Cl
ausen\, 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:20231201T001458Z
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 Cihan
Okay\n\nLecture held in SB-Z11.\n\nAbstract\nTo a group G and a family of
subgroups F\, one can associate a simplicial complex C(F\,G)\, whose simpl
ices are in correspondence with the chains of cosets of G\, with respect t
o F. Abels and Holz studied some homotopy properties of C(F\,G)\, and thei
r relationship with G. For example\, C(F\,G) is simply-connected if and on
ly if G is the amalgamated product of subgroups in F along its intersectio
ns. C. Okay noted that for an arbitrary group G\, specializing the simple-
connectivity of C(F\,G) to the family of abelian subgroups\, forces G to b
e abelian.\n\nIn this talk I will discuss a Lie group analogue of C(F\,G)
with respect to the family of abelian subgroups\, arising from the work of
Adem\, Cohen and Torres-Giese. The main result I will describe is recent
work with O. Antolín-Camarena and S. Gritschacher which deals with the an
alogue 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:20231201T001458Z
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 Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nExotic manifo
lds are smooth manifolds which are homeomorphic but not\ndiffeomorphic to
each other. Constructing exotic manifolds in dimension\nfour has been an a
ctive research area in low dimensional and symplectic\ntopology over the l
ast 30 years. In this talk\, we will first discuss major\nopen problems an
d some recent progress in 4-manifolds theory. Then we\nwill discuss our co
nstructions of exotic 4-manifolds via pencils of complex\ncurves of small
genus and via symplectic and smooth surgeries. Some of\nour results that w
ill 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:20231201T001458Z
UID:BilTop/11
DESCRIPTION:Title:
Algebraic $K$-theory of $THH(\\mathbb{F}_p)$\nby Ozgur Bayindir (Unive
rsity of Paris 13) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbs
tract\nIn this work\, we study $THH(\\mathbb{F}_p)$ from various perspecti
ves. 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 an introduction
to\nalgebraic $K$-theory and the Nikolaus Scholze approach to trace metho
ds.\nIn the second part\, I will introduce our results and the tools we\nd
evelop to study the topological Hochschild homology of graded ring\nspectr
a and formal differential graded algebras.\n\nThis is a joint work with Ta
sos 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:20231201T001458Z
UID:BilTop/12
DESCRIPTION:Title:
The Dade group of a finite group and dimension functions\nby Ergun Yal
cin (Bilkent University) as part of Cihan Okay\n\nLecture held in SB-Z11.\
n\nAbstract\nIf $G$ is a $p$-group and $k$ is a field of characteristic $p
$\, then the Dade group $D(G)$ of $G$ \nis the group whose elements are th
e equivalence classes of capped endo-permutation $kG$-modules\, \nwhere th
e group operation is given by the tensor product over $k$. The 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 situation is mor
e complicated. There are two definitions of a Dade group of a finite\ngrou
p given by Urfer and Lassueur\, however both definitions have some shortco
mings. In a recent work \nwith Gelvin\, we give a new definition for the D
ade group $D(G)$ of a finite group $G$ by introducing a notion \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 th
e group of super class \nfunctions $C(G\, p)$ to the Dade group $D^{\\Omeg
a} (G)$ generated by relative syzygies. Our main theorem \nis the verifica
tion that the subgroup of $C(G\,p)$ consisting of the dimension functions
of k-orientable real representations \nof $G$ lies in the kernel of $\\Psi
_G$. In the proof we consider Moore $G$-spaces which are the equivariant v
ersions \nof spaces which have nonzero reduced homology in only one dimens
ion\, and use the techniques \nfrom homological algebra over the orbit cat
egory.\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:20231201T001458Z
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 Ci
han Okay\n\nLecture held in SB-Z11.\n\nAbstract\nA binary state on a graph
means an assignment of binary values to its vertices. For example\, if on
e encodes a network of spiking neurons as a directed graph\, then the spik
es produced by the neurons at an instant of time is a binary state on the
encoding graph. Allowing time to vary and recording the spiking patterns
of the neurons in the network produces an example of a binary dynamics on
the encoding graph\, namely a one-parameter family of binary states on i
t. The central object of study in this talk is the neighbourhood of a vert
ex $v$ in a graph $\\mathcal{G}$\, namely the subgraph of $\\mathcal{G}$ t
hat is generated by $v$ and all its direct neighbours in $\\mathcal{G}$.
We present a topological/graph theoretic method for extracting 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 demon
strate an application of the method to binary dynamics that arises from sa
mple activity on the Blue Brain Project reconstruction of cortical 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:20231201T001458Z
UID:BilTop/14
DESCRIPTION:Title:
Twisted homology operations\nby Calista Bernard (Stanford University)
as part of Cihan Okay\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 operations capture th
e failure of the $E_n$ multiplication to be strictly commutative\, and the
y prove useful for computations. After reviewing the main ideas from May a
nd Cohen's work\, I will discuss a framework to generalize these operation
s to homology with certain twisted coefficient systems and give a complete
classification of twisted operations for $E_{\\infty}$-algebras. I will a
lso explain computational results that show the existence of new operation
s 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:20231201T001458Z
UID:BilTop/15
DESCRIPTION:Title:
Bieberbach group and decomposing flat manifolds\nby Ho Yiu Chung (Univ
ersity of Southampton) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\
nAbstract\nAn n-dimensional Bieberbach group is a discrete\, cocompact tor
sion-free subgroup of the group of isometries of Euclidean n-space. In thi
s talk\, we will introduce the three Bieberbach theorems in order to under
stand the algebraic structure of Bieberbach groups. Such groups are intere
sting because they arise as fundamental group of compact flat Riemannian m
anifolds. In the second half of the talk\, we will discuss the Vasquez inv
ariant of finite groups which was introduced by A. T. Vasquez in 1970. Thi
s invariant is related to a decomposition theorem of sorts for compact fla
t Riemannian manifolds. We will discuss several results about such invaria
nt.\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:20231201T001458Z
UID:BilTop/16
DESCRIPTION:Title:
Higher order Toda brackets\nby Aziz Kharoof (University of Haifa) as p
art of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nToda brackets ar
e a type of higher homotopy operation. Like Massey products\, they are not
always defined\, and their value is indeterminate. Nevertheless\, they pl
ay an important role in algebraic topology and related fields:
Toda originally constructed them as a tool for computing homotopy g
roups of spheres. Adams later showed that they can be used to calculate di
fferentials in spectral sequences.\n\nAfter reviewing the construction and
properties of the classical Toda bracket\, we shall describe a higher ord
er version\, there are two ways to do that. We will provide a diagrammatic
description for the system we need to define the higher order Toda bracke
ts\, then we will use that to give alternative definition using the homoto
py 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:20231201T001458Z
UID:BilTop/17
DESCRIPTION:Title:
Hochschild cohomology of general twisted tensor products\nby Pablo San
chez Ocal (Texas A&M University) as part of Cihan Okay\n\nLecture held in
SB-Z11.\n\nAbstract\nThe Hochschild cohomology is a tool for studying asso
ciative algebras that has a lot of structure: it is a Gerstenhaber algebra
. This structure is useful because of its applications in deformation 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 Gerstenhaber algebra
structure for general twisted tensor product algebras. This will include
an unpretentious introduction to this cohomology and to our objects of int
erest\, as well as the unexpected generality of the techniques. This is jo
int work with Tekin Karadag\, Dustin McPhate\, Tolulope Oke\, and Sarah Wi
therspoon.\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:20231201T001458Z
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
Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nOur story starts with
a question in data analysis and computational topology/geometry. Given a f
inite sample of points from an unknown manifold embedded in an affine spac
e\, how can we extract information about topological invariants of the sai
d manifold? Even though the answer is known for a long time\, the connecti
ons of the question with computational geometry and data analysis have onl
y recently been made. We will review these connections\, and then move on
to the "representation problem" of homology of filtered complexes. Specifi
cally\, we will explain why "bar-codes" are enough for filtered complexes
over reals\, but why there is no such hope for other seemingly nice posets
. Then we will talk about why matroids and cobordisms (of spheres) might n
aturally provide us the necessary tools for devising a solution for this p
roblem.\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:20231201T001458Z
UID:BilTop/19
DESCRIPTION:Title:
Higher Morita categories\nby Rune Haugseng (Norwegien University of Sc
ience and Technology) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\n
Abstract\nClassical Morita theory for associative algebras can be describe
d in terms of a 2-category with associative algebras as objects\, bimodule
s as morphisms\, and bimodule homomorphisms as 2-morphisms\; this can be f
urther enhanced to a double category that also includes algebra homomorphi
sms. More generally\, we can consider 2-categories and double categories o
f enriched categories and bimodules between them. I will discuss homotopic
al versions of these structures and their higher-dimensional generalizatio
ns to $E_n$-algebras and enriched n-categories\, which are of 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:20231201T001458Z
UID:BilTop/20
DESCRIPTION:Title:
Approximate and discrete vector bundles in theory and applications\nby
Luis Scoccola (Michigan State University) as part of Cihan Okay\n\nLectur
e held in SB-Z11.\n\nAbstract\nSynchronization problems\, such as the prob
lem of reconstructing a 3D shape from a set of 2D projections\, can often
be modeled by principal bundles. Similarly\, the application of local PCA
to a point cloud concentrated around a manifold approximates the tangent b
undle of the manifold. In the first case\, the characteristic classes of t
he bundle provide obstructions to global synchronization\, while\, in the
second case\, they provide topological information of the manifold beyond
its homology\, and give obstructions to dimensionality reduction. I will d
escribe joint work with Jose Perea in which we propose notions of approxim
ate and discrete vector bundle\, study the extent to which they determine
true vector bundles\, and give algorithms for the stable and consistent co
mputation of low-dimensional characteristic classes directly from these co
mbinatorial 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:20231201T001458Z
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 Cihan Okay
\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk we will 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 implemented in the
computer algebra system Kenzo\, which has made it possible to determine ho
mology and homotopy groups of spaces of infinite type. We will 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:20231201T001458Z
UID:BilTop/22
DESCRIPTION:Title:
Variants of the Waldhausen S-construction\nby Julie Bergner (Universit
y of Virginia) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstrac
t\nThe S-construction\, first defined in the setting of cofibration catego
ries by Waldhausen\, gives a way to define the algebraic K-theory associat
ed to certain kinds of categorical input. It was proved by Galvez-Carrill
o\, Kock\, and Tonks that the result of applying this construction to an e
xact category is a decomposition space\, also called a 2-Segal space\, and
Dyckerhoff and Kapranov independently proved the same result for the slig
htly more general input of proto-exact categories. In joint work with Oso
rno\, Ozornova\, Rovelli\, and Scheimbauer\, we proved that these results
can be maximally generalized to the input of augmented stable double Segal
spaces\, so that the S-construction defines an equivalence of homotopy th
eories. In this talk\, we'll review the S-construction and the reasoning
behind these stages of generalization. Time permitting\, we'll discuss at
tempts to characterize those augmented stable double Segal spaces that cor
respond to cyclic spaces\, which is work in progress with Walker 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:20231201T001458Z
UID:BilTop/23
DESCRIPTION:Title:
Free Group Actions on Products of Two Equidimensional Spheres\nby Ozgu
n Unlu (Bilkent University) as part of Cihan Okay\n\nLecture held in SB-Z1
1.\n\nAbstract\nWe will first review some known restrictions on finite gro
ups that can act freely on products of two equidimensional spheres. Then
we will discuss some constructions of free actions of finite p-groups on p
roducts of two equidimensional spheres. Finally\, we will discuss some ope
n problems about free $p$-group actions on two equidimensional 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:20231201T001458Z
UID:BilTop/24
DESCRIPTION:Title:
Duals of P-algebras and their comodules\nby Andrew Baker (University o
f Glasgow) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nP
-algebras are connected graded cocommutative Hopf algebras which are union
s of finite dimensional Hopf algebras (which are also Poincare duality alg
ebras). These are quasi-Frobenius algebras and have some remarkable homolo
gical properties. The motivating examples for which the theory was produce
d are the Steenrod algebra at a prime and large sub and quotient \nHopf al
gebras. \n\nThe dual of a P-algebra is a commutative Hopf algebra and I wi
ll discuss some homological properties of its comodules. In particular the
re is a large class of coherent comodules which admit finitely generated p
rojective resolutions\, but finite dimensional comodules have no non-trivi
al maps from these. \n\nUsing some Cartan-Eilenberg spectral sequences thi
s can be applied to show that certain Bousfield classes of spectra are dis
tinct\, 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:20231201T001458Z
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 Cihan Okay\n\nLecture held i
n SB-Z11.\n\nAbstract\nIn non-equivariant topology the ordinary homology o
f a point is described by the dimension axiom and is quite simple - namely
\, it is concentrated in degree zero. The situation in $G$-equivariant top
ology is different. This is due to the fact that Bredon homology - the equ
ivariant counterpart of the ordinary homology - is naturally graded over $
RO(G)$\, the ring of $G$-representations. Whereas the equivariant dimensio
n axiom describes the part of the Bredon homology of a point which is grad
ed over trivial representations\, it does not put any requirements on the
rest of the grading - in which the homology may be quite complicated.\n\nT
he $RO(G)$-graded Bredon homology theories are represented by $G$-Eilenber
g-MacLane spectra\, and thus the Bredon homology of a point is the same th
ing as coefficients of these spectra. During the talk I will present the m
ethod of computing the $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-Ma
cLane spectra based on the Tate square. As demonstrated by Greenlees\, the
Tate square gives an algorithmic approach to computing the coefficients o
f equivariant spectra. In the talk we will discuss how to use this method
to obtain the $RO(C_2)$-graded coefficients of a $C_2$-Eilenberg-MacLane s
pectrum as a $RO(C_2)$-graded abelian group. We will also present the mult
iplicative structure of the $C_2$-Eilenberg-MacLane spectrum associated to
the Burnside Mackey functor. This allows us to further describe the $RO(C
_2)$-graded coefficients of any $C_2$-Eilenberg-MacLane spectrum as a modu
le over the coefficients of the $C_2$-Eilenberg-MacLane spectrum of the Bu
rnside Mackey functor. Finally\, we will discuss the $RO(C_2)$-graded ring
structure of coefficients of spectra associated to ring Mackey 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:20231201T001458Z
UID:BilTop/26
DESCRIPTION:Title:
Persistence modules and the interleaving distance\nby Tane Vergili (Ka
radeniz Technical University) as part of Cihan Okay\n\nLecture held in SB-
Z11.\n\nAbstract\nIn topological data analysis\, a persistence module is o
btained with applying homology with coefficients in some fixed field to th
e increasing family of topological spaces or complexes. The distance betwe
en two persistence modules can be measured with the interleaving metric. T
he collection of persistence modules with the interleaving metric fails to
be a topological space since it is not a set but a class. For this\, one
can restrict oneself to the identified sets together with the topology ind
uced by the interleaving distance in order to study their basic topologica
l properties. In this talk we are going to discuss persistence modules\, t
he interleaving distance and the topological properties of the considered
sets of persistence modules induced by the interleaving distance.\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:20231201T001458Z
UID:BilTop/27
DESCRIPTION:Title:
Hypergraph homology and its applications\nby Jie Wu (Hebei Normal Univ
ersity) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn p
ractical applications\, hypergraph is considered as the most general mathe
matical model for network beyond pairwise interactions. From topological v
iews\, the notion of hypergraph is a generalization of simplicial complex.
