BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Robert Young (NYU)
DTSTART:20200817T160000Z
DTEND:20200817T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/1
DESCRIPTION:Title: Composing and decomposing surfaces in $\\mathbb{R}^n$ and $\\mathbb{H
}_n$\nby Robert Young (NYU) as part of Topology and geometry: extremal
and typical\n\n\nAbstract\nHow do you build a complicated surface? How ca
n you decompose a surface into simple pieces? Understanding how to constru
ct an object can help you understand how to break it down. In this talk\,
we will present some constructions and decompositions of surfaces based on
uniform rectifiability. We will use these decompositions to study problem
s in geometric measure theory and metric geometry\, such as how to measure
the nonorientability of a surface and how to optimize an embedding of the
Heisenberg group into $L_1$ (joint with Assaf Naor).\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panos Papasoglu (Oxford)
DTSTART:20200831T160000Z
DTEND:20200831T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/2
DESCRIPTION:Title: Uryson width and volume\nby Panos Papasoglu (Oxford) as part of T
opology and geometry: extremal and typical\n\n\nAbstract\nThe Uryson width
of an $n$-manifold gives a way to describe how close is the manifold to a
n $n-1$ dimensional complex. It turns out that this is a useful tool to ap
proach several geometric problems.\n\nIn this talk we will give a brief su
rvey of some questions in `curvature free' geometry and sketch a novel app
roach to the classical systolic inequality of Gromov. Our approach follow
s up recent work of Guth relating Uryson width and local volume growth. Fo
r example we deduce also the following result of Guth: there is an $\\epsi
lon _n>0$ such that for any $R>0$ and any compact aspherical $n$-manifold
$M$ there is a ball $B(R)$ of radius $R$ in the universal cover of $M$ su
ch that $vol(B(R))\\geq \\epsilon _n R^n$.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Pengitore (Ohio State)
DTSTART:20200914T160000Z
DTEND:20200914T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/3
DESCRIPTION:Title: Coarse embeddings and homological filling functions\nby Mark Peng
itore (Ohio State) as part of Topology and geometry: extremal and typical\
n\n\nAbstract\nIn this talk\, we will relate homological filling functions
and the existence of coarse embeddings. In particular\, we will demonstra
te that a coarse embedding of a group into a group of geometric dimension
2 induces an inequality on homological Dehn functions in dimension 2. As a
n application of this\, we are able to show that if a finitely presented g
roup coarsely embeds into a hyperbolic group of geometric dimension 2\, th
en it is hyperbolic. Another application is a characterization of subgroup
s of groups with quadratic Dehn function. If there is enough time\, we wil
l talk about various higher dimensional generalizations of our main result
.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Regina Rotman (Toronto)
DTSTART:20201012T160000Z
DTEND:20201012T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/4
DESCRIPTION:Title: Ricci curvature\, the length of a shortest periodic geodesic and quan
titative Morse theory on loop spaces\nby Regina Rotman (Toronto) as pa
rt of Topology and geometry: extremal and typical\n\n\nAbstract\nI am plan
ning to present the following result of mine: Let $M^n$ be a closed Rieman
nian manifold of dimension $n$ and $\\operatorname{Ric} \\geq (n−1)$. Th
en the length of a shortest periodic geodesic can be at most $8\\pi n$.\n\
nThe technique involves quantitative Morse theory on loop spaces. We will
discuss some related results in geometry of loop spaces on Riemannian mani
folds.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Balitskiy (MIT)
DTSTART:20200921T160000Z
DTEND:20200921T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/5
DESCRIPTION:by Alexey Balitskiy (MIT) as part of Topology and geometry: ex
tremal and typical\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radmila Sazdanović (NCSU)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/6
DESCRIPTION:Title: Big data and applied topology methods in knot theory\nby Radmila
Sazdanović (NCSU) as part of Topology and geometry: extremal and typical\
n\n\nAbstract\nA multitude of knot invariants\, including quantum invarian
ts and their categorifications\, have been introduced to aid with characte
rizing and classifying knots and their topological properties. Relations b
etween knot invariants and their relative strengths at distinguishing knot
s are still mostly elusive. We use Principal Component Analysis (PCA)\, Ba
ll Mapper\, and machine learning to examine the structure of data consisti
ng of various polynomial knot invariants and the relations between them. A
lthough of different origins\, these methods confirm and illuminate simila
r substructures in knot data. These approaches also enable comparison betw
een numerical invariants of knots such as the signature and s-invariant vi
a their distribution within the Alexander and Jones polynomial data. Altho
ugh this work focuses on knot theory the ideas presented can be applied to
other areas of pure mathematics and possibly in data science. The hybrid
approach introduced here can be useful for infinite data sets where repres
entative sampling is impossible or impractical.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Nabutovsky (Toronto)
DTSTART:20201109T170000Z
DTEND:20201109T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/7
DESCRIPTION:Title: Isoperimetric inequality for Hausdorff content and some of its applic
ations\nby Alex Nabutovsky (Toronto) as part of Topology and geometry:
extremal and typical\n\n\nAbstract\nWe will discuss the isoperimetric ine
quality for Hausdorff content and compact metric spaces in (possibly infin
ite-dimensional) Banach spaces. We will also discuss some of its implicati
ons for systolic geometry\, in particular\, systolic inequalities of a new
type that are true for much wider classes of non-simply connected Riemann
ian manifolds than Gromov’s classical systolic inequality.\n\nJoint work
with Y. Liokumovich\, B. Lishak\, and R. Rotman.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Burago (Penn State)
DTSTART:20201123T170000Z
DTEND:20201123T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/8
DESCRIPTION:Title: On some unsolved problems in Geometry and around\nby Dmitri Burag
o (Penn State) as part of Topology and geometry: extremal and typical\n\n\
nAbstract\nThis is not quite a research talk. This is a collection of prob
lems (in random order). Some of them arose from my research (often with co
llaborators)\, some are known or folklore known\, and there is some progre
ss in our work. The problems are followed by comments which often contain
announcements of recent results of mine (with co-authors) and brief discus
sions. At many places\, I may be rather vague and also omit known definiti
ons and discussions of known results.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Elliott (MIT)
DTSTART:20201207T170000Z
DTEND:20201207T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/9
DESCRIPTION:Title: Distortion in loop space\nby Robin Elliott (MIT) as part of Topol
ogy and geometry: extremal and typical\n\n\nAbstract\nHow efficiently can
we represent a large integer multiple $k\\alpha$ of a given non-torsion el
ement $\\alpha$ of a homotopy group of a Riemannian manifold? Here efficie
ncy is measured by the Lipschitz constant $L$ of a representing map\, and
the question is quantitatively answered by bounding the asymptotics of the
minimal $L$ needed to represent $k\\alpha$. In this talk I will talk abou
t related functions defined in terms of the (co)homology of the loop space
of the Riemannian manifold. I will discuss results for producing general
upper bounds and applications of these\, as well as specific constructions
for lower bounds.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sahana Vasudevan (MIT)
DTSTART:20210111T170000Z
DTEND:20210111T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/10
DESCRIPTION:Title: Large genus bounds for the distribution of triangulated surfaces in
moduli space\nby Sahana Vasudevan (MIT) as part of Topology and geomet
ry: extremal and typical\n\n\nAbstract\nTriangulated surfaces are compact
hyperbolic Riemann surfaces that admit a conformal triangulation by equila
teral triangles. They arise naturally in number theory as Riemann surfaces
defined over number fields\, in probability theory as conjecturally relat
ed to Liouville quantum gravity\, and in metric geometry as a model to und
erstand arbitrary hyperbolic surfaces. Brooks and Makover started the stud
y of the geometry of random large genus triangulated surfaces. Mirzakhani
later proved analogous results for random hyperbolic surfaces. These resul
ts\, along with many others\, suggest that the geometry of triangulated su
rfaces mirrors the geometry of arbitrary hyperbolic surfaces especially in
the case of large genus asymptotics. In this talk\, I will describe an ap
proach to show that triangulated surfaces are asymptotically well-distribu
ted in moduli space.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Polterovich (Tel Aviv University)
DTSTART:20210222T170000Z
DTEND:20210222T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/11
DESCRIPTION:Title: Big fibers in symplectic topology\nby Leonid Polterovich (Tel Av
iv University) as part of Topology and geometry: extremal and typical\n\n\
nAbstract\nWe argue that existence of symplectically rigid fibers of integ
rable systems can be put on an equal footing with big fiber theorems from
other areas of mathematics such as the Centerpoint theorem from combina
torics and the Gromov maximal fiber theorem from topology. Our approach in
volves a symplectic counterpart of ideal-valued measures\, and a new cohom
ology theory by Umut Varolgüneş. Symplectic preliminaries will be explai
ned. This is work in progress with Adi Dickstein\, Yaniv Ganor\, and Frol
Zapolsky.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedya Manin (UCSB)
DTSTART:20210125T170000Z
DTEND:20210125T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/12
DESCRIPTION:Title: Linear nullhomotopies for maps to spheres\nby Fedya Manin (UCSB)
as part of Topology and geometry: extremal and typical\n\n\nAbstract\nI w
ill explain the following theorem. Let $X$ be a finite complex ($S^m$ is a
good example to keep in mind). Then every nullhomotopic\, $L$-Lipschitz m
ap $X \\to S^n$ has a $C(X\,n) \\cdot (L+1)$-Lipschitz nullhomotopy. The p
roof is spread over several papers\, and the full story has never been tol
d in one place. Joint and separate work variously with Chambers\, Dotterre
r\, Weinberger\, Berdnikov\, and Guth.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Sauer (KIT)
DTSTART:20210208T170000Z
DTEND:20210208T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/13
DESCRIPTION:Title: Action on Cantor spaces and macroscopic scalar curvature\nby Rom
an Sauer (KIT) as part of Topology and geometry: extremal and typical\n\n\
nAbstract\nWe prove the macroscopic cousins of three conjectures: 1) a con
jectural bound of the simplicial volume of a Riemannian manifold in the pr
esence of a lower scalar curvature bound\, 2) the conjecture that rational
ly essential manifolds do not admit metrics of positive scalar curvature\,
3) a conjectural bound of $\\ell^2$-Betti numbers of aspherical Riemannia
n manifolds in the presence of a lower scalar curvature bound. The macrosc
opic cousin is the statement one obtains by replacing a lower scalar curva
ture bound by an upper bound on the volumes of 1-balls in the universal co
ver. Group actions on Cantor spaces surprisingly play an important role in
the proof. The talk is based on joint work with Sabine Braun.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (Ohio State)
DTSTART:20210308T170000Z
DTEND:20210308T180000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/14
DESCRIPTION:Title: Random cubical complexes\nby Matthew Kahle (Ohio State) as part
of Topology and geometry: extremal and typical\n\n\nAbstract\nVarious mode
ls of random simplicial complex have been studied extensively over the pas
t 15 years or so. We will discuss two models for random cubical complex\,
and what we know so far about their expected topological behavior:\n\n* 2-
dimensional plaquettes in a 4-dimensional torus. This is joint work with P
aul Duncan and Ben Schweinhart.\nhttps://arxiv.org/abs/2011.11903\n\n* Ran
dom 2-dimensional subcomplexes of an $n$-dimensional cube. This is joint w
ork with Elliot Paquette and Érika Roldán.\nhttps://arxiv.org/abs/2001.0
7812\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Alpert (UBC)
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/15
DESCRIPTION:by Hannah Alpert (UBC) as part of Topology and geometry: extre
mal and typical\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanan Diao (UNC Charlotte)
DTSTART:20210405T160000Z
DTEND:20210405T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/16
DESCRIPTION:Title: The ropelength of knots\nby Yuanan Diao (UNC Charlotte) as part
of Topology and geometry: extremal and typical\n\n\nAbstract\nThe ropeleng
th $R(K)$ of a knot $K$ is the minimum length of a unit thickness rope nee
ded to tie the knot. If $K$ is alternating\, it is conjectured that $R(K)\
\ge a {\\rm{Cr}}(K)$ for some constant $a>0$\, where ${\\rm{Cr}}(K)$ is th
e minimum crossing number of $K$. In this talk I will first give a brief i
ntroduction to the ropelength problem. I will then show that there exists
a constant $a_0>0$ such that $R(K)\\ge a_0 \\textbf{b}(K)$ for any knot $K
$\, where $\\textbf{b}(K)$ is the braid index of $K$. It follows that if $
\\textbf{b}(K)\\ge a_1 {\\rm{Cr}}(K)$ for some constant $a_1>0$\, then $R(
K)\\ge a_0 a_1 {\\rm{Cr}}(K)=a {\\rm{Cr}}(K)$. However if $\\textbf{b}(K)$
is small compared to ${\\rm{Cr}}(K)$ (in fact there are alternating knots
with arbitrarily large crossing numbers but fixed braid indices)\, then t
his result cannot be applied directly. I will show that this result can in
fact be applied in an indirect way to prove that the conjecture holds for
a large class of alternating knots\, regardless what their braid indices
are.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madhur Tulsiani (TTIC)
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/17
DESCRIPTION:Title: Explicit optimization lower bounds from topological expansion\nb
y Madhur Tulsiani (TTIC) as part of Topology and geometry: extremal and ty
pical\n\n\nAbstract\nI will explain a recent construction of explicit inst
ances of optimization problems\, which are hard for the family of optimiza
tion algorithms captured by so called “sum-of-squares” (SoS) hierarchy
of semidefinite programs. The SoS hierarchy is a powerful family of algor
ithms\, which captures many known optimization and approximation algorithm
s. Several constructions of random families of instances have been proved
to be hard for these algorithms\, in the literature on optimization and pr
oof complexity (since the duals of these optimization algorithms can be vi
ewed as proof systems). I will describe a recent construction\, based on t
he Ramanujan complexes of Samuels\, Lubotzky and Vishne\, which yields the
first explicit family instances\, where the optimization problem is hard
even to solve approximately (using SoS).\n\nJoint work with Irit Dinur\, Y
uval Filmus\, and Prahladh Harsha.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lerario (SISSA)
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/18
DESCRIPTION:Title: Moduli spaces of geometric graphs\nby Antonio Lerario (SISSA) as
part of Topology and geometry: extremal and typical\n\n\nAbstract\nIn thi
s talk I will investigate the structure of the "moduli space" $W(G\,d)$ of
a geometric graph $G$\, i.e. the set of all possible geometric realizatio
ns in $\\mathbb R^d$ of a given graph $G$ on $n$ vertices. Such moduli spa
ce is Spanier–Whitehead dual to a real algebraic discriminant.\n\nFor ex
ample\, in the case of geometric realizations of $G$ on the real line\, th
e moduli space $W(G\, 1)$ is a component of the complement of a hyperplane
arrangement in $\\mathbb R^n$. (Another example: when $G$ is the empty gr
aph on n vertices\, $W(G\, d)$ is homotopy equivalent to the configuration
space of $n$ points in $\\mathbb R^d$.) Numerous questions about graph en
umeration can be formulated in terms of the topology of this moduli space.
\n\nI will explain how to associate to a graph $G$ a new graph invariant w
hich encodes the asymptotic structure of the moduli space when $d$ goes to
infinity\, for fixed $G$. Surprisingly\, the sum of the Betti numbers of
$W(G\,d)$ stabilizes as $d$ goes to infinity\, and gives the claimed graph
invariant $B(G)$\, even though the cohomology of $W(G\,d)$ "shifts" its d
imension. We call the invariant $B(G)$ the "Floer number" of the graph $G
$\, as its construction is reminiscent of Floer theory from symplectic geo
metry.\n\nJoint work with M. Belotti and A. Newman.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Apanasov (Oklahoma)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260404T094702Z
UID:TG_ET/19
DESCRIPTION:Title: Conformal interbreeding\, Teichmüller spaces and applications\n
by Boris Apanasov (Oklahoma) as part of Topology and geometry: extremal an
d typical\n\n\nAbstract\nWe present a new effect in the theory of deformat
ions of hyperbolic manifolds/orbifolds or their uniform hyperbolic lattice
s (i.e. in the Teichmüller spaces of conformally flat structures on clos
ed hyperbolic 3-manifolds). We show that such varieties may have connected
components whose dimensions differ by arbitrary large numbers. This is ba
sed on our "Siamese twins construction" of non-faithful discrete represent
ations of hyperbolic lattices related to non-trivial "symmetric hyperbolic
4-cobordisms" and the Gromov–Piatetski-Shapiro interbreeding constructi
on. There are several applications of this result\, from new non-trivial h
yperbolic homology 4-cobordisms and wild 2-knots in the 4-sphere\, to boun
ded quasiregular locally homeomorphic mappings\, especially to their asymp
totics in the unit 3-ball solving well known conjectures in geometric func
tion theory.\n
LOCATION:https://stable.researchseminars.org/talk/TG_ET/19/
END:VEVENT
END:VCALENDAR