Online Asymptotic Geometric Analysis Seminar
This seminar is open on Zoom for everyone who is interested to join. The seminars run on Tuesdays at 10:30am (New York, NY time) and Saturdays 11:30am (New York, NY time). If you are interested in giving a talk, please let us know. Also, please suggest speakers which you would like to hear speak. Most talks are 50 minutes, but some 20-minute talks will be paired up as well. The talks will be video recorded conditioned upon the speakers' agreement. PLEASE SHARE THE SEMINAR INFO WITH YOUR DEPRARTMENT AND ANYONE WHO MAY BE INTERESTED!
In order to join a seminar on a Tuesday, click the link: Tuesday link (the link opens half an hour before the talk)
In order to join a seminar on a Saturday, click the link: Saturday link (the link opens half an hour before the talk)
There used to be a password for Zoom for this seminar, but now there is no password required.
Note that on Tuesdays, the lectures start at:
7:30am in Los-Angeles, CA
8:30am in Edmonton, AB
9:30am in Columbia MO; College Station, TX; Chicago, IL
10:30am in Kent, OH; Atlanta, GA; Montreal; New York, NY
11:30am in Rio de Janeiro, Buenos Aires
3:30pm (15:30) in London
4:30pm (16:30) in Paris, Milan, Budapest, Vienna
5:30pm (17:30) in Tel Aviv.
On Saturdays, the lectures start one hour later, that is at:
8:30am in Los-Angeles, CA
9:30am in Edmonton, AB
10:30am in Columbia MO; College Station, TX; Chicago, IL
11:30am in Kent, OH; Atlanta, GA; Montreal; New York, NY
12:30pm in Rio de Janeiro, Buenos Aires
4:30pm (16:30) in London
5:30pm (17:30) in Paris, Milan, Budapest, Vienna
6:30pm (18:30) in Tel Aviv.
Technical aspects: preferably, you should register in Zoom; the basic account is free of charge. The easiest way to present a talk via Zoom is to make the usual slides, open them on your laptop/tablet and share your screen; alternatively, you may share your pdf via Zoom directly. If you possess a tablet with a pencil (or other writing aids), you have many more options: you may use Zoom whiteboard, which has an advantage that other participants with writing aids may also edit the same board; this may be viewed as a disadvantage, but let us hope no talks will be sabotaged:) You may alternatively share the screen and write in any writing app (such as Goodnotes), and this way you may furthermore combine slides with board writing. There are even fancier options, such as using Scribble Together app. Only the meeting host needs to have a pro account in Zoom for smooth running (which will be provided), all other participants simply need a free basic account. We will have to discover in the process if online seminars present any technical hikkups -- we shall see.
In case you received an announcement from one of the organizers, this means that you are already on the mailing list. If not, then in order to sign up for the mailing list, please enter your e-mail address here (this form scrolls down):
(We apologize in case we forgot to add someone to the e-mail list and very much appreciate you entering your e-mail!)
Schedule Spring 2020:
Tuesday, April 7, 10:30AM (New York, NY time)
Alexander Koldobsky, University of Missouri, Columbia, MO, USA
Topic: A new version of the isomorphic Busemann-Petty problem for arbitrary functions
Saturday, April 11, 11:30AM (New York, NY time)
Sergey Bobkov, University of Minnesota, Minneapolis, MN, USA
Topic: A Fourier-analytic approach to transport inequalities
Abstract: We will be discussing a Fourier-analytic approach to optimal matching between independent samples, with an elementary proof of the Ajtai-Komlos-Tusnady theorem. The talk is based on a joint work with Michel Ledoux.
Tuesday, April 14, 10:30AM (New York, NY time)
Elisabeth Werner, Case Western Reserve University, Cleveland, OH, USA
Topic: Constrained convex bodies with maximal affine surface area
Abstract: Given a convex body K in R^n, we study the maximal affine surface area of K, i.e., the quantity
AS(K) = sup_{C} as(C)
where as(C) denotes the affine surface area of C, and the supremum is taken over all convex
subsets of K. In particular, we give asymptotic estimates on the size of AS(K).
Saturday, April 18, 11:30AM (New York, NY time)
Károly Böröczky, Central European University, Budapest, Hungary
Topic: Symmetry and Structure within the Log-Brunn-Minkowski Conjecture
Abstract: After reviewing some formulations of the Log-Brunn-Minkowski Conjecture in R^n in terms of Monge-Ampere equations, of Hilbert Operator and of Brunn-Minkowski Theory, I will report on some recent advances, like Livshyts' and Kolesnikov's improvement on the fundamental approach of Milman and Kolesnikov, and the verification of the conjecture for bodies with n hyperplane symmetries by Kalantzopoulos and myself using an idea due to Bathe and Fradelizi.
Tuesday, April 21, 10:30AM (New York, NY time)
Uri Grupel, University of Innsbruk, Austria
Topic: Metric distortion of random spaces
Abstract: We consider a random set in the unit circle. Is the induced
discrete metric of the set closer to that of another independent random
set or to the evenly spaced set of the same cardinality? We measure the
distortion by looking at the smallest bi-Lipschitz norm of all the
bijections between the two sets. Since the distortion between two random
sets has infinite expectation, the talk will focus on the median. We
show that two random sets have "typically" smaller distortion than a
random set and an evenly spaced set.
Saturday, April 25, 11:30AM (New York, NY time)
Grigoris Paouris, Texas A&M University, College Station, TX, USA
Topic: Quantitative Triangle law and Joint Normality of Lyapunov exponents for products of Gaussian matrices
Abstract: We will discuss spectral properties of products of independent Gaussian square matrices with independent entries. Non-asymptotic results for the statistics of the singular values will be presented as well as the rate of convergence to the triangle law. We will also show quantitative estimates on the asymptotic joint normality of the Lyapunov exponents. The talk is based on a joint work with Boris Hanin.
Tuesday, April 28, 10:30AM (New York, NY time)
Ilaria Fragalà, Politecnico di Milano, Italy
Topic: Symmetry problems for variational functionals: from continuous to discrete.
Abstract: I will discuss some symmetry problems for variational energies on the class of convex polygons
with a prescribed number of sides, in which the regular n-gon can be proved or is expected to be optimal.
Such symmetry results can be viewed as the “discrete” analogue of well-known “continuous” isoperimetric inequalities with balls as optimal domains.
I will focus in particular on the following topics
(i) Discrete isoperimetric type inequalities
(ii) Discrete Faber-Krahn type inequalities
(iii) Overdetermined boundary value problems on polygons.
Saturday, May 2, 11:30AM (New York, NY time)
Alina Stancu, Concordia University, Montreal, Canada
Topic: On the fundamental gap and convex sets in hyperbolic space
Abstract: The lower bound on the fundamental gap of the Laplacian on convex domains in R^n, with Dirichlet boundary conditions, has a long history and has been finally settled a few years ago with parabolic methods by Andrews and Clutterbuck. More recently, the same lower bound, which depends on the diameter of the domain, has been proved for convex sets on the standard sphere in several stages with several groups of authors, 2016-2018. Over the past year, together with collaborators, we have found that the gap on the hyperbolic space behaves strikingly different and we aim to explain it, particularly for this audience, as a difference in the nature of convex sets in H^n versus R^n or S^n.
Tuesday, May 5, 10:30AM (New York, NY time)
Topic: Brunn-Minkowski type inequalities and affine surface area
Abstract: Does the affine surface area verify a concavity inequality of Brunn-Minkowski type? We will try to provide an answer to this question, and we will see that the answer depends on the dimension, and on the type of addition that we choose. The results presented in this talk were obtained in collaboration with Karoly Boroczky, Monika Ludwig and Thomas Wannerer.
Saturday, May 9, 11:30AM (New York, NY time)
Monika Ludwig, Vienna University of Technology, Austria
Topic: Valuations on Convex Functions
Tuesday, May 12, 10:30AM (New York, NY time)
Bo'az Klartag, Weizmann Institute of Science, Rehovot, Israel
Topic: Rigidity of Riemannian embeddings of discrete metric spaces
Abstract: Let M be a complete, connected Riemannian surface and
suppose that S is a discrete subset of M. What can we learn about M
from the knowledge of all distances in the surface between pairs of
points of S? We prove that if the distances in S correspond to the
distances in a 2-dimensional lattice, or more generally in an
arbitrary net in R^2, then M is isometric to the Euclidean plane. We
thus find that Riemannian embeddings of certain discrete metric spaces
are rather rigid. A corollary is that a subset of Z^3 that strictly
contains a two-dimensional lattice cannot be isometrically embedded in
any complete Riemannian surface. This is a joint work with M. Eilat.