In this talk\, we will explain how to naturally extend simplicial homolog
y theory to a homology theory on hypergraphs so that algebraic topology ad
mits broader applications in practice. As applications in data science\, w
e 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:20231201T001458Z
UID:BilTop/28
DESCRIPTION:Title:
Persistent Homology and Injectivity\nby Osman Berat Okutan (Florida St
ate University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstra
ct\nPersistent homology induced by the simplicial Vietoris-Rips filtration
is a standard method for capturing topological information from metric sp
aces. In this talk\, I will describe a more geometric filtration\, obtaine
d through injective metric spaces\, which is equivalent to the Vietoris-Ri
ps filtration up to homotopy. Injective metric spaces are the injective ob
jects in the category of metric spaces. This new filtration allows one to
see new connections between the geometry and topology of the underlying sp
ace. This is a joint work with Sunhyuk Lim and Facundo Memoli.\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:20231201T001458Z
UID:BilTop/29
DESCRIPTION:Title:
Trigraded spectral sequences for principal fibrations\nby Markus Szymi
k (Norwegian University of Science and Technology) as part of Cihan Okay\n
\nLecture held in SB-Z11.\n\nAbstract\nThe Leray--Serre and the Eilenberg-
-Moore spectral sequence are fundamental tools for computing the cohomolog
y of a group or\, more generally\, of a space. In joint work with Frank Ne
umann\, we describe the relationship between these two spectral 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 examples.\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:20231201T001458Z
UID:BilTop/30
DESCRIPTION:Title:
A topological approach to signatures\nby Darrick Lee (EPFL) as part of
Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe path signature is
a characterization of paths initially developed by Chen to study the topol
ogy of loop spaces\, and has recently been used to form the foundations of
rough paths in stochastic analysis\, and provides a powerful feature map
for sequential data in machine learning. In this talk\, we return to the t
opological foundations in Chen's iterated integral cochain models to devel
op 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:20231201T001458Z
UID:BilTop/31
DESCRIPTION:Title:
Simplicial analogues of homotopic distance\nby Ayse Borat (Bursa Techn
ical University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstr
act\nHomotopic distance as introduced by Macias-Virgos and Mosquera-Lois i
n [2]\ncan be realised as a generalisation of topological complexity (TC)
and Lusternik\nSchnirelmann category (cat). In this talk\, we will introdu
ce a simplicial analogue of\nhomotopic distance (in the sense of Ortiz\, L
ara\, Gonzalez and Borat as in [3]) and\nshow that it has a relation with
simplicial complexity (as defined in [1]). We will\nalso take a glance at
contiguity distance - another simplicial analogue of homotopic\ndistance -
as introduced in [2] and improved in [4].\nReferences\n\n[1] J. Gonzalez\
, Simplicial Complexity: Piecewise Linear Motion Planning in Robotics\, Ne
w\nYork Journal of Mathematics 24 (2018)\, 279-292.\n[2] E. Macias-Virgos\
, D. Mosquera-Lois\, Homotopic Distance between Maps\, Mathematical\nProce
edings of the Cambridge Philosophical Society (2021)\, 1-21.\n[3] C. Ortiz
\, A. Lara\, J. Gonzalez\, A. Borat\, A randomized greedy algorithm for pi
ecewise linear\nmotion planning\, Mathematics\, Vol 9\, Issue 19 (2021).\n
[4] A. Borat\, M. Pamuk\, T. Vergili\, Contiguity Distance between Simplic
ial 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:20231201T001458Z
UID:BilTop/32
DESCRIPTION:Title:
An Elmendorf-Piacenza type Theorem for Actions of Monoids\nby Mehmet A
kif Erdal (Yeditepe Universitesi) as part of Cihan Okay\n\nLecture held in
SB-Z11.\n\nAbstract\nIn this talk I will describe a homotopy theory for a
ctions of monoids that is built by analyzing their ``reversible parts". Le
t $M$ 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 model structure
in which weak equivalences and fibrations are determined by the standard e
quivariant homotopy theory of $G(N)$-spaces for each $N\\leq M$. Then\, I
will show that under certain conditions on $M$ this model structure is Qui
llen equivalent to the projective model structure on the category of contr
avariant $\\mathbf{O}(M)$-diagrams of spaces\, where $\\mathbf{O}(M)$ is t
he 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 $M$-equivariant maps. Final
ly\, 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:20231201T001458Z
UID:BilTop/33
DESCRIPTION:Title:
Geometric Approaches on Persistent Homology\nby Baris Coskunuzer (UT D
allas) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nPersi
stent Homology is one of the most important techniques used in Topological
Data Analysis. In the first half of the talk\, we give an introduction to
the subject. In the second half\, we study the persistent homology output
via geometric topology tools. In particular\, we give a geometric descrip
tion of the term “persistence”. The talk will be non-technical\, and a
ccessible 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:20231201T001458Z
UID:BilTop/34
DESCRIPTION:Title:
Involution generators of mapping class groups\nby Mustafa Korkmaz (MET
U) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe mappi
ng class group of a surface plays an important role in low \ndimensional t
opology.\nIts various generating sets are known. Since it is not a quotien
t of a \ndihedral group\,\nit cannot be generated by two involutions. A ge
nerating 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:20231201T001458Z
UID:BilTop/35
DESCRIPTION:Title:
The normalizer decomposition for p-local compact groups\nby Natalia Ca
stellana (Universitat Autònoma de Barcelona) as part of Cihan Okay\n\nLec
ture held in SB-Z11.\n\nAbstract\n(with Eva Belmont\, Jelena Grbic\, Kathr
yn Lesh\, Michelle Strumila) In this project we study the normalizer decom
position of a p-local compact group in a general setting.\nWhen G is a com
pact Lie group\, using the information of the fusion system of G on a maxi
mal\ndiscrete p-toral subgroup\, we recover known decompositions in terms
of p-centric p-stubborn p-toral\nsubgroups up to p-completion. But this me
thods allow to also describe some exotic p-compact groups\nin terms of a p
ushout.\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:20231201T001458Z
UID:BilTop/36
DESCRIPTION:Title:
THH and Shadows of Bicategories\nby Nima Rasekh (EPFL) as part of Ciha
n Okay\n\nLecture held in SB-Z11.\n\nAbstract\nTopological Hochschild homo
logy (THH)\, first defined for ring spectra and then later dg-categories a
nd spectrally enriched categories\, is an important invariant with connect
ions to algebraic K-theory and fixed point methods. The existence of THH i
n such diverse contexts motivated Ponto to introduce a notion that can enc
ompass the various perspectives: a shadow of bicategories. On the other si
de\, many versions of THH have been generalized to the homotopy coherent s
etting providing us with motivation to develop an analogous homotopy coher
ent notion of shadows.\n\nThe goal of this talk is to use an appropriate b
icategorical notion of THH to prove that a shadow on a bicategory is equiv
alent to a functor out of THH of that bicategory. We then use this result
to give an alternative conceptual understanding of shadows as well as an a
ppropriate 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:20231201T001458Z
UID:BilTop/37
DESCRIPTION:Title:
Path Partial Groups\nby Antonio Viruel (Universidad de Málaga) as par
t of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this lecture we
shall show how path concatenation in a simple graph G gives rise to a par
tial group P(G) that we call the path partial group associated to the grap
h G. The construction of path partial groups is indeed functorial and allo
ws us to embed the category of simple graphs into the category of partial
groups. This embedding is full on automorphism so it shows that any group
can be realised as the full group of automorphisms of a partial group\, wh
ile not every group is the full group of automorphisms of an honest group.
Finally\, thinking of partial grops as simplicial complexes\, we show tha
t every group is the group of self homotopy equivalences of a simplicial c
omplex. This is a joint work with Antonio Díaz-Ramos (U. Malaga) and Rém
i 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:20231201T001458Z
UID:BilTop/38
DESCRIPTION:Title:
Higher limits over the fusion orbit category\nby Ergun Yalcin (Bilkent
University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\
nOne of the open problems related to the homotopy theory of fusion\nsystem
s asks whether or not the subgroup decomposition for a p-local finite\ngro
up is sharp. The sharpness of the subgroup decomposition is known to be tr
ue\nfor finite group fusion systems\, but in general this problem is still
open except\nfor some special cases. I will describe some new methods for
calculating higher\nlimits over the fusion orbit category of a discrete g
roup and show how these new\nmethods can be applied to the sharpness probl
em. In particular\, we show that\nthe subgroup decomposition for p-local f
inite groups is sharp\, if it is sharp\nfor every p-local finite group wit
h 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:20231201T001458Z
UID:BilTop/39
DESCRIPTION:Title:
An introduction to Vietoris-Rips complexes\nby Henry Adams (Colorado S
tate University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstr
act\nI will give an introduction to Vietoris-Rips complexes and their uses
in applied and computational topology. If a dataset is sampled from some
unknown underlying space (say a manifold)\, then as more and more samples
are drawn\, the Vietoris-Rips persistent homology of the dataset converges
to the Vietoris-Rips persistent homology of the manifold. But little is k
nown about Vietoris-Rips complexes of manifolds. An exception is the case
of the circle: I will describe how as the scale parameter increases\, the
Vietoris-Rips complexes of the circle obtain the homotopy types of the cir
cle\, the 3-sphere\, the 5-sphere\, ...\, until finally they are contracti
ble. Much less is known about Vietoris-Rips complexes of spheres. I will a
lso briefly explain how Vietoris-Rips complexes relate to generalizations
of the Borsuk-Ulam theorem and to Gromov-Hausdorff distances between spher
es.\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:20231201T001458Z
UID:BilTop/40
DESCRIPTION:Title:
UMAP for the working mathematician\nby Rick Jardine (Western Universit
y) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe Healy
-McInnes UMAP algorithm is a highly successful clustering tool that involv
es interesting ideas from mathematics and data science:\n\n1) Spivak's the
ory of extended pseudo metric spaces (ep-metric spaces)\n2) TDA constructi
ons in ep-metric spaces\n3) weighted graphs\n4) classical dimension reduct
ion\n5) graph optimization: fuzzy sets\, cross entropy\n\nI will explain t
he 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:20231201T001458Z
UID:BilTop/41
DESCRIPTION:Title:
Topologically protected vortex knots and links\nby Toni Annala (Univer
sity of British Columbia) as part of Cihan Okay\n\n\nAbstract\nThe physica
l properties of condensed-matter systems can often be approximated by a "m
ean field" which\, outside a small singular locus of the system (defects)\
, takes values in a topological space M called the order parameter space.
A topological vortex is a codimension two defect\, about which the order p
arameter field winds in a way that corresponds to a non-contractible loop
in M. If the fundamental group of the order parameter space is non-Abelian
\, then these vortices exhibit a remarkable behavior: not all pairs of top
ological vortices are free to pass through each other.\n\nIt is then a nat
ural to wonder if such vortices could be employed in tying robust linked s
tructures in physical fields. As a minimum\, such a structure should not u
ntie via strand crossings and local reconnections\, which are the usual me
ans of decay for knotted and linked vortex loops. In this talk\, we will p
resent several examples of such structures. Our approach is based on the f
act that if the second homotopy group of M is trivial\, then the order par
ameter field admits a combinatorial description\, which\, depending on the
fundamental group of M\, can be expressed graphically. Hence\, finding to
pologically stable tangled structures reduces to constructing nontrivial i
nvariants for "colored" links\, which remain unchanged in strand 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:20231201T001458Z
UID:BilTop/42
DESCRIPTION:Title:
A Krull-Remak-Schmidt theorem for fusion systems\nby Bob Oliver (Unive
rsité PARIS 13) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstr
act\nThe Krull-Remak-Schmidt theorem\, when restricted to finite groups\,
implies \nthat every finite group factorizes as a product of indecomposabl
e subgroups \nwhich are unique up to isomorphism. But the theorem actually
says much \nmore. For example\, as a special case\, it implies that this
factorization is \nunique (not only up to isomorphism) whenever 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 tr
ue for fusion systems over finite \n$p$-groups (in fact\, for fusion syste
ms over discrete $p$-toral groups). In \nthis talk\, I plan to begin by di
scussing the original theorem for groups \nand sketching its proof\, and t
hen\, after a brief introduction to fusion \nsystems\, describe how these
ideas can be carried over \nto prove the corresponding result in that sett
ing.\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:20231201T001458Z
UID:BilTop/43
DESCRIPTION:Title:
Sequential Motion Planning assisted by Group Actions\nby Enrique Torre
s (Trinity Western University) as part of Cihan Okay\n\nLecture held in SB
-Z11.\n\nAbstract\nIn this talk I will revisit the concept of effectual an
d effective topological complexity (TC) in the context of sequential motio
n planning. These invariants provide a natural context to incorporate grou
p actions into the study of the motion planning problem. Related to these
invariants\, I will talk about a third version of TC that incorporates the
group action into its planners\, which we call orbital topological comple
xity. I will discuss how they relate to each other and to the TC of the qu
otient space. I will also present some calculations for actions of the gro
up 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:20231201T001458Z
UID:BilTop/44
DESCRIPTION:Title:
Fusion systems\, linking systems and punctured groups\nby Ellen Henke
(TU Dresden) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\
nSaturated fusion systems and associated linking systems are categories mo
delling the $p$-local structure of finite groups. In particular\, linking
systems contain the algebraic information that is needed to study $p$-comp
leted classifying spaces of fusion systems similarly to $p$-completed cla
ssifying spaces of finite groups. If $G$ is a finite group and $S$ is a Sy
low $p$-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 morp
hisms between two objects are the injective group homomorphisms induced by
conjugation with elements of $G$. Saturated fusion systems which do not a
rise in this way are called exotic.\n\n\n\nThe concept of a linking system
was generalized by Oliver and Ventura to transporter systems. Andrew Cher
mak introduced moreover group-like structures\, called localities\, which
correspond in a certain way to transporter systems. I will give an introdu
ction to the subject and outline how the theory of localities can be used
to prove new theorems on fusion systems. Moreover\, I will report on a pro
ject with Assaf Libman and Justin Lynd\, where we study "punctured groups'
'. Here a transporter system (or a locality) associated to fusion system $
\\F$ over $S$ is called a punctured group if the object set is the collect
ion of all non-identity subgroups. It should be noted in this 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 system whose obj
ect set is the full collection of subgroups of $S$. In particular\, to eve
ry group fusion system one can associate a punctured group. In the project
with Libman and Lynd\, we determine for many of the known exotic fusion s
ystems 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:20231201T001458Z
UID:BilTop/45
DESCRIPTION:Title:
The Gromov-Hausdorff distance between spheres\nby Facundo Mémoli (Ohi
o State University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAb
stract\nThe Gromov-Hausdorff distance is a fundamental tool in Riemanian g
eometry\, and also in applied geometry and topology. Whereas it is often e
asy to estimate the value of the distance between two given metric spaces\
, its precise value is rarely easy to determine. Some of these estimates
follow from considerations related to the notion of 'persistent 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 between certain pair
s of spheres (endowed with their geodesic distance). These results involve
lower bounds\, which arise from certain versions of the Borsuk-Ulam theor
em which are applicable to discontinuous maps\, and from the construction
of specialized ``correspondences" between spheres which yield matching up
per 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:20231201T001458Z
UID:BilTop/46
DESCRIPTION:Title:
An introduction to infinity categories\nby David Blanc (Haifa Universi
ty) as part of Cihan Okay\n\n\nAbstract\nIn studying the homotopy theory o
f topological spaces it soon becomes apparent that the homotopy category i
tself is not sufficient\, since many homotopy invariants cannot be describ
ed or calculated in that category.\n\nSince there are other settings\, suc
h as the chain complexes of homological algebra\, in which this holds\, Qu
illen proposed an axiomatization of such situations in terms of model cate
gories. However\, these turn out\n\nto be too restrictive for dealing with
certain questions\, and in particular with homotopy commutative diagrams
and the invariants (such as Toda brackets) which they encode. Dwyer and Ka
n suggested an\n\nalternative simplicial approach\, which later devolved i
nto several independent models for what we now call infinity categories\,
in terms of simplicially enriched categories\, simplicial spaces\, quasi-c
ategories\, and others.\n\nIn the talk we will provide examples of questio
ns best addressed in this setting\, and briefly describe the form they tak
e 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:20231201T001458Z
UID:BilTop/47
DESCRIPTION:Title:
Simplicial sets\nby Aziz Kharoof (Bilkent University) as part of Cihan
Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThis talk aims to introduce
and recall basic notions on simplicial sets. Apart from basic definitions\
, we would like to discuss the following notions: weak equivalences\, Kan
complexes\, Kan fibrations\, and geometric realization. Also\, the adjunct
ion between singular simplicial set and geometric realization should be co
vered.\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:20231201T001458Z
UID:BilTop/48
DESCRIPTION:Title:
Quasicategories\nby Aziz Kharoof (Bilkent University) as part of Cihan
Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk we will introdu
ce the first model of infinity categories\, namely quasicategories. We wil
l 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 topolog
ical space gives rise to a quasicategory – i.e.\, via the fundamental in
finity-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:20231201T001458Z
UID:BilTop/49
DESCRIPTION:Title:
Basic constructions in quasicategories\nby Igor Sikora (Bilkent Univer
sity) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe go
al of this talk is the discussion of the basic notions and constructions i
n the theory of infinity categories. We want to discuss the following cons
tructions: the product of quasicategries\, homotopy category of a quasicat
egory\, 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:20231201T001458Z
UID:BilTop/50
DESCRIPTION:Title:
Model categories I - basic definitions\nby Mustafa Akkaya (Bilkent Uni
versity) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe
goal of this talk is to provide basic definitions of the theory model cat
egories. We would like to introduce the definition of a model category and
its homotopy category. In particular\, this will require a discussion of
fibrations\, cofibrations and weak equivalences\, fibrant and cofibrant ob
jects\, cylinder and path objects. Then we will proceed to the notion of l
eft and right homotopy and define the homotopy category of a model categor
y. The whole theory will be shown using two examples: Quillen model struct
ure on topological spaces and Quillen model structure on simplicial 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:20231201T001458Z
UID:BilTop/51
DESCRIPTION:Title:
Model Categories II - Derived functors and Quillen adjunctions\nby Igo
r Sikora (Bilkent University) as part of Cihan Okay\n\nLecture held in SB-
Z11.\n\nAbstract\nHaving the notion of a homotopy category\, we will defin
e the notion of a derived functor. Further on\, we will proceed to the ide
a of comparing model structures and their homotopy categories by Quillen f
unctors. Therefore we will cover Quillen functors\, Quillen adjunctions an
d Quillen equivalences. We will also prove that Quillen model structures o
n simplicial sets and topological spaces are Quillen equivalent. The talk
will finish with a model structure on simplicial sets which is relevant fo
r the theory of quasicategories\, i.e.\, the Joyal model structure.\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:20231201T001458Z
UID:BilTop/52
DESCRIPTION:Title:
Simplicial Categories I\nby Igor Sikora (Bilkent University) as part o
f Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we wil
l discuss the second model of infinity categories: categories enriched ove
r simplicial sets. We will start with a short overview of enriched categor
ies and follow to the simplicial categories. We will also introduce simpli
cial functors and the homotopy category of a simplicial category. 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:20231201T001458Z
UID:BilTop/53
DESCRIPTION:Title:
Simplicial categories II - Dwyer-Kan localizations\nby Aziz Kharoof (B
ilkent University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbs
tract\nThe goal of this talk will be to understand the idea of localizatio
n of a category with respect to the class of maps and see how Dwyer-Kan lo
calization is an example of such. Therefore we will start with the notion
of a localization of a category. Then we will proceed to several approache
s to the Dwyer-Kan localization - as a derived functor with specific resol
ution and the hammock version\, that gives a constructive description of t
he homotopy category. We will discuss the relation of DK localization 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:20231201T001458Z
UID:BilTop/54
DESCRIPTION:Title:
Segal spaces I\nby Özgün Ünlü (Bilkent University) as part of Ciha
n Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThis talk will prepare a ba
ckground for the third model of infinity categories: complete Segal spaces
. Therefore the following topics should be discussed: bisimplicial sets\,
model structures on functor categories\, Reedy model structure as an examp
le of the injective model structure and Rezk nerve of a category.\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:20231201T001458Z
UID:BilTop/55
DESCRIPTION:by Bob Oliver (Université PARIS 13) as part of Cihan Okay\n\n
Lecture 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:20231201T001458Z
UID:BilTop/56
DESCRIPTION:Title:
Segal spaces II\nby Igor Sikora (Bilkent University) as part of Cihan
Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we will contin
ue introducing the third model of infinity categories: complete Segal spac
es. The following notions will be covered: Segal spaces\, homotopy categor
y of Segal spaces\, completeness of Segal spaces and CSS model 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:20231201T001458Z
UID:BilTop/57
DESCRIPTION:Title:
Homotopy Coherent Nerve\nby Redi Haderi (Bilkent University) as part o
f Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we aim
to understand the equivalences between two different models of infinity-c
ategories: Simplicial categories and quasi-categories. We will define the
homotopy coherent nerve as a functor from simplicial categories to simplic
ial sets\, construct its left adjoint\, and we will show how this gives us
a Quillen equivalence between the described model categories.\n
LOCATION:https://researchseminars.org/talk/BilTop/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART;VALUE=DATE-TIME:20230516T130000Z
DTEND;VALUE=DATE-TIME:20230516T140000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/58
DESCRIPTION:Title:
Complete Segal spaces and generalizations to higher $(\\infty\,n)$-categor
ies\nby Julie Bergner (University of Virginia) as part of Cihan Okay\n
\nLecture held in SB-Z11.\n\nAbstract\nComplete Segal spaces provide one o
f the nicest models for $(\\infty\,1)$-categories from the perspective of
homotopy theory\, since the model structure can be obtained as a localizat
ion of the Reedy model structure on simplicial spaces. In this talk\, we'
ll recall complete Segal spaces and their model structure\, and then compa
re them with other models. We will then look at some of the ways these co
mparisons can be generalized higher $(\\infty\,n)$-categories.\n
LOCATION:https://researchseminars.org/talk/BilTop/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Antonio Torres Castillo (CIMAT)
DTSTART;VALUE=DATE-TIME:20230522T153000Z
DTEND;VALUE=DATE-TIME:20230522T170000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/59
DESCRIPTION:Title:
Stable homotopy type of p-local finite groups via biset functors\nby V
ictor Antonio Torres Castillo (CIMAT) as part of Cihan Okay\n\nLecture hel
d in SB-Z11.\n\nAbstract\nThe Martino-Priddy conjecture (now a theorem) sa
ys that the p-fusion of G can be recovered (up to isomorphism) from the un
stable homotopy type of BG^p. By making strong use of the Segal conjecture
\, the same authors approached a stable analogous of that result. In this
talk\, we will explore some consequences of the (so-called) stable Martino
-Priddy conjecture and their generalizations for p-local finite groups.\n
LOCATION:https://researchseminars.org/talk/BilTop/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (The University of Virginia)
DTSTART;VALUE=DATE-TIME:20230523T133000Z
DTEND;VALUE=DATE-TIME:20230523T150000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/60
DESCRIPTION:Title:
A story about spans\nby Walker Stern (The University of Virginia) as p
art of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nSpans in a categ
ory C arise in a variety of disparate contexts\, from the study partially
defined functions between sets to Lagrangian correspondences in symplectic
geometry. In this talk\, I will give an overview of some of these connect
ions and tell a story which leads from algebras in categories of spans to
operads. Along the way\, I will discuss past and ongoing work (part of the
latter joint with Ivan Contreras and Rajan Mehta) analyzing and classifyi
ng various algebraic structures in spans.\n
LOCATION:https://researchseminars.org/talk/BilTop/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haihan Wu (The University of California\, Davis)
DTSTART;VALUE=DATE-TIME:20230524T153000Z
DTEND;VALUE=DATE-TIME:20230524T170000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/61
DESCRIPTION:Title:
Webs and Clasps\nby Haihan Wu (The University of California\, Davis) a
s part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe discovery
of the Jones polynomial triggered mathematical\ndevelopments in areas inc
luding knot theory and quantum algebra. One way\nto define the Jones polyn
omial is by using the braiding in the Temperley-Lieb\ncategory\, which can
be defined with planar matching. We can use diagrams\nand graphical calcu
lations in the Temperley-Lieb category to study the rep-\nresentation theo
ry of quantum sl2. The irreducible representations can be\n“visualized
” as the Jones-Wenzl projectors\, which can be used to compute\ncolored
Jones polynomial and quantum sl2 3-manifold invariant.\n\nThe sl2 case is
generalized to other simple Lie algebras by introducing triva-\nlent verti
ces\, and the generalized graphical categories are called spiders or web\n
categories. Clasps are defined as analogues of the Jones-Wenzl projectors\
, and\nwe can use clasps to compute colored quantum link invariants\, quan
tum 3-\nmanifold invariants\, 3-j symbols\, and 6-j symbols of different q
uantum groups.\n\nIn this talk\, I will review the background material\, a
nd talk about re-\ncent developments on definition of web categories and c
lasp expansions for\ndifferent Lie types.\n
LOCATION:https://researchseminars.org/talk/BilTop/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230925T103000Z
DTEND;VALUE=DATE-TIME:20230925T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/62
DESCRIPTION:Title:
Homotopical characterization of strong contextuality (part I)\nby Aziz
Kharoof (Bilkent University) as part of Cihan Okay\n\nLecture held in SB-
Z11.\n\nAbstract\nSimplicial distributions introduced in the paper “Simp
licial quantum contextuality” provide a topological approach to the stud
y of contextuality for collections of probability distributions. The space
of measurements and the space of outcomes are represented by simplicial s
ets\, so one can ask what is the role of the homotopy theory of simplicial
sets here. In this talk\, we will give a homotopical characterization of
strongly contextual simplicial distributions with binary outcomes\, specif
ically those defined on the cone of a 1-dimensional space. To prove this\,
we introduce the corresponding category for simplicial distribution on th
e cone of a 1-dimensional space and give the characterization of strong co
ntextuality in terms of this category.\n
LOCATION:https://researchseminars.org/talk/BilTop/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART;VALUE=DATE-TIME:20231002T103000Z
DTEND;VALUE=DATE-TIME:20231002T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/63
DESCRIPTION:Title:
Homotopical characterization of strong contextuality (part II)\nby Azi
z Kharoof (Bilkent University) as part of Cihan Okay\n\nLecture held in SB
-Z11.\n\nAbstract\nSimplicial distributions introduced in the paper “Sim
plicial quantum contextuality” provide a topological approach to the stu
dy of contextuality for collections of probability distributions. The spac
e of measurements and the space of outcomes are represented by simplicial
sets\, so one can ask what is the role of the homotopy theory of simplicia
l sets here. In this talk\, we will give a homotopical characterization of
strongly contextual simplicial distributions with binary outcomes\, speci
fically those defined on the cone of a 1-dimensional space. To prove this\
, we introduce the corresponding category for simplicial distribution on t
he cone of a 1-dimensional space and give the characterization of strong c
ontextuality in terms of this category.\n
LOCATION:https://researchseminars.org/talk/BilTop/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART;VALUE=DATE-TIME:20231009T103000Z
DTEND;VALUE=DATE-TIME:20231009T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/64
DESCRIPTION:Title:
Colimits of categories\, zig-zags and necklaces\nby Redi Haderi (Bilke
nt University) as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstrac
t\nColimits of simplicial categories are generally considered hard to unde
rstand in explicit terms. Important simplicial categories\, such as those
freely generated by simplicial sets\, arise as such colimits. In fact\, th
e free simplicial category - coherent nerve adjunction has been demonstrat
ed by Lurie to be a Quillen equivalence.\nWe discuss how the problem of co
mputing colimits of simplicial categories reduces to computing colimits of
categories. Then\, we present a theorem which describes the latter in exp
licit terms (to the best of our knowledge\, not in the literature). As an
application\, we provide a computational proof of the Necklace Theorem of
Dugger and Spivak.\n
LOCATION:https://researchseminars.org/talk/BilTop/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora
DTSTART;VALUE=DATE-TIME:20231023T103000Z
DTEND;VALUE=DATE-TIME:20231023T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/65
DESCRIPTION:Title:
Equivariant contextuality\nby Igor Sikora as part of Cihan Okay\n\nLec
ture held in SB-Z11.\n\nAbstract\nSimplicial quantum contextuality\, intro
duced by Okay\, Kharoof and Ipek\, is a framework for using topological me
thods based on simplicial sets to study quantum contextuality. It subsumes
earlier approaches - topological (Okay\, Roberts\, Bartlett\, Raussendorf
) and sheaf-theoretic (Abramsky\, Brandenburger).\n\nIn this talk we will
discuss how group action can be composed into this framework. To this end\
, we will use such tools as Borel construction and partial groups in the s
ense of Broto-Gonzalez. We will start with the notions of equivariant simp
licial distributions and equivariant contextuality and connect them with t
he Borel construction. Then we will proceed with the cohomological aspects
\, which are based on the extensions of partial groups and cofibre sequenc
es of simplicial sets.\n\nThe talk is based on a joint work with Cihan Oka
y\, to appear on arxiv soon.\n
LOCATION:https://researchseminars.org/talk/BilTop/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Cantarero
DTSTART;VALUE=DATE-TIME:20231030T140000Z
DTEND;VALUE=DATE-TIME:20231030T150000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/66
DESCRIPTION:Title:
Configuration spaces of commuting elements\nby Jose Cantarero as part
of Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe rational cohomol
ogy of the configuration space of commuting\nelements in a compact Lie gro
up is determined by the action of the Weyl group on the configuration spac
e of its maximal torus. This can be used to determine (co)homological stab
ility phenomena and other unstable computations. In this talk I will begin
with some motivation for the study of these spaces and the case of SU(2)\
, where the homotopy type can be completely determined. Then I will descri
be the stability results mentioned previously and other interesting cohomo
logy computations. This is joint work with Ángel R. Jiménez.\n
LOCATION:https://researchseminars.org/talk/BilTop/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koray Karabina
DTSTART;VALUE=DATE-TIME:20231106T103000Z
DTEND;VALUE=DATE-TIME:20231106T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/67
DESCRIPTION:Title:
Secure Boundary Matrix Reduction Algorithm Using Homomorphic Encryption\nby Koray Karabina as part of Cihan Okay\n\nLecture held in SB-Z11.\n\nA
bstract\nTopological Data Analysis (TDA) offers a suite of computational t
ools that provide quantified shape features in high-dimensional data\, whi
ch can be utilized by modern statistical and predictive machine learning m
odels. In particular\, persistent homology (PH) takes in data and derives
compact representations of latent topological structures\, known as persis
tence diagrams. PH has been widely adopted for model development on sensit
ive data\, motivating the computation of PH on encrypted data. In this pre
sentation\, I will provide brief introductions to TDA and secure computing
and then demonstrate how to modify the boundary matrix reduction algorith
m to compute PH on encrypted data using homomorphic encryption.\n
LOCATION:https://researchseminars.org/talk/BilTop/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Torres Castillo
DTSTART;VALUE=DATE-TIME:20231113T103000Z
DTEND;VALUE=DATE-TIME:20231113T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/68
DESCRIPTION:Title:
Partial group cohomology\nby Victor Torres Castillo as part of Cihan O
kay\n\nLecture held in SB-Z11.\n\nAbstract\nPartial groups were introduced
by Chermak as a tool to approach the issue of the existence and uniquenes
s of a centric linking system for a saturated fusion system. Roughly speak
ing\, a partial group is a set with a partially defined product (you can s
till multiply certain strings of elements together\, but not always).\nIn
this talk\, we will discuss the main similarities and differences between
the categories of partial groups and (actual) groups. Then\, we will intro
duce the cohomology of a partial group inspired by the Gabriel-Zisman coho
mology\, as defined by Galvez-Neumann-Tonks.\nThe talk is based on a joint
work in progress with Cihan Okay and Igor Sikora.\n
LOCATION:https://researchseminars.org/talk/BilTop/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Kirtisoglu
DTSTART;VALUE=DATE-TIME:20231120T103000Z
DTEND;VALUE=DATE-TIME:20231120T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/69
DESCRIPTION:Title:
Thomason's Homotopy Colimit Theorem\nby Mehmet Kirtisoglu as part of C
ihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we will d
iscuss the proof of Thomason's homotopy colimit theorem. The theorem state
s that given a functor from a small category to the category of small cate
gories\, the homotopy colimit construction on the nerves of the categorie
s in the diagram is naturally homotopy equivalent to the nerve space of th
e Grothendieck Construction.\n
LOCATION:https://researchseminars.org/talk/BilTop/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern
DTSTART;VALUE=DATE-TIME:20231127T103000Z
DTEND;VALUE=DATE-TIME:20231127T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/70
DESCRIPTION:Title:
$(\\infty\,2)$-categories and lax colimits\nby Walker Stern as part of
Cihan Okay\n\nLecture held in SB-Z11.\n\nAbstract\nMany higher-categorica
l structures\, most notably $(\\infty\,1)$-categories themselves\, form $(
\\infty\,2)$-categories. It is thus highly desirable to characterize such
structures in terms of $(\\infty\,2)$-categorical universal properties. On
e recent framework allowing us to understand such $(\\infty\,2)$-categoric
al universal properties is the theory of (co)limits in $(\\infty\,2)$-cate
gories. In this talk\, I will explain the developing theory of (partially)
lax colimits in $(\\infty\,2)$-categories\, and discuss how it recovers a
number of previous notions in the literature. I will then explain how one
can generalize from the $(\\infty\,1)$-categorical setting to obtain a co
finality criterion for $(\\infty\,2)$-functors. This work was joint with F
ernando Abellán.\n
LOCATION:https://researchseminars.org/talk/BilTop/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ivan Piterman
DTSTART;VALUE=DATE-TIME:20231204T103000Z
DTEND;VALUE=DATE-TIME:20231204T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/71
DESCRIPTION:Title:
Advances on Quillen's conjecture\nby Kevin Ivan Piterman as part of Ci
han Okay\n\nLecture held in SB-Z11.\n\nAbstract\nThe study of the p-subgro
up complexes began motivated by group cohomology and equivariant cohomolog
y of topological spaces "modulo the prime p". For example\, Kenneth Brown
proved that the reduced Euler characteristic of this complex is divisible
by the size of a Sylow p-subgroup\, giving rise to a sort of "Homological
Sylow theorem". Later\, he showed that the mod-p equivariant cohomology of
the p-subgroup complex of a finite group coincides with the mod-p cohomol
ogy of the group. Deeper relations with finite group theory\, representati
on theory\, and finite geometries were also explored. For instance\, uniqu
eness of certain simple groups\, finite geometries for sporadic groups\, L
efschetz modules\, and\, more recently\, endotrivial modules.\n\nIn 1978\,
Daniel Quillen conjectured that the poset of non-trivial p-subgroups of a
finite group G is contractible if and only if G has non-trivial p-core. Q
uillen established the conjecture for solvable groups and some families of
groups of Lie type. The major step towards the resolution of the conjectu
re was done by Michael Aschbacher and Stephen D. Smith at the beginning of
the nineties. They roughly proved that if p>5 and G is a group of minimal
order failing the conjecture\, then G contains a simple component PSU(n\,
q^2) failing a certain homological condition denoted by (QD) (namely\, the
top-degree homology group of its p-subgroup poset does not vanish).\n\nIn
this talk\, I will present recent advances in the conjecture\, with a par
ticular focus on the prime p=2\, which was not covered by the methods deve
loped by Aschbacher-Smith. In particular\, we show that the study of the c
onjecture for the prime p=2 basically reduces to studying (QD) on the pose
t of p-subgroups of certain families of classical groups. Part of this wor
k is in collaboration with S.D. Smith\n
LOCATION:https://researchseminars.org/talk/BilTop/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART;VALUE=DATE-TIME:20231211T103000Z
DTEND;VALUE=DATE-TIME:20231211T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/72
DESCRIPTION:Title:
Filling Radius and Persistent Homology\nby Baris Coskunuzer as part of
Cihan Okay\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we disc
uss interesting relations between notions from applied topology and metric
geometry in point cloud setting. First\, we introduce several notions in
both fields to measure the size of a manifold. Then\, for a point cloud X
in R^n\, we relate the life spans of the topological features to their ext
rinsic and Gromov’s filling radius in R^n\, and by using this relation\,
we give bounds for them with Urysohn width. Next\, we discuss an interest
ing relationship between the life spans of the topological features in PD_
k(X) in R^n and l^\\infty principal components (PCA_\\infty) of the point
cloud X.\n
LOCATION:https://researchseminars.org/talk/BilTop/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART;VALUE=DATE-TIME:20231211T133000Z
DTEND;VALUE=DATE-TIME:20231211T143000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/73
DESCRIPTION:Title:
Topological Machine Learning and Applications in Drug Discovery and Cancer
Detection\nby Baris Coskunuzer as part of Cihan Okay\n\nLecture held
in SB-Z11.\n\nAbstract\nIn this talk\, we'll introduce fundamental techniq
ues in topological machine learning and showcase their application in two
specific contexts. The first application is on computer-aided drug discove
ry\, utilizing Multiparameter Persistence for graph representation learnin
g. Our second application revolves around cancer detection from histopatho
logical images via cubical persistence. We apply our methodologies across
five distinct cancer types\, demonstrating superior performance compared t
o state-of-the-art deep learning methods. The talk is accessible to gradua
te students in math\, science\, and engineering\, assuming no prior backgr
ound in topology or machine learning.\n
LOCATION:https://researchseminars.org/talk/BilTop/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imma Gálvez Carrillo
DTSTART;VALUE=DATE-TIME:20231218T103000Z
DTEND;VALUE=DATE-TIME:20231218T113000Z
DTSTAMP;VALUE=DATE-TIME:20231201T001458Z
UID:BilTop/74
DESCRIPTION:by Imma Gálvez Carrillo as part of Cihan Okay\n\nLecture held
in SB-Z11.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilTop/74/
END:VEVENT
END:VCALENDAR