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 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.

Spring 2020: abstracts, slides, videos of the talks

Fall 2020: abstracts, slides, videos of the talks

Spring 2021: abstracts, slides, videos of the talks

Schedule Fall 2021:

  • Tuesday, August 31, 2021, 10:30AM (New York, NY time)

    Bernardo Gonzalez Merino, University of Murcia, Spain

    Topic: On optimal approximation of functions by log-polynomials

    Abstract: Lasserre in 2015 proved that given any $n$-dimensional compact set $K$ there exists a unique $d$-homogeneous polynomial on $n$-variables $g_d$, $d$ even, such that $K\subset G_1(g_d)=\{x\in\R^n:g_d(x)\leq 1\}$ minimizing $|G_1(g)|$ among all polynomials fulfilling such property $K\subset G_1(g)$. In particular, $G_1(g_2)$ coincides with the Lwner ellipsoid of $K$. In this talk, we will explain how to extend (in two different ways) Lasserre's result to some functional settings. Second, we will prove a theorem characterizing the minimizing functions by means of some touching conditions. Finally, we will also comment on some bounds about the corresponding $d$-outer volume (and integral) ratio between the approximating body (or function) and the original set (or function). This is a joint work together with David Alonso-Gutirrez and Rafael Villa.

    Video of the talk

    Slides of the talk

  • Tuesday, September 7, 2021, 10:30AM (New York, NY time)

    No seminar (conference in Germany at this time)

  • Tuesday, September 14, 2021, 10:30AM (New York, NY time)

    Nir Lev, Bar Ilan University, Ramat Gan, Israel

    Topic: Fuglede's tiling-spectrality conjecture for convex domains

    Abstract: Which domains in Euclidean space admit an orthogonal basis of exponential functions? For example, the cube is such a domain, but the ball is not. In 1974, Fuglede made a fascinating conjecture that these domains could be characterized geometrically as the domains which can tile the space by translations. While this conjecture was disproved for general sets, in a recent paper with Máté Matolcsi we did prove that Fuglede's conjecture is true for convex domains in all dimensions. I will survey the subject and discuss this result.

  • Tuesday, September 21, 2021, 10:30AM (New York, NY time)

    Tomasz Tkocz, Carnegie Melon University, Pittsburgh, PA, USA

    Topic: Rademacher-Gaussian tail comparison for complex coefficients

    Abstract: We shall present a generalisation of Pinelis Rademacher-Gaussian tail comparison to complex coefficients. Based on joint work with Chasapis and Liu.

    Video of the talk

    Slides of the talk

  • Tuesday, September 28, 2021, 10:30AM (New York, NY time)

    Sophie Huberts, CWI, Amsterdam, Netherlands

    Topic: Combinatorial Diameter of Random Polyhedra

    Abstract: The long-standing polynomial Hirsch conjecture asks if the combinatorial diameter of any polyhedron can be bounded by a polynomial of the dimension and number of facets. Inspired by this question, we study the combinatorial diameter of two classes of random polyhedra. We prove nearly-matching upper and lower bounds, assuming that the number of facets is very large compared to the dimension. One key ingredient is a proof that the complexity of a two-dimensional projection of a random polyhedron is concentrated around the mean. Both analyzing the diameter of random polyhedra and this concentration estimate were 34-year old open research questions first posed by Borgwardt.

    Video of the talk

    Slides of the talk

  • Tuesday, October 5, 2021, 10:30AM (New York, NY time)

    No seminar because of time conflict with Nirenberg lectures by Klartag and Chen

  • Tuesday, October 12, 2021, 10:30AM (New York, NY time)

    Juan-Carlos Alvarez Paiva, University of Lille, France

    Topic: The asymmetric case of Hilbert's fourth problem

    Abstract: Hilbert's fourth problem asks to study and construct the class of metrics on open convex subsets of projective $n$-space for which projective lines are geodesics. The problem is often considered solved (by Busemann, Pogorelov, and Szabo), but it is often forgotten that Hilbert also had in mind asymmetric metrics such as those that arise in Minkowski's geometry of numbers (i.e., asymmetric norms) and, indeed, apart from the thesis of Hamel (under Hilbert's supervision), nothing has been done on this problem until recently. In this work I'll explain how classic results in convex geometry together with some easy symplectic geometry can be used to solve this problem in various interesting cases. In particular, we will see how to construct all continuous asymmetric metrics on $n$-dimensional projective space for which projective lines are geodesics.

    Video of the talk

    Slides of the talk

  • Tuesday, October 19, 2021, 10:30AM (New York, NY time)

    Sinai Robins, Universidade de Sao Paolo, Brazil

    Topic: The null set of a of a polytope, and the Pompeiu property for polytopes

    Abstract: We study the null set $N(\P)$ of the Fourier transform of a polytope P in $\R^d$, and we find that this null set does not contain (almost all) circles in $\R^d$. As a consequence, the null set does not contain the algebraic varieties $\{ z \in \C^d \mid z_1^2 + \cdots + z_d^2 = \alpha \}$, for each fixed $\alpha \in \C$. In 1929, Pompeiu asked the following question. Suppose we have a convex subset P in R^d, and a function f, defined over R^d, such that the integral of f over P vanishes, and all of the integrals of f, taken over each rigid motion of P, also vanish. Does it necessarily follow that f = 0? If the answer is affirmative, then the convex body P is said to have the Pompeiu property. It is a conjecture that in every dimension, balls are the only convex bodies that do not have the Pompeiu property. Here we get an explicit proof that the Pompeiu property is true for all polytopes, by combining our work with the work of Brown, Schreiber, and Taylor from 1973. Our proof uses the Brion-Barvinok theorem in combinatorial geometry, together with some properties of the Bessel functions. The original proof that polytopes (as well as other bodies) possess the Pompeiu property was given by Brown, Schreiber, and Taylor (1973) for dimension 2. In 1976, Williams observed that the same proof also works for $d>2$ and, using eigenvalues of the Laplacian, gave another proof valid for $d \geq 2$ that polytopes indeed have the Pompeiu property. The null set of the Fourier transform of polytopes has also been used by various people to tackle problems in multi-tiling Euclidean space. Thus, the null set of a polytope is interesting for several applications, including recent discrete versions of this problem. This is joint work with Fabrcio Caluza Machado.

    Video of the talk

    Slides of the talk

  • Tuesday, October 26, 2021, 10:30AM (New York, NY time)

    Joe Neeman, UT Austin, TX, USA

    Topic: Vector-valued noise stability and quantum max-cut

    Abstract: Borell's inequality characterizes the boolean-valued functions on Gaussian space that have extremal Gaussian noise stability. We prove a similar inequality for functions that take values in the sphere. We will also briefly discuss an application to the computational complexity of approximating certain quantum ground states. This is a joint work with Yeongwoo Hwang, Ojas Parekh, Kevin Thompson and John Wright

  • Tuesday, November 2, 2021, 10:30AM (New York, NY time)

    Margalit Glasgow, Stanford University, Palo Alto, USA

    Topic: Combinatorial Characterization of Rank of Bernoulli Random Matrices

    Abstract: We study the rank of the adjacency matrix A of a random Erdos Reyni graph G~G(n,p). It is well known that when p < log(n)/n, with high probability, A is singular. We prove that when p = omega(1/n), with high probability, the corank of A is equal to the number of isolated vertices remaining in G after the Karp Sipser leaf-removal process, which removes vertices of degree 1 and their unique neighbor. We discuss related results for the asymmetric Bernoulli random matrix, and an application of our techniques to show that the 3-core of G is non-singular with high probability.

  • Tuesday, November 9, 2021, 10:30AM (New York, NY time)

    Eli Putterman, Weizmann Institute of Science, Rehovot, Israel

    Topic: TBA


  • Tuesday, November 16, 2021, 10:30AM (New York, NY time)

    Andreas Bernig, Frankfurt, Germany

    Topic: Intrinsic volumes on Kaehler manifolds

    Abstract: The classical Steiner formula for the volume of parallel bodies is the easiest way to define intrinsic volumes of convex bodies. It admits a differential-geometric analogue, Weyl's tube formula, which applies to submanifolds in euclidean spaces. Surprinsingly, the coefficients in Weyl's tube formula only depend on the intrinsic geometry of the submanifold, and not on the embedding. They are also called "intrinsic volumes". In Alesker's modern framework of "valuations on manifolds", both notions of intrinsic volume really are the same. Weyl's theorem can then be rephrased by saying that for every riemannian manifold, there is a canonical algebra of valuations (the Lipschitz-Killing algebra), and this assignment is compatible with isometric embeddings. In a joint work with Joe Fu, Thomas Wannerer, and Gil Solanes, we give a complex version of this theorem. It states that for each Kaehler manifold, there is a canonical algebra of valuations (the Kaehler-Lipschitz-Killing algebra), and this assignment is compatible with holomorphic isometric embeddings. One consequence is that the kinematic formulas on flat hermitian spaces and complex projective spaces are formally the same.

  • Tuesday, November 23, 2021, 10:30AM (New York, NY time)

    Christos Saroglou, University of Ioannina, Greece

    Topic: TBA


  • Tuesday, November 30, 2021, 10:30AM (New York, NY time)

    Susanna Spektor, Sheridan College, Toronto, ON, Canada

    Topic: On the applications of the Khinchine type inequality for Independent and Dependent Poisson random variables.

    Abstract: We will obtain the Khinchine type inequality for Poisson random variables in two settings-when random variables are independent and when the sum of them is equal to a fixed number. We will look at the applications of these inequalities in Statistics..

  • Tuesday, December 7, 2021, 10:30AM (New York, NY time)

    Stefan Steinerberger, University of Washington, Seattle, WA

    Topic: Mean-Value Inequalities for Harmonic Functions

    Abstract: The mean-value theorem for harmonic functions says that we can bound the integral of a harmonic function in a ball by the average value on the boundary (and, in fact, there is equality). What happens if we replace the ball by a general convex or even non-convex set? As it turns out, this very simple question has connections to classical potential theory, probability theory, PDEs and even mechanics: one of the arising questions dates back to Saint Venant (1856) and was investigated using a specially built soap bubble machine in the 1920s. There are some fascinating new isoperimetric problems: for example, the worst case convex domain in the plane seems to look a lot like the letter "D" but we cannot prove it. I will discuss some recent results and many open problems.