Saturday, May 16, 11:30AM (New York, NY time)
Galyna Livshyts, Georgia Tech, Atlanta, GA, USA
Topic: On the Log-Brunn-Minkowski conjecture and related questions
Abstract: We shall discuss the Log-Brunn-Minkowski conjecture, a conjectured strengthening of the Brunn-Minkowski inequality proposed by Boroczky, Lutwak, Yang and Zhang, focusing on the local versions of this and related questions. The discussion will involve introduction and explanation of how the local version of the conjecture arises naturally, a collection of ‘’hands on’’ examples and elementary geometric tricks leading to various related partial results, statements of related questions as well as a discussion of more technically involved approaches and results. Based on a variety of joint results with several authors, namely, Colesanti, Hosle, Kolesnikov, Marsiglietti, Nayar, Zvavitch. REMARK: THIS TALK IS A LAST MINUTE REPLACEMENT OF THE EARLIER ANNOUNCED TALK BY TIKHOMIROV; TIKOMIROV'S TALK IS NOW SCHEDULED FOR THE FALL.
Tuesday, May 19, 10:30AM (New York, NY time)
Olivier Guedon, Université Gustave Eiffel, Paris, France
Topic: Floating bodies and random polytopes
Abstract: I will present some results about the geometry of centrally-symmetric random polytopes, generated by $N$ independent copies of a random vector $X$ taking values in $\R^n$. Under minimal assumptions on $X$, for $N \gtrsim n$ and with high probability, the polytope contains a deterministic set that is naturally associated with the random vector---namely, the polar of a certain floating body. This solves the long-standing question on whether such a random polytope contains a canonical body.
This is joint work with F. Krahmer, C. Kummerle, S. Mendelson and H. Rauhut.
Saturday, May 23, 11:30AM (New York, NY time)
Vitaly Milman, Tel Aviv University and Liran Rotem, Technion, Haifa, Israel
Topic: Novel view on classical convexity theory
Abstract: In this talk we will introduce and study the class of flowers. A flower in R^n is an arbitrary union of balls which contain the origin. While flowers are not necessarily convex, they are in one to one correspond with the class of convex bodies containing the origin, so by studying flowers we are also studying convex bodies from a new viewpoint. We will give several equivalent definitions of flowers and describe some of their basic properties. We will also discuss how to apply an arbitrary (real) function to a flower, and the corresponding construction for convex bodies. In particular, we will explain how to raise a flower to a given power. Finally, we will discuss some elements of the asymptotic theory of flowers. In particular we will present a Dvoretzky-type theorem for flowers which actually gives better estimates than the corresponding estimates for convex bodies.
Based on two papers by the speakers, the first of which is joint with E. Milman.
Tuesday, May 26, 10:30AM (New York, NY time)
Alexandros Eskenazis, Institut de Mathématiques de Jussieu, Sorbonne Université, Paris, France
Topic: The dimensional Brunn-Minkowski inequality in Gauss space
Abstract: We will present a complete proof of the dimensional Brunn-Minkowski inequality for origin symmetric convex sets in Gauss space. This settles a problem raised by Gardner and Zvavitch (2010). The talk is based on joint work with G. Moschidis.
Saturday, May 30, 11:30AM (New York, NY time)
Topic: High-dimensional tennis balls
Abstract: In this talk, it will be explained what a high-dimensional tennis ball is, how one can construct it and its connection to V. Milman's question about well-complemented almost Euclidean subspaces of spaces uniformly isomorphic to $\ell_2^n$.
Tuesday, June 2, 10:30AM (New York, NY time)
Yair Shenfeld, Princeton University, NJ, USA
Topic: The extremal structures of the Alexandrov-Fenchel inequality
Abstract: The Alexandrov-Fenchel inequality is one of the fundamental results in the theory of convex bodies. Yet its equality cases, which are solutions to isoperimetric-type problems, have been open for more than 80 years. I will discuss recent progress on this problem where we confirm some conjectures by R. Schneider. Joint work with Ramon van Handel.
Saturday, June 6, 11:30AM (New York, NY time)
Mark Meckes, Case Western Reserve University, Cleveland, USA
Topic: Magnitude and intrinsic volumes of convex bodies
Abstract: Magnitude is an isometric invariant of metric spaces with origins in category theory. Although it is very difficult to exactly compute the magnitude of interesting subsets of Euclidean space, it can be shown that magnitude, or more precisely its behavior with respect to scaling, recovers many classical geometric invariants, such as volume, surface area, and Minkowski dimension. I will survey what is known about this, including results of Barcelo--Carbery, Gimperlein--Goffeng, Leinster, Willerton, and myself, and sketch the proof of an upper bound for the magnitude of a convex body in Euclidean space in terms of intrinsic volumes.
Tuesday, June 9, 10:30AM (New York, NY time)
Topic: Volume product, polytopes and finite dimensional Lipschitz-free spaces.
Abstract: We shall present some results on the volume product of polytopes, including the question of its maximum among polytopes with a fixed number of vertices. Then we shall focus on the polytopes that are unit balls of Lipschitz-free Banach spaces associated to finite metric spaces. We characterize when these polytopes are Hanner polytopes and when two such polytopes are isometric to each others. We also also study the maximum of the volume product in this class.
Based on joint works with Matthew Alexander, Luis C. Garcia-Lirola and Artem Zvavitch.
Saturday, June 13, 11:30AM (New York, NY time)
Julian Haddad, Federal University of Minas Gerais, Belo Horizonte, Brasil
Topic: From affine Poincaré inequalities to affine spectral inequalities
Abstract: We develop the basic theory of $p$-Rayleigh quotients in
bounded domains, in the affine case, for $p \geq 1$. We establish
p-affine versions of the affine Poincaré inequality and introduce the
affine invariant $p$-Laplace operator $\Delta_p^{\mathcal A}$ defining
the Euler-Lagrange equation of the minimization problem. For $p=1$ we
obtain the existence of affine Cheeger sets and study preliminary
results towards a possible spectral characterization of John's
position.
Tuesday, June 16, 10:30AM (New York, NY time)
Semyon Alesker, Tel Aviv University, Israel
Topic: Multiplicative structure on valuations and its analogues over local fields.
Abstract: Valuation on convex sets is a classical notion of convex geometry. Multiplicative structure on translation invariant smooth valuations was introduced by the speaker
years ago. Since then several non-trivial properties of it have been discovered as well as a few applications to integral geometry. In the first part of the talk we will review some of these properties.
Then we discuss analogues of the algebra of even translation invariant valuations over other locally compact (e.g. complex, p-adic) fields. While any interpretation of these new algebras is missing at the moment,
their properties seem (to the speaker) to be non-trivial and having some intrinsic beauty.
Saturday, June 20, 11:30AM (New York, NY time)
Topic: The best constant in the Khinchine inequality for slightly dependent random variables
Abstract: We solve the open problem of determining the best constant in the Khintchine inequality under condition that the Rademacher random variables are slightly dependent. We also mention some applications in statistics of the above result. The talk is based on a joint work with Susanna Spektor.
Tuesday, June 23, 10:30AM (New York, NY time)
Elizabeth Meckes, Case Western Reserve University, Cleveland, USA
Topic: On the eigenvalues of Brownian motion on \mathbb{U}(n)
Abstract: Much recent work in the study of random matrices has focused on the non-asymptotic theory; that is, the study of random matrices of fixed, large size. I will discuss one such example: the eigenvalues of unitary Brownian motion. I will describe an approach which gives uniform quantitative almost-sure estimates over fixed time intervals of the distance between the random spectral measures of this parametrized family of random matrices and the corresponding measures in a deterministic parametrized family \{\nu_t\}_{t\ge 0} of large-n limiting measures. I will also discuss larger time scales. This is joint work with Tai Melcher.
Saturday, June 27, 11:30AM (New York, NY time)
Topic: Modewise methods for tensor dimension reduction
Abstract: Although tensors are a natural multi-modal extension of matrices, going beyond two modes (that is, rows and columns) presents many interesting non-trivialities. For example, the notion of singular values is no longer well-defined, and there are various versions of the rank. One of the most natural (and mathematically challenging) definitions of the tensor rank is so-called CP-rank: for a tensor X, it is a minimal number of rank one tensors whose linear combination constitutes X. Main focus of my talk will be an extension of the celebrated Johnson-Lindenstrauss lemma to low CP-rank tensors. Namely, I will discuss how modewise randomized projections can preserve tensor geometry in the subspace oblivious way (that is, a projection model is not adapted for a particular tensor subspace). Modewise methods are especially interesting for the tensors as they preserve the multi-modal structure of the data, acting on a tensor directly, without initial conversion of tensors to matrices or vectors. I will also discuss an application for the least squares fitting CP model for tensors. Based on our joint work with Mark Iwen, Deanna Needell, and Ali Zare.
Tuesday, June 30, 10:30AM (New York, NY time)
Topic: Sharp stability of the Brunn-Minkowski inequality
Abstract: We consider recent results concerning the stability of the classic Brunn-Minkowski inequality. In particular we shall focus on the linear stability for homothetic sets. Resolving a conjecture of Figalli and Jerison, we show there are constants C,d>0 depending only on n such that for every subset A of R^n of positive measure, if |(A+A)/2 - A| <= d |A|, then |co(A) - A| <= C |(A+A)/2 - A| where co(A) is the convex hull of A. The talk is based on joint work with Hunter Spink and Marius Tiba.
Schedule Fall 2020:
Tuesday, August 25, 10:30AM (New York, NY time)
TBA
Topic: TBA
Abstract: TBA
Saturday, August 29, 11:30AM (New York, NY time)
Marton Naszodi, Alfred Renyi Inst. of Math. and Eotvos Univ., Budapest, Hungary
Topic: Some new quantitative Helly-type theorems
Abstract:
Quantitative Helly-type theorems were introduced by Bárány, Katchalski and Pach in 1982,
who, among other results, showed the following. There is a constant C_d depending on
the dimension d only, such that if the intersection of a finite family of convex bodies in R^d is
of volume at most one, then the intersection of some subfamily of 2d members is of volume
at most C_d. We consider colorful and fractional versions of this result.
Tuesday, September 1, 10:30AM (New York, NY time)
TBA
Topic: TBA
Abstract: TBA
Saturday, September 5, 11:30AM (New York, NY time)
Adam Kashlak, University of Alberta, Edmonton, Canada
Topic: TBA
Abstract: TBA
Tuesday, September 8, 10:30AM (New York, NY time)
Masha Gordina, University of Connecticut, USA
Topic: TBA
Abstract: TBA
Saturday, September 12, 11:30AM (New York, NY time)
Grigory Ivanov, IST Wien and MIPT, Moscow, Russia
Topic: John's ellipsoid of a log-concave function
Abstract: We extend the notion of John's ellipsoid (the largest volume ellipsoid contained in a
convex body) of a convex body to the setting of log-concave functions.
We prove a necessary and sufficient condition for the unit ball to be the John ellipsoid of
an integrable log-concave function.
As an application, we prove a quantitative Helly-type result about the integral of the
pointwise minimum of a family of log-concave functions. Joint work with Márton Naszódi.
Tuesday, September 15, 10:30AM (New York, NY time)
Ferenc Fodor, University of Szeged, Hungary
Topic: TBA
Abstract: TBA
Tuesday, September 22, 10:30AM (New York, NY time)
Dan Mikulincer, Weizmann Institute of Science, Rehovot, Israel
Topic: TBA
Abstract: TBA
Tuesday, September 29, 10:30AM (New York, NY time)
Topic: TBA
Abstract: TBA
Tuesday, October 6, 10:30AM (New York, NY time)
Paata Ivanisvili, North Carolina State University, NC, USA
Topic: TBA
Abstract: TBA
Tuesday, October 13, 10:30AM (New York, NY time)
Keith Ball, University of Warwick, UK
Topic: TBA
Abstract: TBA
Tuesday, October 20, 10:30AM (New York, NY time)
Naomi Feldheim, Bar Ilan University, Israel
Topic: TBA
Abstract: TBA
Tuesday, October 27, 10:30AM (New York, NY time)
Rafal Latala, University of Warsaw, Poland
Topic: TBA
Abstract: TBA
Tuesday, November 3, 10:30AM (New York, NY time)
Kateryna Tatarko, Texas A&M University, College Station, TX, USA
Topic: TBA
Abstract: TBA
Tuesday, November 10, 10:30AM (New York, NY time)
Dima Faifman, Tel Aviv University, Israel
Topic: TBA
Abstract: TBA
Tuesday, November 17, 10:30AM (New York, NY time)
Mark Sellke, Stanford University, Palo Alto, CA, USA
Topic: TBA
Abstract: TBA
Tuesday, November 24, 10:30AM (New York, NY time)
Pierre Youssef, NYU Abu Dhabi, United Arab Emirates
Topic: TBA
Abstract: TBA
Tuesday, December 1, 10:30AM (New York, NY time)
Susanna Spektor, Sheridan College, Toronto, ON, Canada
Topic: TBA
Abstract: TBA
Tuesday, December 8, 10:30AM (New York, NY time)
Topic: TBA
Abstract: TBA
Tuesday, December 15, 10:30AM (New York, NY time)
Shay Sadovsky, Tel Aviv University, Israel
Topic: TBA
Abstract: TBA
Tuesday, January 19, 2021, 10:30AM (New York, NY time)
Alexey Garber, The University of Texas Rio Grande Valley, Brownsville, TX, USA
Topic: TBA
Abstract: TBA
Organizers: