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 Fall 2022:


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

    Dmitri Burago, Penn State University

    Topic: Something like a Mozaic from Geometry, Dynamics, PDEs, and maybe more.

    Abstract: I give very different talks under the same title, this leaves me flexibility. I never know in advance what I want to talk about:) I am going to begin with some unsolved problems, which, in my opinion, deserve more attention that they receive. For some problems, there are partial solutions, which I would try to sketch or at least discuss. I plan then to go to problems where the progress is more substantial, as time permits. What I plan is indeed a mozaic. I am not sure how many topics I would be able to touch upon and which ones would be more of interest, my collaborators include D. Chen, S. Ivanov, B. Kleiner, Ya. Kurylev, M. Lassas, J. Lu, A. Novikov, L. Polterovich. Maybe, I would concentrate оn two or three topics, maybe many more short stories, depending on the reaction.

    Slides of the talk

    Video of the talk




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

    Eduardo Lucas, University of Murcia

    Topic: On discrete Brunn-Minkowski type inequalities

    Abstract: Finding discrete analogues of well-known inequalities in convex geometry has gained traction in recent decades. In this talk, we will discuss recent discrete results concerning the Brunn-Minkowski inequality, involving both the cardinality measure and, specially, the lattice point enumerator measure, defined as the cardinality of the intersection of a bounded set with the integer lattice. We will also consider extensions to the L_p setting, both for p>1 and the more limited 0\leq p<1. The inequalities will be related to their continuous analogues, and a few additional consequences will be extracted as well. This is a joint work with Maria A. Hernandez Cifre and Jesus Yepes Nicolas.

    Slides of the talk

    Video of the talk




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

    No seminar, intersection with this ICERM workshop




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

    Sudan Xing, University of Alberta, Canada

    Topic: On Multiple Lp curvilinear-Brunn-Minkowski inequality

    Abstract: In this talk, the extension of the curvilinear summation for bounded Borel measurable sets to the Lp space for multiple power parameters is introduced. Based on the multiple Lp-curvilinear summation, we establish the multiple Lp curvilinear-Brunn-Minkowski inequality for bounded Borel measurable sets. We also present the proof of multiple Lp Borell-Brascamp-Lieb inequality as well as its normalized version for functions. This talk is based on the joint work with Dr. Michael Roysdon.

    Slides of the talk

    Video of the talk







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

    No seminar, intersection with this ICERM workshop




  • THURSDAY, October 6, 2022, 9AM (New York, NY time) -- note the special time!!!

    Maud Szusterman, Universite de Paris, France

    Topic: Bezout inequality with mixed volumes : is the simplex the only minimizer?

    Abstract: A few years ago, C. Saroglou, I. Soprunov, and A. Zvavitch, could rephrase the Bezout inequality (between algebraic varieties) in terms of mixed volumes, yielding a set of inequalities for the simplex. Thanks to Diskant's inequality, these inequalities also hold for an arbitrary convex body K, up to a factor n. The authors conjectured that the simplex is characterized as the only convex body minimizing the ratio, and proved that this characterization holds among polytopes. In a subsequent paper, they introduced a similar, a priori larger ratio, for which the simplex is indeed the unique minimizer. While several classes of convex bodies (decomposable, smooth, ...) have been excluded from the set of possible minimizers of the smaller ratio, the conjecture remains open. I wish to present two conditions, which both exclude a body from being a minimizer : one is a dual condition, the other has geometric flavour, and involves isoperimetric ratios.

    Slides of the talk

    Video of the talk




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

    Huy Tuan Pham, Stanford University

    Topic: Talagrand’s selector process conjecture and suprema of positive empirical processes

    Abstract: Understanding suprema of stochastic processes is an important subject in probability theory with many applications. While much is known in the case of Gaussian processes thanks to Talagrand’s celebrated majorizing measure theorem, moving beyond the Gaussian case is a much more challenging quest. In this talk, I will discuss recent joint work with Jinyoung Park that resolves a conjecture of Talagrand on suprema of certain stochastic processes driven by sparse Bernoulli random variables (known as selector processes), and a question of Talagrand on general positive empirical processes. Combining with the recent resolution of the (generalized) Bernoulli conjecture, this gives the first steps towards the last missing piece in the study of suprema of general empirical processes. Our proof of Talagrand’s conjecture is combinatorial, and I will discuss how one of the ideas in our proof of Talagrand’s conjecture leads to the proof of the Kahn-Kalai conjecture, an important question in probabilistic combinatorics and random graph theory.

    Slides of the talk

    Video of the talk




  • 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)

    Barbara Brandolini, University of Palermo, Italy

    Topic: Isoperimetric sets for weighted twisted eigenvalues

    Abstract: In this talk we discuss a shape optimization problem for the first twisted eigenvalue of the weighted operator $L=-\textrm{div}\left(\gamma(x)\nabla \right)$ among sets with fixed weighted measure. If $\gamma(x)$ satisfies some convenient assumptions, like in the cases $\gamma(x)=e^{-|x|^2}$ or $\gamma(x)=x_N^k \> (k \ge 0)$, we show that this eigenvalue is minimized by the union of two disjoint isoperimetric sets sharing the same measure. The talk is a based on a recent work in collaboration with Antoine Henrot, Anna Mercaldo and Maria Rosaria Posteraro.

    Slides of the talk




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

    Kasia Wyczesany, Carnegie Melon University, Pittsburgh, PA, USA

    Topic: Zoo of Dualities

    Abstract: In this talk, we will discuss order reversing quasi involutions, which are dualities on their image, and their properties. We prove that any order reversing quasi involution is of a special form, which arose from the consideration of optimal transport problem with respect to costs that attain infinite values. We will discuss how this unified point of view on order reversing quasi involutions helps to deeper the understanding of the underlying structures and principles. We will provide many examples and ways to construct new order reversing quasi involutions from given ones. This talk is based on joint work with Shiri Artstein-Avidan and Shay Sadovsky.

    Slides of the talk

    Video of the talk




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

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

    Topic: Density of topologically nontrivial minimal cones

    Abstract: In this talk, I will discuss some explicit lower bounds on the density of minimal cones of dimension less than 7 provided that the complements of the cone are topologically nontrivial in certain senses. This is joint with Jacob Bernstein.

    Video of the talk




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

    Pazit Haim-Kislev, Tel-Aviv University

    Topic: An isobarycentric problem

    Abstract: In a joint work with Shoni Gilboa and Boaz Slomka we consider an isoperimetric type inequality: Given a finite Borel measure on R^n, which sets have maximal measure among all subsets with prescribed barycenter? As a corollary, we partially answer a question by Henk and Pollehn, which is equivalent to a special case of the Log-Minkowski inequality.

    Slides of the talk

    Video of the talk




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

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

    Topic: Generalised convexity and related limit theorems

    Abstract: The standard convex hull of a subset of Euclidean space is defined as the intersection of all images (under the action of a group of rigid motions) of a half-space containing the given set. We propose a generalisation of this classical notion, that we call a (K,H)-hull, and which is obtained from the above construction by replacing a half-space with some other convex closed subset K of the Euclidean space, and a group of rigid motions by a subset H of the group of invertible affine transformations. The main emphasis is on limit theorems for generalised convex hulls of random samples from K. The talk is based on recent works with Alexander Marynych and Zakhar Kabluchko.

    Slides of the talk

    Video of the talk




  • 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, California Institute of Technology, Pasadena, USA

    Topic: Some applications of mixed volumes in data science: random tessellation forests and optimal regularizers

    Abstract: Many modern problems in data science aim to efficiently and accurately extract important features and make predictions from complex data sets. Naturally occurring structure in the data underpins the success of many contemporary approaches, but large gaps between theory and practice remain. In this talk I will discuss two different applications where efforts to provide theoretical guarantees and guidance for data analysis tasks has drawn connections to the Brunn-Minkowski theory of convex bodies. First I will present theoretical guarantees for a large class of random forest algorithms based on the theory of stationary random tessellations where the bounds depend on certain mixed volumes related to the geometry of the induced partitions. Second, I will discuss recent progress on finding optimal convex and non-convex regularizers for a given probability distribution modeling a data source. In particular, we are able to characterize an optimal star body regularizer by interpreting a relevant functional as a dual mixed volume. This talk is based on joint works with Ngoc Mai Tran, Oscar Leong, Yong Sheng Soh, and Venkat Chandrasekaran. .




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

    Dongbin Li, University of Delaware, Newark, DE, USA

    Topic: An information-theoretic approach to the Kneser-Poulsen conjecture in discrete geometry

    Abstract: The Kneser-Poulsen conjecture in discrete geometry asserts that the volume of a union of balls in Euclidean space decreases if their centers are brought closer. In this talk, we will introduce an information-theoretic approach to tackle this problem. Our approach revolves around a broad question regarding whether Rényi entropies of independent sums decrease when one of the summands is contracted by a 1-Lipschitz map. We answer this broad question affirmatively in various cases. Specifically, we show that when $W$ is a radially symmetric log-concave random vector in $\R^d$, then for any random vector $X$ in $\R^d$ and any 1-Lipschitz map $T$, we have $h_2(T(X)+W) \leq h_2(X+W),$ which can be viewed as an entropic analogue of the Kneser-Poulsen conjecture. The talk is based on a joint work with Gautam Aishwarya, Irfan Alam, Sergii Myroshnychenko, and Oscar Zatarain-Vera.




  • 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)

    Orli Herscovici, Georgia Institute of Technology, Atlanta, GA

    Topic: TBA

    Abstract: TBA.




  • Tuesday, January 31, 2023, 10:30AM (New York, NY time)

    Michael Roysdon, Tel Aviv University, Israel

    Topic: TBA

    Abstract: TBA.




  • Tuesday, February 7, 2023, 10:30AM (New York, NY time)

    Steven Hoehner, Longwood University

    Topic: TBA

    Abstract: TBA.




  • Tuesday, February 14, 2023, 10:30AM (New York, NY time)

    Rotem Assouline, Weizmann Institute of Science, Israel

    Topic: TBA

    Abstract: TBA.




  • Tuesday, February 21, 2023, 10:30AM (New York, NY time)

    Petros Valettas, University of Missouri, Columbia

    Topic: TBA

    Abstract: TBA.




  • Tuesday, February 28, 2023, 10:30AM (New York, NY time)

    Paul Simanjuntak, University of Missouri, Columbia, USA

    Topic: TBA

    Abstract: TBA.







    Organizers: