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.



The Zoom link to join the seminar

The seminar "sea-side" social via gather.town for after the talk




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.



Abstracts, slides, videos of the past talks



Schedule Spring 2022:


  • Tuesday, January 25, 2022, 10:30AM (New York, NY time)

    Matthieu Fradelizi, Universite Gustave Eiffel, Paris, France

    Topic: Volume of sums of convex sets, mixed volumes, determinants and zonoids.

    Abstract: Following, on one hand, analogies between information theory, determinants and mixed volumes and, on the other hand, the relationship between algebraic geometry and convex geometry, many inequalities between mixed volumes of sums of convex sets were conjectured these years like Bezout or Alexandrov-Fenchel's type inequalities. Weak forms of these conjectures imply comparisons of volumes of projections of convex sets. We show these relationships, analyse these conjectures, give counter-examples and partial proofs. In particular we prove these conjectures for zonoids. Work in collaboration with Mokshay Madiman, Mathieu Meyer and Artem Zvavitch.

    Slides of the talk

    Video of the talk




  • Tuesday, February 1, 2022, 10:30AM (New York, NY time)

    Ahmed El Alaoui, Cornell University, Ithaka, NY

    Topic: Algorithmic Stochastic Localization for the Sherrington-Kirkpatrick Model

    Abstract: We propose an algorithm which efficiently samples from the SK measure with no external field at all inverse temperatures beta < 1/2. The approach uses a discretized version of the Stochastic Localization (SL) process of Eldan (2013), and the analysis relies on a comparison with a planted model combined with a new information-theoretic interpretation of the SL process. We believe this algorithm should succeed for all beta<1. Finally, we show that due to disorder chaos, 'stable' algorithms cannot approximately sample from the SK measure for beta>1. This result, which pertains to sampling, parallels the use of the overlap gap property to show algorithmic impossibility results for random optimization problems. This is a joint work with Andrea Montanari and Mark Sellke.

    Slides of the talk

    Video of the talk




  • Tuesday, February 8, 2022, 10:30AM (New York, NY time)

    No seminar because of the clash with this workshop




  • Tuesday, February 15, 2022, 10:30AM (New York, NY time)

    Max Fathi, Etablissement public experimental - Decret No2019-209 du 20 mars 2019, France

    Topic: Stability of the spectral gap under a curvature-dimension condition

    Abstract: A theorem of Lichnerowicz (1958) states that the spectral gap (or sharp Poincare constant) of a smooth n-dimensional Riemannian manifold with curvature bounded from below by n-1 is bounded by n, which is the spectral gap of the unit n-sphere. This bound has since been extended to metric-measure spaces satisfying a curvature-dimension condition. In this talk, I will present a result on stability of the bound: if a space has almost minimal spectral gap, then the pushforward of the volume measure by a normalized eigenfunction is close to a Beta distribution with parameter n/2, with a sharp estimate on the L1 optimal transport distance. Joint work with Ivan Gentil and Jordan Serres.

    Slides of the talk

    Video of the talk




  • Tuesday, February 22, 2022, 10:30AM (New York, NY time)

    Zakhar Kabluchko, Institut fur Mathematische Stochastik, Munster, Germany

    Topic: Expected face numbers of random beta polytopes

    Abstract: Let $X_1,\ldots, X_n$ be independent random points in the $d$-dimensional unit ball with density proportional to $(1-\|x\|^2)^\beta$, where $\beta>-1$ is a parameter. For $\beta=0$ we recover the uniform distribution on the unit ball, the limiting case $\beta \to -1$ corresponds to the uniform distribution on the unit sphere, while the case $\beta\to \infty$ corresponds to the standard Gaussian distribution. The convex hull $[X_1,\ldots,X_n]$ is called the beta polytope (with parameters $n$, $d$, $\beta$). We shall review results on the expected number of $k$-dimensional faces of beta polytopes and two closely related classes of polytopes called beta' and the beta* polytopes. Several objects in stochastic geometry such as the typical cell of the Poisson-Voronoi tessellation or the zero cell of the homogeneous Poisson hyperplane tessellation (in Euclidean space or on the sphere) are related to beta' polytopes, while their analogues in the hyperbolic space are related to beta* polytopes. The expected face numbers of these polytopes can be computed exactly.

    Slides of the talk

    Video of the talk




  • Tuesday, March 1, 2022, 10:30AM (New York, NY time)

    Chiara Meroni, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Topic: Semialgebraicity and constructions with convex bodies

    Abstract: Convex geometry has been classically studied from an analytical point of view. In the past two decades, there has been increasing interest in approaching it using tools from real and complex algebraic geometry, with a focus on semialgebraic convex bodies, beyond polytopes. I will introduce some notions and objects that encode this interaction and analyze their behavior in two different constructions: the fiber body of a convex body and the intersection body of a polytope. This is based on two joint works, one with Leo Mathis and one with Katalin Berlow, Marie-Charlotte Brandenburg and Isabelle Shankar.

    Slides of the talk

    Video of the talk




  • Tuesday, March 8, 2022, 10:30AM (New York, NY time)

    Silouanos Brazitikos, University of Athens, Greece

    Topic: On a version of the slicing problem for the surface area of convex bodies

    Abstract: We study the slicing inequality for the surface area instead of volume. This is the question whether there exists a constant $\alpha_n$ depending (or not) on the dimension $n$ so that \begin{equation*}S(K)\ls\alpha_n|K|^{\frac{1}{n}}\max_{\xi\in S^{n-1}}S(K\cap\xi^{\perp })\end{equation*} where $S$ denotes surface area and $|\cdot |$ denotes volume. For any fixed dimension we provide a negative answer to this question, as well as to a weaker version in which sections are replaced by projections onto hyperplanes. We also study the same problem for sections and projections of lower dimension and for all the quermassintegrals of a convex body.

    Slides of the talk

    Video of the talk




  • Tuesday, March 15, 2022, 10:30AM (New York, NY time)

    Stephanie Mui, Courant Institute, New York, NY, USA

    Topic: On the Lp Alexandrov problem for negative p

    Abstract: Huang, Lutwak, Yang, and Zhang introduced the Lp integral curvature and posed the corresponding Lp Aleksandrov problem, the natural Lp extension of the classical integral curvature and Aleksandrov problem respectively. The problem asks about the existence of a convex body with prescribed Lp integral curvature measure. For the f given even measures, the question will be solved for p ? (-1, 0). Furthermore, a sufficient measure concentration condition will be provided for the case of p = -1, again provided that the given measure is even.

    Slides of the talk

    Video of the talk




  • Tuesday, March 22, 2022, 10:30AM (New York, NY time)

    Dario Cordero-Erasquin, Sorbonne Universite, Paris, France

    Topic: Improved log-concavity for rotationally invariant measures of symmetric convex sets

    Abstract: We prove that the (B) conjecture for dilates of symmetric convex sets and the Gardner-Zvavitch conjecture on dimensional Brunn-Minkowski inequalities are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance to Cauchy measures as well. For the proof, new sharp spectral inequalities (in particular a sharp weighted Poincar� inequality) are obtained for even probability measures that are log-concave with respect to a rotationally invariant measure. Joint work with Liran Rotem.

    Video of the talk




  • Tuesday, March 29, 2022, 10:30AM (New York, NY time)

    Katherina von Dichter, Technische Universitat Munchen, Germany

    Topic: Mean inequality for symmetrizations of convex bodies

    Abstract: We deal with four symmetrizations of a convex set $C$: the intersection, the harmonic and the arithmetic mean, and the convex hull of $C$ and $-C$. A well-known result of Firey shows that those means build up a subset-chain in the given order. We determine the dilatation factors, depending on the asymmetry of $C$, to reverse the containments between any of those symmetrizations, and tighten the relations proven by Firey and show a stability result concerning those factors near the simplex..

    Slides of the talk

    Video of the talk




  • Tuesday, April 5, 2022, 10:30AM (New York, NY time)

    Theo McKenzie, University of Berkeley, CA

    Topic: Many nodal domains in random regular graphs

    Abstract: Discrete graphs have been used as a model for quantum chaos for over 20 years, and it is conjectured that eigenvectors of large regular graphs have Gaussian statistics. If we partition a graph according to the positive and negative components of an eigenvector of the adjacency matrix, the resulting connected subcomponents are called nodal domains, and one consequence of Gaussian behavior would be that there are many nodal domains. Dekel, Lee, and Linial observed that according to simulations, most eigenvectors of the adjacency matrix of random regular graphs have many nodal domains, unlike dense Erdos-R�nyi graphs. In this talk, we show that for the most negative eigenvalues of the adjacency matrix of a random regular graph, there is an almost linear number of nodal domains. Joint work with Shirshendu Ganguly, Sidhanth Mohanty, and Nikhil Srivastava..

    Slides of the talk

    Video of the talk




  • Tuesday, April 12, 2022, 10:30AM (New York, NY time)

    Gergely Ambrus, Alfred Renyi Institute of Mathematics, and the University of Szeged, Budapest, Hungary

    Topic: A generalization of Bang's lemma

    Abstract: Plank problems have received a surge of attention recently. In this talk, I will present a generalization of Bang's lemma, which is one of the crucial tools of the subject. This leads to an extension of Kadets' theorem on covering systems, several results related to translative coverings, and further applications to plank problems. .

    Slides of the talk

    Video of the talk




  • Tuesday, April 19, 2022, 10:30AM (New York, NY time)

    Dan Mikulincer, MIT, Boston, MS

    Topic: Causal optimal transport and the Brownian transport map

    Abstract: We consider a version of the optimal transport problem, adapted to the filtration of the Wiener space and show that the optimal solution is supported on a graph of a function, dubbed the Brownian transport map. Using tools from Ito's and Malliavin's calculus, we show that the map is Lipschitz when the target measure satisfies appropriate convexity assumptions. This facilitates the proof of several new functional inequalities. In other settings, where a globally Lipschitz transport map cannot exist, we derive Sobolev estimates which are intimately connected to the KLS conjecture. Joint work with Yair Shenfeld.

    Slides of the talk

    Video of the talk




  • Tuesday, April 26, 2022, 10:30AM (New York, NY time)

    Mokshay Madiman, University of Delaware, US

    Topic: Submodularity and fractional subadditivity in geometric functional analysis and information theory

    Abstract: We consider two interesting properties of natural set functions that arise in geometric functional analysis and information theory, motivated by the analogies between these fields. Specifically, we consider submodularity and fractional subadditivity properties of functionals such as the volume of Minkowski sums and the entropy of convolutions, sometimes but not always under convexity constraints. The talk will survey results obtained over the last 15 years with a number of collaborators, including Barron, Barthe, Fradelizi, Ghassemi, Marsiglietti, Tetali, and Zvavitch.

    Slides of the talk

    Video of the talk




  • Tuesday, May 3, 2022, 10:30AM (New York, NY time)

    Joseph Lehec, Paris-Dauphine, France

    Topic: Bourgain's slicing problem and KLS isoperimetry up to polylog

    Abstract: In a recent joint work with Bo'az Klartag we show that the Kannan, Lovasz, Simonovits conjecture holds true up to a polylog factor in the dimension. This also implies a polylog bound for Bourgain's hyperplane conjecture by a previous result of Eldan and Klartag. In this talk I'll explain the main steps of the proof.

    Slides of the talk

    Video of the talk




  • Tuesday, May 10, 2022, 10:30AM (New York, NY time)

    Simon Larson, Chalmers University of Techlology, Gothenburg, Sweden

    Topic: An inequality for the normal derivative of the Lane-Emden ground state

    Abstract: For an open subset of ℝd we consider minimizers of the Dirichlet integral among Lq-normalized functions with 1 ≤ q ≤ 2. In this talk I will discuss a sharp lower bound on the L2-norm of the normal derivative in terms of the corresponding energy. The results are valid for arbitrary bounded open Lipschitz sets, and for particular values of q generalize bounds that had previously been obtained under the additional assumption that the set is convex. Based on joint work with Rupert Frank.

    Slides of the talk

    Video of the talk




  • Tuesday, May 17, 2022, 10:30AM (New York, NY time)

    Jacob Henkel, Friedrich-Schiller-Universitat Jena, Germany

    Topic: On some new examples and (non)-existence of Minkowski valuations with certain properties

    Abstract: Let $W$ be an irreducible representation of $\mathrm{SL}(n)$ of finite dimension. We ask whether there exists a non trivial continuous and translation invariant Minkowski valuation $\mathcal{K}(\mathbb{R}^n) \to \mathcal{K}(W)$ which is $\mathrm{SL}(n)$ equivariant. Here $\mathcal{K}(\bullet)$ denotes the space of convex bodies in the corresponding vector space. For $W = \mathbb{R}^n$ and $W = (\mathbb{R}^n)^*$ the answer is positive and by a result of Monika Ludwig all such valuations are multiples of the difference body and the projection body respectively. We show that $W = \mathbb{R}$ is the only additional case where such a valuation exists. New examples arise if we omit translation invariance. This is a joint work with Thomas Wannerer.




