BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Robert Young (NYU)
DTSTART:20200817T160000Z
DTEND:20200817T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/1
DESCRIPTION:Title: Co
mposing and decomposing surfaces in $\\mathbb{R}^n$ and $\\mathbb{H}_n$\nby Robert Young (NYU) as part of Topology and geometry: extremal and ty
pical\n\n\nAbstract\nHow do you build a complicated surface? How can you d
ecompose a surface into simple pieces? Understanding how to construct an o
bject can help you understand how to break it down. In this talk\, we will
present some constructions and decompositions of surfaces based on unifor
m rectifiability. We will use these decompositions to study problems in ge
ometric measure theory and metric geometry\, such as how to measure the no
norientability of a surface and how to optimize an embedding of the Heisen
berg group into $L_1$ (joint with Assaf Naor).\n
LOCATION:https://researchseminars.org/talk/TG_ET/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panos Papasoglu (Oxford)
DTSTART:20200831T160000Z
DTEND:20200831T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/2
DESCRIPTION:Title: Ur
yson width and volume\nby Panos Papasoglu (Oxford) as part of Topology
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 an $n-1$
dimensional complex. It turns out that this is a useful tool to approach
several geometric problems.\n\nIn this talk we will give a brief survey of
some questions in `curvature free' geometry and sketch a novel approach t
o the classical systolic inequality of Gromov. Our approach follows up re
cent work of Guth relating Uryson width and local volume growth. For examp
le we deduce also the following result of Guth: there is an $\\epsilon _n>
0$ such that for any $R>0$ and any compact aspherical $n$-manifold $M$ the
re is a ball $B(R)$ of radius $R$ in the universal cover of $M$ such that
$vol(B(R))\\geq \\epsilon _n R^n$.\n
LOCATION:https://researchseminars.org/talk/TG_ET/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Pengitore (Ohio State)
DTSTART:20200914T160000Z
DTEND:20200914T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/3
DESCRIPTION:Title: Co
arse embeddings and homological filling functions\nby Mark Pengitore (
Ohio State) as part of Topology and geometry: extremal and typical\n\n\nAb
stract\nIn this talk\, we will relate homological filling functions and th
e existence of coarse embeddings. In particular\, we will demonstrate that
a coarse embedding of a group into a group of geometric dimension 2 induc
es an inequality on homological Dehn functions in dimension 2. As an appli
cation of this\, we are able to show that if a finitely presented group co
arsely embeds into a hyperbolic group of geometric dimension 2\, then it i
s hyperbolic. Another application is a characterization of subgroups of gr
oups with quadratic Dehn function. If there is enough time\, we will talk
about various higher dimensional generalizations of our main result.\n
LOCATION:https://researchseminars.org/talk/TG_ET/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Regina Rotman (Toronto)
DTSTART:20201012T160000Z
DTEND:20201012T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/4
DESCRIPTION:Title: Ri
cci curvature\, the length of a shortest periodic geodesic and quantitativ
e Morse theory on loop spaces\nby Regina Rotman (Toronto) as part of T
opology and geometry: extremal and typical\n\n\nAbstract\nI am planning to
present the following result of mine: Let $M^n$ be a closed Riemannian ma
nifold of dimension $n$ and $\\operatorname{Ric} \\geq (n−1)$. Then the
length of a shortest periodic geodesic can be at most $8\\pi n$.\n\nThe te
chnique involves quantitative Morse theory on loop spaces. We will discuss
some related results in geometry of loop spaces on Riemannian manifolds.\
n
LOCATION:https://researchseminars.org/talk/TG_ET/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Balitskiy (MIT)
DTSTART:20200921T160000Z
DTEND:20200921T170000Z
DTSTAMP:20260422T212926Z
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://researchseminars.org/talk/TG_ET/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radmila Sazdanović (NCSU)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/6
DESCRIPTION:Title: Bi
g data and applied topology methods in knot theory\nby Radmila Sazdano
vić (NCSU) as part of Topology and geometry: extremal and typical\n\n\nAb
stract\nA multitude of knot invariants\, including quantum invariants and
their categorifications\, have been introduced to aid with characterizing
and classifying knots and their topological properties. Relations between
knot invariants and their relative strengths at distinguishing knots are s
till mostly elusive. We use Principal Component Analysis (PCA)\, Ball Mapp
er\, and machine learning to examine the structure of data consisting of v
arious polynomial knot invariants and the relations between them. Although
of different origins\, these methods confirm and illuminate similar subst
ructures in knot data. These approaches also enable comparison between num
erical invariants of knots such as the signature and s-invariant via their
distribution within the Alexander and Jones polynomial data. Although thi
s work focuses on knot theory the ideas presented can be applied to other
areas of pure mathematics and possibly in data science. The hybrid approac
h introduced here can be useful for infinite data sets where representativ
e sampling is impossible or impractical.\n
LOCATION:https://researchseminars.org/talk/TG_ET/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Nabutovsky (Toronto)
DTSTART:20201109T170000Z
DTEND:20201109T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/7
DESCRIPTION:Title: Is
operimetric inequality for Hausdorff content and some of its applications<
/a>\nby Alex Nabutovsky (Toronto) as part of Topology and geometry: extrem
al and typical\n\n\nAbstract\nWe will discuss the isoperimetric inequality
for Hausdorff content and compact metric spaces in (possibly infinite-dim
ensional) Banach spaces. We will also discuss some of its implications for
systolic geometry\, in particular\, systolic inequalities of a new type t
hat are true for much wider classes of non-simply connected Riemannian man
ifolds than Gromov’s classical systolic inequality.\n\nJoint work with Y
. Liokumovich\, B. Lishak\, and R. Rotman.\n
LOCATION:https://researchseminars.org/talk/TG_ET/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Burago (Penn State)
DTSTART:20201123T170000Z
DTEND:20201123T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/8
DESCRIPTION:Title: On
some unsolved problems in Geometry and around\nby Dmitri Burago (Penn
State) as part of Topology and geometry: extremal and typical\n\n\nAbstra
ct\nThis is not quite a research talk. This is a collection of problems (i
n random order). Some of them arose from my research (often with collabora
tors)\, some are known or folklore known\, and there is some progress in o
ur work. The problems are followed by comments which often contain announc
ements of recent results of mine (with co-authors) and brief discussions.
At many places\, I may be rather vague and also omit known definitions and
discussions of known results.\n
LOCATION:https://researchseminars.org/talk/TG_ET/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Elliott (MIT)
DTSTART:20201207T170000Z
DTEND:20201207T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/9
DESCRIPTION:Title: Di
stortion in loop space\nby Robin Elliott (MIT) as part of Topology and
geometry: extremal and typical\n\n\nAbstract\nHow efficiently can we repr
esent a large integer multiple $k\\alpha$ of a given non-torsion element $
\\alpha$ of a homotopy group of a Riemannian manifold? Here efficiency is
measured by the Lipschitz constant $L$ of a representing map\, and the que
stion is quantitatively answered by bounding the asymptotics of the minima
l $L$ needed to represent $k\\alpha$. In this talk I will talk about relat
ed functions defined in terms of the (co)homology of the loop space of the
Riemannian manifold. I will discuss results for producing general upper b
ounds and applications of these\, as well as specific constructions for lo
wer bounds.\n
LOCATION:https://researchseminars.org/talk/TG_ET/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sahana Vasudevan (MIT)
DTSTART:20210111T170000Z
DTEND:20210111T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/10
DESCRIPTION:Title: L
arge genus bounds for the distribution of triangulated surfaces in moduli
space\nby Sahana Vasudevan (MIT) as part of Topology and geometry: ext
remal and typical\n\n\nAbstract\nTriangulated surfaces are compact hyperbo
lic Riemann surfaces that admit a conformal triangulation by equilateral t
riangles. They arise naturally in number theory as Riemann surfaces define
d over number fields\, in probability theory as conjecturally related to L
iouville quantum gravity\, and in metric geometry as a model to understand
arbitrary hyperbolic surfaces. Brooks and Makover started the study of th
e geometry of random large genus triangulated surfaces. Mirzakhani later p
roved analogous results for random hyperbolic surfaces. These results\, al
ong with many others\, suggest that the geometry of triangulated surfaces
mirrors the geometry of arbitrary hyperbolic surfaces especially in the ca
se of large genus asymptotics. In this talk\, I will describe an approach
to show that triangulated surfaces are asymptotically well-distributed in
moduli space.\n
LOCATION:https://researchseminars.org/talk/TG_ET/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Polterovich (Tel Aviv University)
DTSTART:20210222T170000Z
DTEND:20210222T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/11
DESCRIPTION:Title: B
ig fibers in symplectic topology\nby Leonid Polterovich (Tel Aviv Univ
ersity) as part of Topology and geometry: extremal and typical\n\n\nAbstra
ct\nWe argue that existence of symplectically rigid fibers of integrable s
ystems can be put on an equal footing with big fiber theorems from other a
reas of mathematics such as the Centerpoint theorem from combinatorics
and the Gromov maximal fiber theorem from topology. Our approach involves
a symplectic counterpart of ideal-valued measures\, and a new cohomology t
heory by Umut Varolgüneş. Symplectic preliminaries will be explained. Th
is is work in progress with Adi Dickstein\, Yaniv Ganor\, and Frol Zapolsk
y.\n
LOCATION:https://researchseminars.org/talk/TG_ET/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedya Manin (UCSB)
DTSTART:20210125T170000Z
DTEND:20210125T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/12
DESCRIPTION:Title: L
inear nullhomotopies for maps to spheres\nby Fedya Manin (UCSB) as par
t of Topology and geometry: extremal and typical\n\n\nAbstract\nI will exp
lain the following theorem. Let $X$ be a finite complex ($S^m$ is a good e
xample to keep in mind). Then every nullhomotopic\, $L$-Lipschitz map $X \
\to S^n$ has a $C(X\,n) \\cdot (L+1)$-Lipschitz nullhomotopy. The proof is
spread over several papers\, and the full story has never been told in on
e place. Joint and separate work variously with Chambers\, Dotterrer\, Wei
nberger\, Berdnikov\, and Guth.\n
LOCATION:https://researchseminars.org/talk/TG_ET/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Sauer (KIT)
DTSTART:20210208T170000Z
DTEND:20210208T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/13
DESCRIPTION:Title: A
ction on Cantor spaces and macroscopic scalar curvature\nby Roman Saue
r (KIT) as part of Topology and geometry: extremal and typical\n\n\nAbstra
ct\nWe prove the macroscopic cousins of three conjectures: 1) a conjectura
l bound of the simplicial volume of a Riemannian manifold in the presence
of a lower scalar curvature bound\, 2) the conjecture that rationally esse
ntial manifolds do not admit metrics of positive scalar curvature\, 3) a c
onjectural bound of $\\ell^2$-Betti numbers of aspherical Riemannian manif
olds in the presence of a lower scalar curvature bound. The macroscopic co
usin is the statement one obtains by replacing a lower scalar curvature bo
und by an upper bound on the volumes of 1-balls in the universal cover. Gr
oup actions on Cantor spaces surprisingly play an important role in the pr
oof. The talk is based on joint work with Sabine Braun.\n
LOCATION:https://researchseminars.org/talk/TG_ET/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (Ohio State)
DTSTART:20210308T170000Z
DTEND:20210308T180000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/14
DESCRIPTION:Title: R
andom cubical complexes\nby Matthew Kahle (Ohio State) as part of Topo
logy and geometry: extremal and typical\n\n\nAbstract\nVarious models of r
andom simplicial complex have been studied extensively over the past 15 ye
ars or so. We will discuss two models for random cubical complex\, and wha
t we know so far about their expected topological behavior:\n\n* 2-dimensi
onal plaquettes in a 4-dimensional torus. This is joint work with Paul Dun
can and Ben Schweinhart.\nhttps://arxiv.org/abs/2011.11903\n\n* Random 2-d
imensional subcomplexes of an $n$-dimensional cube. This is joint work wit
h Elliot Paquette and Érika Roldán.\nhttps://arxiv.org/abs/2001.07812\n
LOCATION:https://researchseminars.org/talk/TG_ET/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Alpert (UBC)
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260422T212926Z
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://researchseminars.org/talk/TG_ET/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanan Diao (UNC Charlotte)
DTSTART:20210405T160000Z
DTEND:20210405T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/16
DESCRIPTION:Title: T
he ropelength of knots\nby Yuanan Diao (UNC Charlotte) as part of Topo
logy and geometry: extremal and typical\n\n\nAbstract\nThe ropelength $R(K
)$ of a knot $K$ is the minimum length of a unit thickness rope needed 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 the minim
um crossing number of $K$. In this talk I will first give a brief introduc
tion to the ropelength problem. I will then show that there exists a const
ant $a_0>0$ such that $R(K)\\ge a_0 \\textbf{b}(K)$ for any knot $K$\, whe
re $\\textbf{b}(K)$ is the braid index of $K$. It follows that if $\\textb
f{b}(K)\\ge a_1 {\\rm{Cr}}(K)$ 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 sma
ll compared to ${\\rm{Cr}}(K)$ (in fact there are alternating knots with a
rbitrarily large crossing numbers but fixed braid indices)\, then this res
ult cannot be applied directly. I will show that this result can in fact b
e applied in an indirect way to prove that the conjecture holds for a larg
e class of alternating knots\, regardless what their braid indices are.\n
LOCATION:https://researchseminars.org/talk/TG_ET/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madhur Tulsiani (TTIC)
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/17
DESCRIPTION:Title: E
xplicit optimization lower bounds from topological expansion\nby Madhu
r Tulsiani (TTIC) as part of Topology and geometry: extremal and typical\n
\n\nAbstract\nI will explain a recent construction of explicit instances o
f optimization problems\, which are hard for the family of optimization al
gorithms captured by so called “sum-of-squares” (SoS) hierarchy of sem
idefinite programs. The SoS hierarchy is a powerful family of algorithms\,
which captures many known optimization and approximation algorithms. Seve
ral constructions of random families of instances have been proved to be h
ard for these algorithms\, in the literature on optimization and proof com
plexity (since the duals of these optimization algorithms can be viewed as
proof systems). I will describe a recent construction\, based on the Rama
nujan 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\, Yuval Fi
lmus\, and Prahladh Harsha.\n
LOCATION:https://researchseminars.org/talk/TG_ET/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Lerario (SISSA)
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/18
DESCRIPTION:Title: M
oduli spaces of geometric graphs\nby Antonio Lerario (SISSA) as part o
f Topology and geometry: extremal and typical\n\n\nAbstract\nIn this talk
I will investigate the structure of the "moduli space" $W(G\,d)$ of a geom
etric graph $G$\, i.e. the set of all possible geometric realizations in $
\\mathbb R^d$ of a given graph $G$ on $n$ vertices. Such moduli space is S
panier–Whitehead dual to a real algebraic discriminant.\n\nFor example\,
in the case of geometric realizations of $G$ on the real line\, the modul
i space $W(G\, 1)$ is a component of the complement of a hyperplane arrang
ement in $\\mathbb R^n$. (Another example: when $G$ is the empty graph on
n vertices\, $W(G\, d)$ is homotopy equivalent to the configuration space
of $n$ points in $\\mathbb R^d$.) Numerous questions about graph enumerati
on can be formulated in terms of the topology of this moduli space.\n\nI w
ill explain how to associate to a graph $G$ a new graph invariant which en
codes the asymptotic structure of the moduli space when $d$ goes to infini
ty\, 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 invari
ant $B(G)$\, even though the cohomology of $W(G\,d)$ "shifts" its dimensio
n. We call the invariant $B(G)$ the "Floer number" of the graph $G$\, as
its construction is reminiscent of Floer theory from symplectic geometry.\
n\nJoint work with M. Belotti and A. Newman.\n
LOCATION:https://researchseminars.org/talk/TG_ET/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Apanasov (Oklahoma)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260422T212926Z
UID:TG_ET/19
DESCRIPTION:Title: C
onformal interbreeding\, Teichmüller spaces and applications\nby Bori
s Apanasov (Oklahoma) as part of Topology and geometry: extremal and typic
al\n\n\nAbstract\nWe present a new effect in the theory of deformations of
hyperbolic manifolds/orbifolds or their uniform hyperbolic lattices (i.e
. in the Teichmüller spaces of conformally flat structures on closed hype
rbolic 3-manifolds). We show that such varieties may have connected compon
ents whose dimensions differ by arbitrary large numbers. This is based on
our "Siamese twins construction" of non-faithful discrete representations
of hyperbolic lattices related to non-trivial "symmetric hyperbolic 4-cobo
rdisms" and the Gromov–Piatetski-Shapiro interbreeding construction. The
re are several applications of this result\, from new non-trivial hyperbol
ic homology 4-cobordisms and wild 2-knots in the 4-sphere\, to bounded qua
siregular locally homeomorphic mappings\, especially to their asymptotics
in the unit 3-ball solving well known conjectures in geometric function th
eory.\n
LOCATION:https://researchseminars.org/talk/TG_ET/19/
END:VEVENT
END:VCALENDAR