# Online Asymptotic Geometric Analysis Seminar

** Welcome to the Online AGA seminar webpage!
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! Please let the organizers know if you would like to be added to the mailing list.
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**

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.

### 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)

### Bo Berndtsson, Chalmers University of Technology and the University of Goteborg, Sweden

#### Topic: Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem

#### Abstract: We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter. Time permitting, we will also comment on Nazarov's proof and estimates of Bergman kernels.

### 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)

### Kateryna Tatarko, Texas A&M University, College Station, TX, USA and the University of Alberta, Canada

#### Topic: On the unique determination of ellipsoids by dual intrinsic volumes

#### Abstract: In this talk, we show that an ellipsoid is uniquely determined up to an isometry by its dual Steiner polynomial. We reduce this result to the moment problem, and as a by-product obtain an alternative proof of the analogous known result for classical Steiner polynomials in $R^3$. This is joint work with S. Myroshnychenko and V. Yaskin.

### Saturday, September 5, 11:30AM (New York, NY time)

### Adam Kashlak, University of Alberta, Edmonton, Canada

#### Topic: Analytic Permutation Testing via Kahane--Khintchine Inequalities

#### Abstract: The permutation test is a versatile type of exact nonparametric significance test that requires drastically fewer assumptions than similar parametric tests by considering the distribution of a test statistic over a discrete group of distributionally invariant transformations. The main downfall of the permutation test is the high computational cost of running such a test making this approach laborious for complex data and experimental designs and completely infeasible in any application requiring speedy results. We rectify this problem through application of Kahane--Khintchine-type inequalities under a weak dependence condition and thus propose a computation free permutation test---i.e. a permutation-less permutation test. This general framework is studied within both commutative and non-commutative Banach spaces. We further improve these Kahane-Khintchine-type bounds via a transformation based on the incomplete beta function and Talagrand's concentration inequality. For k-sample testing, we extend the theory presented for Rademacher sums to weakly dependent Rademacher chaoses making use of modified decoupling inequalities. We test this methodology on classic functional data sets including the Berkeley growth curves and the phoneme dataset. We also consider hypothesis testing on speech samples under two experimental designs: the Latin square and the complete randomized block design.

### Tuesday, September 8, 10:30AM (New York, NY time)

### Grigory
Ivanov, IST Austria, Austria, and MIPT, Moscow, Russia.

#### Topic: Functional John-Löwner ellipsoids of a log-concave function

#### Abstract: We extend the notion of the John ellipsoid (the largest volume ellipsoid contained within a convex body) to the setting of log-concave functions. For every s > 0, we define a class of log-concave functions derived from ellipsoids. For any log-concave function f, and any fixed s > 0, we consider functions belonging to this class and find the one with the largest integral under the condition that it is pointwise less than or equal to f. We show that it exists and is unique, and call it the John s-function of f. We give a characterization of this function similar to the one provided by John in his fundamental
theorem. As an application, we obtain a quantitative Helly-type result about the integral of the pointwise minimum of a family of log-concave functions.
Next, we will discuss the concept of duality for log-concave functions and extend the notion of the Löwner ellipsoid (the smallest volume ellipsoid containing a convex body) to the setting of log-concave functions. Time permitting, we will discuss the difference between the behavior of convex sets and log-concave functions concerning our problems.
Based on joint works with Márton Naszódi and Igor Tsiutsiurupa.

### Saturday, September 12, 11:30AM (New York, NY time)

### Masha Gordina, University of Connecticut, Storrk, CT, USA

#### Topic: Uniform doubling on SU(2) and beyond

#### Abstract: Suppose G is a compact Lie group equipped with a left-invariant Riemannian metric. Such metrics usually form a finite-dimensional cone. The Riemannian volume measure corresponding to such a metric is the Haar measure of the group (up to a multiplicative constant). Because of compactness, each left-invariant metric g has the doubling property, that is, there exists a doubling constant D=D(G, g) such that the volume of the ball of radius 2r is at most D times the volume of the ball of radius r. We are concerned with the following question: does there exist a constant D(G) such that, for all left-invariant metrics g on G, the constant D(G, g) is bounded above by D(G)? This is what we call uniformly doubling. The conjecture is that any compact Lie group is uniformly doubling. The only cases for which the conjecture is known are Riemannian tori and the group SU(2). The talk will describe a number of analytic consequences of uniform doubling (in absence of curvature bounds) and our approach to proving uniform doubling on SU(2). The work in progress for U(2) might be mentioned as well. This is joint work with Nathaniel Eldredge (University Northern Colorado) and Laurent Saloff-Coste (Cornell University). Reference: Left-invariant geometries on SU(2) are uniformly doubling, GAFA 2018.

### Tuesday, September 15, 10:30AM (New York, NY time)

### Santosh Vempala, Georgia Institute of Technology, Atlanta, GA, USA

#### Topic: Reducing Isotropy to KLS: An n^3\psi^2 Volume Algorithm

#### Abstract: Computing the volume of a convex body is an ancient problem whose study has led to many interesting mathematical developments. In the most general setting, the convex body is given only via a membership oracle. In this talk, we present a faster algorithm for isotropic transformation of an arbitrary convex body in R^n, with complexity n^3\psi^2, where \psi bounds the KLS constant for isotropic convex bodies. Together with the known bound of \psi = O(n^{1/4}) [2017] and the Cousins-Vempala n^3 volume algorithm for well-rounded convex bodies [2015], this gives an n^{3.5} volume algorithm for general convex bodies, the first improvement on the n^4 algorithm of Lovász-Vempala [2003]. A positive resolution of the KLS conjecture (\psi = O(1)) would imply an n^3 volume algorithm.
No background on algorithms, KLS or ABC will be assumed for the talk.
Joint work with He Jia, Aditi Laddha and Yin Tat Lee.

Remark: a follow up talk with more details will take place at the Georgia Tech High Dimensional Seminar on Wednesday, September 16, at 3:15pm (NYC time).
Zoom link here.

### Saturday, September 19, 11:30AM (New York, NY time)

### Ferenc Fodor, University of Szeged, Hungary

#### Topic: Strengthened inequalities for the mean width and the $\ell$-norm

#### Abstract: According to a result of Barthe the regular simplex maximizes the mean width of convex bodies whose John ellipsoid is the Euclidean unit ball. This is equivalent to the fact that the regular simplex maximizes the $\ell$-norm of convex bodies whose L\"owner ellipsoid is the Euclidean unit ball.
The reverse statement that the regular simplex minimizes the mean width of convex bodies whose L\"owner ellipsoid is the Euclidean unit ball is also true as proved by Schmuckenschl\"ager. In this talk we prove strengthened stability versions of these results and some related stability statements for the convex hull of the support of centered isotropic measures on the unit sphere. This is joint work with K\'aroly J. B\"or\"oczky (Budapest, Hungary) and Daniel Hug (Karlsruhe, Germany).

### Tuesday, September 22, 10:30AM (New York, NY time)

### Dan Mikulincer, Weizmann Institute of Science, Rehovot, Israel

#### Topic: Stability of Stein kernels, moment maps and invariant measures

#### Abstract: Suppose that \mu is some nice measure on a Euclidean space. We can associate it with several different constructions of interest: Stein kernels, arising from Stein's theory, the moment map, which is of a more geometric flavour and a particular choice of a stochastic process for which \mu is the invariant measure. We will discuss the connections between these different objects and show that they are stable with respect to the original measure. That is, a small perturbation to either construction will yield a new measure which is close to \mu. Joint work with Max Fathi.

### 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: Enflo's problem

#### Abstract: A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. I will speak about the joint work with Ramon van Handel and Sasha Volberg where we prove that Rademacher and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the Hamming cube.

### Tuesday, October 13, 10:30AM (New York, NY time)

### Keith Ball, University of Warwick, UK

#### Topic: Rational approximations to the zeta function

#### Abstract: I will describe the construction of a sequence of rational functions with rational coefficients that converge to the zeta function. These approximations extend and make precise the spectral interpretations of the Riemann zeros found by Connes and by Berry and Keating.

### 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)

#### Topic: L_p-Borell-Brascamp-Lieb type inequalities

#### Abstract: (joint work with Sudan Xing) Many recent advances in the $L_p$-Brunn-Minkowski theory have been made in recent years; of particular interest, the L_p-BM conjecture has been shown to be true for p \geq 1-c(n) for some sufficiently small constant c(n) depending on the dimension. The goal of this talk is to introduce a functional counterpart of the $L_p$-Minkowski operations and to establish related Brascamp-Lieb inequalities. In particular, the following result is mentioned, which generalizes a result of Bobkov-Colesanti-Fragala:
Let $p \geq 1$, $t \in (0,1)$, $\gamma \leq 1$, and $\alpha \geq -\gamma$. Suppose that $\phi$ is a monotone $\alpha$-concave functional acting on the class of Borel subsets of $\R^n$. Then, for any triple of Borel measurable functions $f,g,h: R^n \to \R_+$ satisfying a reasonable concavity condition, one has that
\tilde{\phi}(h) \geq ((1-t) \tilde{\phi}(f)^{\beta} + t \tilde{\phi}(g)^{\beta]^{1/beta}, \beta = (p\alpha\gamma)/(\alpha+\gamma), and $\tilde{\phi}$ denotes the extension of $\phi$ to the functions f,g,h.
Related $L_p$-BM inequalities for s-concave measures and isoperimetric type inequalities will be mentioned provided there's sufficient time.

#### 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: Chasing Convex Bodies

#### Abstract: I will explain the chasing convex bodies problem posed by Friedman and Linial in 1991. In this problem, an online player receives a request sequence K_1,...,K_T of convex sets in d dimensional space and moves his position online into each requested set. The player's movement cost is the length of the resulting path. Chasing convex bodies asks if there is an online algorithm with cost competitive against the offline optimal path. This is both an interesting metrical task system and (equivalent to) a competitive analysis view on online convex optimization.
This problem has recently been solved twice. The first solution gives a 2^{O(d)} competitive algorithm while the second gives a nearly optimal min(d,sqrt(d*log(T))) competitive algorithm for T requests. The latter result is based on the Steiner point, which is the exact optimal solution to a related geometric problem called Lipschitz selection and dates from 1840. In the talk, I will briefly outline the first solution and fully explain the second.
Partially based on joint works with Sébastien Bubeck, Bo'az Klartag, Yin Tat Lee, and Yuanzhi Li.

### Saturday, November 21, 10:30AM (New York, NY time)

#### 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)

#### Topic: TBA

#### Abstract: TBA

### Saturday, December 5, 11:30AM (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

## Schedule Spring 2021:

### Tuesday, January TBA, 2021, 10:30AM (New York, NY time)

### Alexey Garber, The University of Texas Rio Grande Valley, Brownsville, TX, USA

#### Topic: TBA

#### Abstract: TBA

### Tuesday, January TBA, 2021, 10:30AM (New York, NY time)

### Fanny Augieri, Université Paris Diderot, Paris, France

#### Topic: TBA

#### Abstract: TBA

### Organizers: