Online Asymptotic Geometric Analysis Seminar

Welcome to the Online AGA seminar webpage!

Note that in Spring 2023, we are changing the seminar time! Now it is 9:30 am EST on Thursdays, rather than 10:30 am EST on Tuesdays.

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 for after the talk

Note that on Thursdays, the lectures start at:

6:30am in Los-Angeles, CA
7:30am in Edmonton, AB
8:30am in Columbia MO; College Station, TX; Chicago, IL
9:30am in Kent, OH; Atlanta, GA; Montreal; New York, NY
10:30am in Rio de Janeiro, Buenos Aires
2:30pm (14:30) in London
3:30pm (15:30) in Paris, Milan, Budapest, Vienna
4:30pm (16:30) in Tel Aviv.

Abstracts, slides, videos of the past talks

Schedule Spring 2024:

  • Thursday, January 11, 2023, 9:30AM (New York, NY time)

    Martin Rapaport, Universite Gustave Eiffel, Paris, France

    Topic: On the monotonicity of discrete entropy for log-concave random variables on $\mathbb{Z}^{d}$.

    Abstract: In this talk, the focus is on the discrete entropy of log-concave random vectors in $\mathbb{Z}^{d}$. Initially, we will provide motivation, context, and a brief overview as well as discuss the definition of log-concavity on $\mathbb{Z}^{d}$ that we are using. Subsequently, we will prove a discrete generalised Entropy Power Inequality (EPI) for isotropic log-concave sums of independent identically distributed random vectors. To achieve this, we will explain our proof strategy, which primarily involves two important stages: an approximation result between discrete entropy and differential entropy as well as a discrete analogue of the upper bound on the isotropic of a log-concave function, which is of independent interest. To accomplish these goals, tools from convex geometry are needed since the isotropic position is required. Thus, the talk fits into the interactions between information theory and convex geometry. Finally, several open questions will be discussed. This talk is based on joint work with Matthieu Fradelizi and Lampros Gavalakis.

    Slides of the talk

    Video of the talk

  • Thursday, January 18, 2024, 9:30AM (New York, NY time)

    Emma Pollard, Boise State University, US

    Topic: Symmetrization Resistance

    Abstract: An asymmetric random variable X is said to be symmetrization resistant if every independent random variable Y that produces a symmetric sum X+Y has a greater variance than that of X. Asymmetric Bernoulli random variables were shown to be symmetrization resistant by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999); Pal (2008) gave a proof using stochastic calculus. Proving symmetrization resistance appears to be difficult: little is known about other asymmetric distributions. We introduce the notion of entropic symmetrization resistance which is the same as symmetrization resistance except that the entropy (rather than variance) of Y must exceed that of X. We show that Bernoulli random variables exhibit entropic symmetrization resistance exactly when they exhibit symmetrization resistance. We also extend the underlying entropy and variance inequalities to the hypercube. Finally, we explore the possibility of extensions to non-Bernoulli random variables. This talk is based on joint work with Mokshay Madiman.

    Slides of the talk

    Video of the talk

  • Thursday, January 25, 2024, 9:30AM (New York, NY time)

    Jnyaneshwar Baslingker, Indian Institute of Science

    Topic: Log-concavity in 1D Coulomb Gas ensumbles

    Abstract: The ordered elements in several one-dimensional Coulomb gas ensembles arising in probability and mathematical physics are shown to have log- concave distributions. Examples include the beta ensembles with convex potentials (in the continuous setting) and the orthogonal polynomial ensembles (in the discrete setting). In particular, we prove the log-concavity of the Tracy-Widom β distributions, Airy distribution, Airy-2 process. Log-concavity of last passage times in percolation is proven using their connection to Meixner ensembles. As a result we prove the log-concavity of top rows of Young diagrams under Poissonized Plancherel measure, which is Poissonized version of a conjecture of Chen. This is ongoing joint work with Manjunath Krishnapur and Mokshay Madiman.

    Slides of the talk

    Video of the talk

  • Thursday, February 1, 2024, 9:30AM (New York, NY time)

    Devraj Duggal, University of Minnesota, MN

    Topic: On Spherical Covariance Representations

    Abstract: We first motive the study of covariance representations by surveying preceding results in the Gauss space. Their spherical counterparts are then derived thereby allowing applications to the spherical concentration phenomenon. The applications include second order concentration inequalities. This talk is based on joint work with Sergey Bobkov.

    Slides of the talk

    Video of the talk

  • Thursday, February 8, 2024, 9:30AM (New York, NY time)

    Marius Tiba, University of Oxford, UK

    Topic: Sharp stability for the Brunn-Minkowski inequality for arbitrary sets

    Abstract: The Brunn-Minkowski inequality states that for (open) sets A and B in R^d, we have |A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}. Equality holds if and only if A and B are convex and homothetic sets in R^d. In this talk, we present a sharp stability result for the Brunn-Minkowski inequality, concluding a long line of research on this problem. We show that if we are close to equality in the Brunn-Minkowski inequality, then A and B are close to being homothetic and convex, establishing the exact dependency between the three notions of closeness. This is based on joint work with Alessio Figalli and Peter van Hintum.

    Slides of the talk

    Video of the talk

  • Thursday, February 22, 2024, 9:30AM (New York, NY time)

    No seminar, intersection with a workshop

  • TUESDAY, February 27, 2024, 9:30AM (New York, NY time) -- NOTE THE TALK IS ON TUESDAY NOT THURSDAY

    Steven Hoehner, Longwood University

    Topic: A New Geometric Definition of Euler's Number with an Application to Random Polytopes

    Abstract: Place $N$ geodesic caps on the sphere $\mathbb{S}^{d-1}=\{x\in\R^d:\,\|x\|_2=1\}$, each of measure $1/N$. How much of the sphere can we cover? When $d\geq 3$ and $N\geq 3$, it is not obvious from a geometric standpoint that such a partial covering can capture a substantial proportion of the measure of $\mathbb{S}^{d-1}$. Using a probabilistic approach, in which the caps are chosen uniformly and independently from the sphere, shows that the expected proportion covered is $1-e^{-1}+o(1)$. Thus a natural question arises: is the random covering optimal, as the number of caps and dimension tend to infinity? We show that the answer to this question is affirmative. Our main result is an asymptotic estimate for the maximum volume of a partial covering with caps of different sizes. As a corollary, we obtain a new geometric definition of Euler's number in terms of the volume of the sphere in high dimensions. We will discuss the proof, which uses concentration of measure along with tools from probability and statistics. Finally, we discuss possible applications related to the optimality of random polytopes in high dimensions. This talk is based on joint work with Gil Kur.

    Slides of the talk

    Video of the talk

  • Thursday, March 7, 2024, 9:30AM (New York, NY time)

    Hannah Alpert, Auburn University

    Topic: Unintuitive properties of Urysohn 1-width

    Abstract: A metric space has small Urysohn 1-width if it admits a continuous map to a 1-dimensional complex where the preimage of each point has small diameter. An open problem is, if a space's universal cover has small Urysohn 1-width, must the original space also have small Urysohn 1-width? Naively we would guess yes, but various strange examples suggest maybe not. Joint work with Panos Papasoglu, Arka Banerjee, Alexey Balitskiy, and Larry Guth.

    Slides of the talk

    Video of the talk

  • Thursday, March 14, 2024, 9:30AM (New York, NY time)

    No seminar, intersection with a workshop

  • Thursday, March 21, 2024, 9:30AM (New York, NY time)

    Beatrice Helen Vritsiou, University of Alberta, Edmonton, Canada

    Topic: On the Illumination Conjecture for convex bodies with many symmetries

    Abstract: We will present a unified treatment of the Hadwiger-Boltyanski Illumination Conjecture for 1-symmetric convex bodies in ALL dimensions, and we will also show how to settle the conjecture (along with its equality cases) for some instances of 1-unconditional convex bodies. This is joint work with Wen Rui Sun.

  • Thursday, April 11, 2024, 9:30AM (New York, NY time)

    Colin Tang, Carnegie Melon University, Pittsburgh, PA

    Topic: Simplex slicing: an asymptotically-sharp lower bound

    Abstract: We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a $1-o(1)$ factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e} \approx 1.27$. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, mainly changing the contour of integration of a meromorphic function.

    Slides of the talk

    Video of the talk

  • FALL 2024

    Dylan Langharst, Institut de Mathematiques de Jussieu, Sorbonne Universite, Paris, France

    Topic: TBA

    Abstract: TBA.

  • Thursday, May 2, 2024, 9:30AM (New York, NY time)

    Shay Sadovsky, Tel Aviv University, Israel

    Topic: Godbersen's conjecture for locally anti-blocking polytopes

    Abstract: Godbersen's conjecture states that for any convex body $K$, the mixed volume $V(K[j],-K[n-j])$ is tightly bounded by $\binom{n}{j} Vol(K)$. The main object of this talk will be the class locally anti-blocking polytopes, which will be introduced in detail. The special properties of this class allow us to prove Godbersen's conjecture for it. We will also discuss other results that have been proved for locally anti-blocking bodies such as Kalai's 3d conjecture, recently proved by Sanyal and Winter, and various geometric inequalities proved together with Artstein-Avidan and Sanyal.

  • TBD time and date

    Boaz Slomka, Open University of Israel, Raanana, Israel

    Topic: TBA

    Abstract: TBA.