  • Tuesday, May 24, 2022, 10:30AM (New York, NY time)

    No seminar because of the clash with this workshop




    Schedule Fall 2022:


  • Tuesday, August 31, 2022, 10:30AM (New York, NY time)

    Dmitri Burago, Penn State University

    Topic: TBA

    Abstract: TBA.




  • Tuesday, September 6, 2022, 10:30AM (New York, NY time)

    Eduardo Lucas, University of Murcia

    Topic: TBA

    Abstract: TBA.




  • Tuesday, September 13, 2022, 10:30AM (New York, NY time)

    Orli Herscovici, Georgia Institute of Technology, Atlanta, GA

    Topic: TBA

    Abstract: TBA.




  • Tuesday, September 20, 2022, 10:30AM (New York, NY time)

    Michael Roysdon, Tel Aviv University, Israel

    Topic: TBA

    Abstract: TBA.




  • Tuesday, September 27, 2022, 10:30AM (New York, NY time)

    No seminar, intersection with this ICERM workshop




  • Tuesday, October 4, 2022, 10:30AM (New York, NY time)

    Maud Szusterman, Universit� de Paris, France

    Topic: TBA

    Abstract: TBA.




  • Tuesday, October 11, 2022, 10:30AM (New York, NY time)

    Hui Tuan Pham, Stanford University

    Topic: TBA

    Abstract: TBA.




  • Tuesday, October 18, 2022, 10:30AM (New York, NY time)

    No seminar, intersection with this ICERM workshop




  • Tuesday, October 25, 2022, 10:30AM (New York, NY time)

    Ilya Molchanov, Institute of Mathematical Statistics and Actuarial Science (IMSV), Bern, Switzerland

    Topic: TBA

    Abstract: TBA.




  • Tuesday, November 1, 2022, 10:30AM (New York, NY time)

    Kasia Wyczesany, Tel Aviv University, Tel Aviv, Israel

    Topic: TBA

    Abstract: TBA.




  • Tuesday, November 8, 2022, 10:30AM (New York, NY time)

    Lu Wang, Yale University, New Haven, CT, US

    Topic: TBA

    Abstract: TBA.




  • Tuesday, November 15, 2022, 10:30AM (New York, NY time)

    TBA, TBA

    Topic: TBA

    Abstract: TBA.




  • Tuesday, November 22, 2022, 10:30AM (New York, NY time)

    Barbara Brandolini, University of Naples, Italy

    Topic: TBA

    Abstract: TBA.




  • Tuesday, November 29, 2022, 10:30AM (New York, NY time)

    Thomas Jahn, TU Chemnitz, Germany

    Topic: On The Optimal Constants in the Two-Sided Stechkin Inequalities

    Abstract: The $\ell_1$-norm of a monotonically decreasing sequence of nonnegative numbers can be sandwiched by a sum involving the best $n$-term approximation errors measured in the $\ell_q$-norm, suitably scaled by positive constants. But what are the optimal constants? In this talk, you will get in touch with the contributions of Copson, Stechkin, Pietsch, Temlyakov, and Bennett, the geometry behind the problem, and variants of the inequality, where the $\ell_1$-norm is replaced by its weak counterpart or where sums are replaced by integrals. This is joint work with Tino Ullrich.




  • Tuesday, December 6, 2022, 10:30AM (New York, NY time)

    Eliza O'Reilly, TBA

    Topic: TBA

    Abstract: TBA.




  • Tuesday, December 13, 2022, 10:30AM (New York, NY time)

    TBA, TBA

    Topic: TBA

    Abstract: TBA.




  • Tuesday, January 17, 2023, 10:30AM (New York, NY time)

    Francesco Chiacchio, University of Naples, Italy

    Topic: TBA

    Abstract: TBA.




  • Tuesday, January 24, 2023, 10:30AM (New York, NY time)

    Steven Hoehner, Longwood University

    Topic: TBA

    Abstract: TBA.







    Organizers: