[iasmath-seminars] Mathematics Seminars - Week of March 4, 2019
Kristina Phillips
kphillips at ias.edu
Fri Mar 1 17:32:40 EST 2019
INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540
Mathematics Seminars
Week of March 4, 2019
--------------
Please note the following seminars will be held in the West Building Lecture
Hall the week of March 4.
· Computer Science/Discrete Mathematics Seminar I – Monday, March 4
· Symplectic Dynamics/Geometry Seminar – Monday, March 4
· Computer Science/Discrete Mathematics Seminar II – Tuesday, March
5
· Working Group on Geometric Applications of the Langlands
Correspondence – Wednesday, March 6
The following seminars have been cancelled.
· Members' Seminar – Monday, March 4
· Variational Methods in Geometry Seminar – Tuesday, March 5 (both
1:00pm & 3:30pm talks)
· Symplectic Dynamics Working Group – Tuesday, March 5
--------------
Monday, March 4
Workshop on Geometric Functionals: Analysis and Applications
Topic: Compactness of conformally compact Einstein
manifolds in dimension 4
Speaker: Alice Chang, Princeton University
Time/Room: 10:00am - 11:00am/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142664>
http://www.math.ias.edu/seminars/abstract?event=142664
Computer Science/Discrete Mathematics Seminar I
Topic: Local and global expansion of graphs
Speaker: Yuval Peled, New York University
Time/Room: 11:00am - 12:00pm/West Building Lecture Hall
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=143187>
http://www.math.ias.edu/seminars/abstract?event=143187
Workshop on Geometric Functionals: Analysis and Applications
Topic: Singularities of Teichmueller harmonic map flow
Speaker: Melanie Rupflin, University of Oxford
Time/Room: 11:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142667>
http://www.math.ias.edu/seminars/abstract?event=142667
Seminar on Theoretical Machine Learning
Topic: FFJORD: Free-form Continuous Dynamics for Scalable
Reversible Generative Models
Speaker: Will Grathwohl, University of Toronto
Time/Room: 12:15pm - 1:45pm/Princeton University, CS 302
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=139487>
http://www.math.ias.edu/seminars/abstract?event=139487
Members' Seminar
Speaker: No seminar (workshop)
Time/Room: 2:00pm - 3:00pm/No seminar (workshop)
Workshop on Geometric Functionals: Analysis and Applications
Topic: Self-similar solutions of mean curvature flow and
entropy
Speaker: Jacob Bernstein, Johns Hopkins University; Member,
School of Mathematics
Time/Room: 2:30pm - 3:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142670>
http://www.math.ias.edu/seminars/abstract?event=142670
Symplectic Dynamics/Geometry Seminar
Topic: Gysin sequences and cohomology ring of symplectic
fillings
Speaker: Zhengyi Zhou, Member, School of Mathematics
Time/Room: 3:30pm - 4:30pm/West Building Lecture Hall
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=143193>
http://www.math.ias.edu/seminars/abstract?event=143193
Workshop on Geometric Functionals: Analysis and Applications
Topic: Kaehler constant scalar curvature metrics on blow
ups and resolutions of singularities
Speaker: Claudio Arezzo, International Centre for Theoretical
Physics, Trieste
Time/Room: 4:00pm - 5:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142673>
http://www.math.ias.edu/seminars/abstract?event=142673
Joint IAS/Princeton University Algebraic Geometry Seminar
Topic: Volumes and intersection theory on moduli spaces
of Abelian differentials
Speaker: Dawei Chen, Boston College; Member, School of
Mathematics
Time/Room: 5:00pm - 6:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=141992>
http://www.math.ias.edu/seminars/abstract?event=141992
Tuesday, March 5
Workshop on Geometric Functionals: Analysis and Applications
Topic: L^p curvatures : some analysis questions from
gauge theory
Speaker: Tristan Rivière, ETH Zürich; Member, School of
Mathematics
Time/Room: 10:00am - 11:00am/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142679>
http://www.math.ias.edu/seminars/abstract?event=142679
Computer Science/Discrete Mathematics Seminar II
Topic: To Be Announced
Speaker: Swastik Kopparty, Rutgers University; Member, School
of Mathematics
Time/Room: 10:30am - 12:30pm/West Building Lecture Hall
Workshop on Geometric Functionals: Analysis and Applications
Topic: Spacetime positive mass theorem
Speaker: Lan-Hsuan Huang, University of Connecticut; von
Neumann Fellow, School of Mathematics
Time/Room: 11:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142682>
http://www.math.ias.edu/seminars/abstract?event=142682
Variational Methods in Geometry Seminar
Speaker: no seminar (Variational Methods in Geometry Workshop
week)
Time/Room: 1:00pm - 3:00pm/no seminar (Variational Methods in Geometry
Workshop week)
Symplectic Dynamics Working Group
Speaker: No Seminar
Time/Room: 1:30pm - 3:00pm/No Seminar
Workshop on Geometric Functionals: Analysis and Applications
Topic: Periodic Geodesics and Geodesic Nets on Riemannian
Manifolds
Speaker: Regina Rotman, University of Toronto; Member, School
of Mathematics
Time/Room: 2:30pm - 3:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142685>
http://www.math.ias.edu/seminars/abstract?event=142685
Variational Methods in Geometry Seminar
Speaker: no seminar (Variational Methods in Geometry Workshop
week)
Time/Room: 3:30pm - 5:30pm/no seminar (Variational Methods in Geometry
Workshop week)
Workshop on Geometric Functionals: Analysis and Applications
Topic: Liouville Equations and Functional Determinants
Speaker: Andrea Malchiodo, Scuola Normale Superiore
Time/Room: 4:00pm - 5:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142676>
http://www.math.ias.edu/seminars/abstract?event=142676
Wednesday, March 6
Workshop on Geometric Functionals: Analysis and Applications
Topic: Normalized harmonic map flow
Speaker: Michael Struwe, ETH Zürich
Time/Room: 10:00am - 11:00am/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142691>
http://www.math.ias.edu/seminars/abstract?event=142691
Workshop on Geometric Functionals: Analysis and Applications
Topic: Loop products, closed geodesics and
self-intersections
Speaker: Nancy Hingston, The College of New Jersey
Time/Room: 11:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142694>
http://www.math.ias.edu/seminars/abstract?event=142694
Workshop on Geometric Functionals: Analysis and Applications
Topic: Nature of some stationary varifolds near
multiplicity 2 tangent planes
Speaker: Neshan Wickramasekera, University of Cambridge;
Member, School of Mathematics
Time/Room: 2:30pm - 3:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142688>
http://www.math.ias.edu/seminars/abstract?event=142688
Working Group on Geometric Applications of the Langlands Correspondence
Speaker: Daniel Litt, University of Georgia; Member, School of
Mathematics
Time/Room: 3:30pm - 5:30pm/West Building Lecture Hall
Workshop on Geometric Functionals: Analysis and Applications
Topic: Existence and uniqueness of Green's function to a
nonlinear Yamabe problem
Speaker: Yanyan Li, Rutgers University
Time/Room: 4:00pm - 5:00pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142700>
http://www.math.ias.edu/seminars/abstract?event=142700
Mathematical Conversations
Topic: From Celestial Mechanics to the Arnold Conjectures
Speaker: Umberto Hryniewicz, Universidade Federal do Rio de
Janeiro; von Neumann Fellow, School of Mathematics
Time/Room: 6:00pm - 7:30pm/Dilworth Room
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=136645>
http://www.math.ias.edu/seminars/abstract?event=136645
Thursday, March 7
Workshop on Geometric Functionals: Analysis and Applications
Topic: Compactness and finiteness theorems (almost)
without curvature
Speaker: Gerard Besson, Université de Grenoble
Time/Room: 10:00am - 11:00am/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142703>
http://www.math.ias.edu/seminars/abstract?event=142703
Venkatesh Working Group
Time/Room: 10:00am - 12:00pm/West Building Lecture Hall
Workshop on Geometric Functionals: Analysis and Applications
Topic: One-cycle sweepout estimates of essential surfaces
in closed Riemannian manifolds
Speaker: Stéphane Sabourau, Université Paris-Est Créteil
Time/Room: 11:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142706>
http://www.math.ias.edu/seminars/abstract?event=142706
Analysis Seminar
Topic: TBD
Speaker: TBD
Time/Room: 1:00pm - 2:00pm/Simonyi Hall 101
Working Seminar in Algebraic Number Theory
Speaker: tba
Time/Room: 2:15pm - 3:15pm/Princeton University
Workshop on Geometric Functionals: Analysis and Applications
Topic: $L^2$ curvature for surfaces in Riemannian
manifolds
Speaker: Ernst Kuwert, University of Freiburg
Time/Room: 2:30pm - 3:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142709>
http://www.math.ias.edu/seminars/abstract?event=142709
Joint IAS/Princeton University Number Theory Seminar
Topic: Special cycles on orthogonal Shimura varieties
Speaker: Eugenia Rosu, University of Arizona
Time/Room: 4:30pm - 5:30pm/Princeton University, Fine Hall 214
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=139909>
http://www.math.ias.edu/seminars/abstract?event=139909
Friday, March 8
Workshop on Geometric Functionals: Analysis and Applications
Topic: Ricci flows that attain their initial data weakly
Speaker: Peter Topping, University of Warwick
Time/Room: 10:00am - 11:00am/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142712>
http://www.math.ias.edu/seminars/abstract?event=142712
Workshop on Geometric Functionals: Analysis and Applications
Topic: Filling metric spaces
Speaker: Alexander Nabutovsky, University of Toronto; Member,
School of Mathematics
Time/Room: 11:30am - 12:30pm/Simonyi Hall 101
Abstract Link: <http://www.math.ias.edu/seminars/abstract?event=142715>
http://www.math.ias.edu/seminars/abstract?event=142715
1 Compactness of conformally compact Einstein manifolds in dimension 4
Alice Chang
Abstract: Given a class of conformally compact Einstein manifolds with
boundary, we are interested to study the compactness of the class under some
local and non-local boundary constraints. I will report some joint work with
Yuxin Ge and Jie Qing including compactness results which are improvements
of the earlier conditions obtained by Chang-Ge and compactness results under
perturbation conditions when the L2 norm of the Weyl curvature is small. As
a by product, we will derive the global uniqueness of conformally compact
Einstein metrics on the 4-Ball constructed in the earlier work of
Graham-Lee.
http://www.math.ias.edu/seminars/abstract?event=142664
2 Local and global expansion of graphs
Yuval Peled
The emerging theory of High-Dimensional Expansion suggests a number of
inherently different notions to quantify expansion of simplicial complexes.
We will talk about the notion of local spectral expansion, that plays a key
role in recent advances in PCP theory, coding theory and counting
complexity. Our focus is on bounded-degree complexes, where the problems can
be stated in a graph-theoretic language:
Let $G$ be a graph. For a vertex $v \in G$, we denote by $G_v$ the subgraph
of $G $ that is induced by the neighbors of $v$. We say that $G$ is
$(a,b)$-regular if (I) $G$ is $a$-regular and (II) $G_v$ is $b$-regular for
every vertex $v$. We analyse the spectral expansion of $(a,b)$-regular
graphs:
What is the largest spectral gap in the adjacency operator of an
$(a,b)$-regular graph $G$? What is the relation between the local expansion
of the graphs ${G_v : v \in G}$ and the global expansion of $G$? We will
also present a new construction of $(a,b)$-regular local-and-global
expanders.
Joint work with Michael Chapman and Nati Linial.
http://www.math.ias.edu/seminars/abstract?event=143187
3 Singularities of Teichmueller harmonic map flow
Melanie Rupflin
Abstract: We discuss singularities of Teichmueller harmonic map flow, which
is a geometric flow that changes maps from surfaces into branched minimal
immersions, and explain in particular how winding singularities of the map
component can lead to singular behaviour of the metric component.
http://www.math.ias.edu/seminars/abstract?event=142667
4 FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative
Models
Will Grathwohl
A promising class of generative models maps points from a simple
distribution to a complex distribution through an invertible neural network.
Likelihood-based training of these models requires restricting their
architectures to allow cheap computation of Jacobian determinants.
Alternatively, the Jacobian trace can be used if the transformation is
specified by an ordinary differential equation. In this paper, we use
Hutchinson's trace estimator to give a scalable unbiased estimate of the
log-density. The result is a continuous-time invertible generative model
with unbiased density estimation and one-pass sampling, while allowing
unrestricted neural network architectures. We demonstrate our approach on
high-dimensional density estimation, image generation, and variational
inference, achieving the state-of-the-art among exact likelihood methods
with efficient sampling.
http://www.math.ias.edu/seminars/abstract?event=139487
5 Self-similar solutions of mean curvature flow and entropy
Jacob Bernstein
Abstract: Colding-Minicozzi introduced a natural entropy for hypersurfaces
in euclidean space that is non-increasing under the mean curvature flow
(MCF) and is a natural measure of the hypersurface's geometric complexity.
In particular, hypersurfaces of low entropy turn out to be "simple" in
various senses. This phenomena is most striking for self-similar solutions
of MCF and I will discuss recent results illustrating this. This is all
joint work with Lu Wang.
http://www.math.ias.edu/seminars/abstract?event=142670
6 Gysin sequences and cohomology ring of symplectic fillings
Zhengyi Zhou
It is conjectured that contact manifolds admitting flexible fillings have
unique exact fillings. In this talk, I will show that exact fillings (with
vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold
share the same product structure on cohomology if one of the multipliers is
of even degree smaller than n-1. The main argument uses Gysin sequences from
symplectic cohomology twisted by sphere bundles.
http://www.math.ias.edu/seminars/abstract?event=143193
7 Kaehler constant scalar curvature metrics on blow ups and resolutions of
singularities
Claudio Arezzo
Abstract: After recalling the gluing construction for Kaehler constant
scalar curvature and extremal (`a la Calabi) metrics starting from a compact
or ALE orbifolds with isolated singularities, I will show how to compute the
Futaki invariant of the adiabatic classes in this setting, extending
previous work by Stoppa, Szekelyhidi and Odaka. Besides giving new existence
and non-existence results, the connection with the Tian-Yau-Donaldson
Conjecture and the K-stability of the resolved manifold will be discussed
and the relevance towards the interpretation of the ADM mass for Kaehler
manifolds.The original part of this talk will cover joint works with A.
Della Vedova, R. Lena, K. Corrales and L. Mazzieri.
http://www.math.ias.edu/seminars/abstract?event=142673
8 Volumes and intersection theory on moduli spaces of Abelian differentials
Dawei Chen
Computing volumes of moduli spaces has significance in many fields. For
instance, Witten's conjecture regarding intersection numbers on the
Deligne–Mumford moduli space of stable Riemann surfaces has a fascinating
connection to the Weil–Petersson volume, which motivated Mirzakhani to give
a proof via Teichmueller theory, hyperbolic geometry, and symplectic
geometry. The initial two other proofs of Witten's conjecture by Kontsevich
and by Okounkov–Pandharipande also used various ideas in combinatorial
ribbon graphs, Gromov–Witten theory, and Hurwitz theory. In this talk I will
introduce an analogue of Witten's intersection numbers on moduli spaces of
Abelian differentials to compute the Masur–Veech volumes induced by the flat
metric associated with Abelian differentials. This is joint work with Martin
Moeller, Adrien Sauvaget, and Don Zagier (arXiv:1901.01785).
http://www.math.ias.edu/seminars/abstract?event=141992
9 L^p curvatures : some analysis questions from gauge theory
Tristan Rivière
Abstract : What are the possible limits of smooth curvatures with uniformly
bounded $L^p$ norms ?
We shall see that the attempts to give a satisfying answer to this natural
question from the calculus of variation of gauge theory brings us to
numerous analysis challenges.
http://www.math.ias.edu/seminars/abstract?event=142679
10 Spacetime positive mass theorem
Lan-Hsuan Huang
Abstract: The spacetime positive mass theorem says that an asymptotically
flat initial data set with the dominant energy condition must have a
timelike energy-momentum vector, unless the initial data set is in the
Minkowski spacetime. We will review backgrounds and recent progress toward
this statement.
http://www.math.ias.edu/seminars/abstract?event=142682
11 Periodic Geodesics and Geodesic Nets on Riemannian Manifolds
Regina Rotman
Abstract: I will talk about periodic geodesics, geodesic loops, and geodesic
nets on Riemannian manifolds. More specifically, I will discuss some
curvature-free upper bounds for compact manifolds and the existence results
for non-compact manifolds. In particular, geodesic nets turn out to be
useful for proving results about geodesic loops and periodic geodesics.
http://www.math.ias.edu/seminars/abstract?event=142685
12 Liouville Equations and Functional Determinants
Andrea Malchiodo
Abstract: Functional Determinants are quantities constructed out of spectra
of conformally covariant operators, and are explicit in dimension two and
four, due to formulas by Polyakov and Branson-Oersted. Extremizing them in a
conformal class amounts to solving Liouville equations with principal parts
of different order but all scaling invariant. We discuss some existence,
uniqueness, non-uniqueness results and some open problems. This is joint
work with M.Gursky and P.Esposito.
http://www.math.ias.edu/seminars/abstract?event=142676
13 Normalized harmonic map flow
Michael Struwe
Abstract: Finding non-constant harmonic 3-spheres for a closed target
manifold N is a prototype of a super-critical variational problem. In fact,
the
direct method fails, as the infimum of the Dirichlet energy in any homotopy
class of maps from the 3-sphere to any closed N is zero; moreover, the
harmonic map heat flow may blow up in finite time, and even the identity map
from the 3-sphere to itself is not stable under this flow.
To overcome these difficulties, we propose the normalized harmonic map flow
as a new tool, and we show that for this flow the identity map
from the 3-sphere to itself now, indeed, is stable; moreover, the flow
converges to a harmonic 3-sphere also when we perturb the target
geometry. While our results are strongest in the perturbative setting, we
also outline a possible global theory.
http://www.math.ias.edu/seminars/abstract?event=142691
14 Loop products, closed geodesics and self-intersections
Nancy Hingston
Abstract: Let M be a compact Riemannian manifold. Morse theory for the
energy function on the free loopspace LM of M gives a link between geometry
and topology, between the growth of the index of the iterates of closed
geodesics on M, and the algebraic structure given by the Chas-Sullivan
product on the homology of LM. I will discuss this link, and a new
geometric property of the loop coproduct: the nonvanishing of the kth
iterate of the coproduct on a homology class ensures the existence of a loop
with a (k+1)-fold intersection in every representative of the class. No
knowledge of loop products will be assumed. Joint work with Nathalie Wahl.
http://www.math.ias.edu/seminars/abstract?event=142694
15 Nature of some stationary varifolds near multiplicity 2 tangent planes
Neshan Wickramasekera
Abstract: It is a basic open question in geometric measure theory to
understand regularity of a stationary integral varifold. Even a.e.
regularity remains an open question. The central issue is analyzing the
varifold near a point Z with a tangent plane of multiplicity q > 1. The talk
will focus on the analytic machinery developed recently to address this
question when q=2 for two cases: (i) the varifold corresponds to a Lipschitz
two-valued graph of arbitrary codimension (joint work with S. Becker-Kahn)
(ii) the varifold has codimension 1, stable regular part and no density 3/2
points near Z (this last condition is met if e.g. the varifold corresponds
to a rectifiable current).
http://www.math.ias.edu/seminars/abstract?event=142688
16 Existence and uniqueness of Green's function to a nonlinear Yamabe
problem
Yanyan Li
Abstract: For a given finite subset S of a compact Riemannian manifold (M;
g) whose Schouten curvature tensor belongs to a given cone, we establish a
necessary and
sufficient condition for the existence and uniqueness of a conformal metric
on $M \setminus S$ such that each point of S corresponds to an
asymptotically flat end and
that the Schouten tensor of the new conformal metric belongs to the boundary
of the given cone. This is a joint work with Luc Nguyen.
http://www.math.ias.edu/seminars/abstract?event=142700
17 From Celestial Mechanics to the Arnold Conjectures
Umberto Hryniewicz
The study of the planar-circular-restricted 3-body problem led to Poincaré's
"last geometric theorem", nowadays known as the Poincaré-Birkhoff theorem.
It is a fixed point theorem for certain area-preserving annulus
homeomorphisms. Birkhoff's proof did not allow for generalizations, and we
had to wait until the 1960's when Arnold realized that the Poincaré-Birkhoff
theorem (in the smooth case) is a consequence of a certain conjecture on the
number of fixed points of Hamiltonian diffeomorphisms. The conjecture was
one among others of the same flavor, and they motivated the invention of
Floer theory. In this talk I would like to give more details on this
remarkable chain of events.
http://www.math.ias.edu/seminars/abstract?event=136645
18 Compactness and finiteness theorems (almost) without curvature
Gerard Besson
Abstract : It is a joint work with G. Courtois, S. Gallot and A.Sambusetti.
We prove a compactness theorem for metric spaces with anupper bound on the
entropy and other conditions that will be discussed.Several finiteness
results will be drawn. It is a work in progress.
http://www.math.ias.edu/seminars/abstract?event=142703
19 One-cycle sweepout estimates of essential surfaces in closed Riemannian
manifolds
Stéphane Sabourau
Abstract: We present new-curvature one-cycle sweepout estimates in
Riemannian geometry, both on surfaces and in higher dimension. More
precisely, we derive upper bounds on the length of one-parameter families of
one-cycles sweeping out essential surfaces in closed Riemannian manifolds.
In particular, we show that there exists a homotopically substantial
one-cycle sweepout of the essential sphere in the complex projective space,
endowed with an arbitrary Riemannian metric, whose one-cycle length is
bounded in terms of the volume (or diameter) of the manifold. This is the
first estimate on sweepout volume in higher dimension without curvature
assumption.
http://www.math.ias.edu/seminars/abstract?event=142706
20 $L^2$ curvature for surfaces in Riemannian manifolds
Ernst Kuwert
Abstract: For surfaces immersed into a compact Riemannian manifold, we
consider the curvature functional given by the $L^2$ integral of the second
fundamental form. We discuss an an area bound in terms of that functional,
with application to the existence of minimizers (joint work with V.
Bangert).
http://www.math.ias.edu/seminars/abstract?event=142709
21 Special cycles on orthogonal Shimura varieties
Eugenia Rosu
Extending on the work of Kudla-Millson and Yuan-Zhang-Zhang, together with
Yott we are constructing special divisors for a specific GSpin Shimura
variety. We further construct a generating series that has as coefficients
the cohomology classes corresponding to the special divisors classes Z(x,
g)_K on the GSpin Shimura variety M_K and show the modularity of the
generating series in the cohomology group over C.
http://www.math.ias.edu/seminars/abstract?event=139909
22 Ricci flows that attain their initial data weakly
Peter Topping
http://www.math.ias.edu/seminars/abstract?event=142712
23 Filling metric spaces
Alexander Nabutovsky
Abstract: Uryson k-width of a metric space X measures how close X is to
being k-dimensional. Several years ago Larry Guth proved that if M is a
closed n-dimensional manifold, and the volume of each ball of radius 1 in M
does not exceed a certain small
constant e(n), then the Uryson (n-1)-width of M is less than 1. This result
is a significant generalization of the famous Gromov's inequality relating
the volume and the filling radius that plays a central role in systolic
geometry.
Guth asked if one can generalize his result in two directions: first, from
closed manifolds to n-dimensional metric spaces using the Hausdorff measure
instead of volume, and, then, to metric spaces of any dimension using
n-dimensional Hausdorff
content instead of Hausdorff measure.
If true, such a result will immediately lead to interesting new inequalities
even for closed Riemannian manifolds.
In my talk I am are going to discuss Guth's theorem and an ongoing joint
project towards resolution of Guth's problem.
http://www.math.ias.edu/seminars/abstract?event=142715
IAS Math Seminars Home Page:
http://www.math.ias.edu/seminars
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://imap.math.ias.edu/pipermail/iasmathsemo/attachments/20190301/48fa0549/attachment-0001.html>
More information about the Iasmathsemo
mailing list