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

Schedule Spring 2021:

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

    Yuansi Chen, Duke University, Durham, NC, USA

    Topic: Recent progress on the KLS conjecture and the stochastic localization scheme of Eldan

    Abstract: Kannan, Lovasz and Simonovits (KLS) conjectured in 1993 that the Cheeger isoperimetric coefficient of any log-concave density is achieved by half-spaces up to a universal constant factor. This conjecture also implies other important conjectures such as Bourgain's slicing conjecture (1986) and the thin-shell conjecture (2003). In this talk, first we briefly survey the origin and the main consequences of these conjectures. Then we present the development and the refinement of the main proof technique, namely Eldan's stochastic localization scheme, which results in the current best bounds of the Cheeger isoperimetric coefficient in the KLS conjecture.

    Slides of the talk

    Video of the talk

  • Tuesday, January 12, 2021:

    No seminar. This winter school is happening at the time of the seminar.

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

    Mark Agranovsky, Bar Ilan University, Ramat Gan, Israel

    Topic: On integrable domains and surfaces

    Abstract: Integrability of domains or surfaces in R^n is defined in terms of sectional or solid volume functions, evaluating the volumes of the intersections with affine planes or half-spaces. Study of relations between the geometry of domains and types of their volume functions is motivated by a problem of V.I. Arnold about algebraically integrable bodies, which in turn goes back to celebrated Newton's Lemma about ovals. The talk will be devoted to a survey of some recent works in this area.

    Slides of the talk

    Video of the talk

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

    Konstantin Drach, Aix-Marseille Universite, Marseille, France

    Topic: Reversing classical inequalities under curvature constraints

    Abstract: A convex body $K$ is called uniformly convex if all the principal curvatures at every point along its boundary are bounded by a given constant $\lambda > 0$ either above (\textit{$\lambda$-concave} bodies), or below (\textit{$\lambda$-convex} bodies). We allow the boundary of $K$ to be non-smooth, in which case the bounds on the principal curvatures are defined in the barrier sense. Under uniform convexity assumption, for convex bodies of, say, given volume there are non-trivial upper and lower bounds for various functionals, such as the surface area, in- and outer-radius, diameter, width, etc. The bound in one direction usually constitutes the classical inequality (for example, the lower bound for the surface area is the isoperimetric inequality). The bound in another direction becomes a well-posed and in many cases highly non-trivial \emph{reverse optimization problem}. In the talk, we will give an overview of the results and open questions on the reverse optimization problems under curvature constraints in various ambient spaces.

    Video of the talk

    Slides of the talk

  • Tuesday, February 2, 2021, 11:30AM (New York, NY time) - Note the special time an hour later!

    Rachel Greenfeld, UCLA, Los-Angeles, CA, USA

    Topic: Translational tilings: structure and decidability

    Abstract: Let F be a finite subset of Z^d. We say that F is a translational tile of Z^d if it is possible to cover Z^d by translates of F with no overlaps. Given a finite subset F of Z^d, could we determine whether F is a translational tile in finite time? Suppose that F does tile, does it admit a periodic tiling? A well known argument of Wang shows that these two questions are closely related. In the talk, we will discuss the relation between periodicity and decidability; and present some new results, joint with Terence Tao, on the rigidity of tiling structures in Z^2, and their applications to decidability.

    Slides of the talk

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

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

    Topic: Convex polytopes that tile space with translations: Voronoi domains and spectral sets

    Abstract: In this talk I am going to discuss convex d-dimensional polytopes that tile R^d with translations and their properties related to two conjectures. The first conjecture, the Fuglede conjecture, claims that every spectral set in R^d tiles the space with translations; this conjecture was recently settled for convex domains by Lev and Matolcsi. The second conjecture, the Voronoi conjecture, claims that every convex polytope that tiles R^d with translations is the Voronoi domain for some d-dimensional lattice. The conjecture originates from the Voronois geometric theory of positive definite quadratic forms and is related to many questions in mathematical crystallography including Hilberts 18th problem. I mostly plan to discuss recent progress in the Voronoi conjecture and the proof of the conjecture for five-dimensional parallelohedra; in the general setting the Voronoi conjecture is still open. The talk is based on a joint work with Alexander Magazinov (Skoltech).

    Video of the talk

    Slides of the talk

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

    Han Huang, Georgia Institute of Technology, Atlanta, GA, USA

    Topic: Rank of Sparse Bernoulli Matrices.

    Abstract: Let A be an n by n Bernoulli(p) matrix with p satisfies 1<= pn/ log(n) < +infty. For a fixed positive integer k, the probability that (n-k+1)-th singular value of A equals 0 is (1+o(1)) of the probability that A contains k zero columns or k zero rows.

    Video of the talk

    Slides of the talk

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

    No seminar: this conference intersects with the seminar time.

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

    Maria de los Angeles Alfonseca-Cubero, North Dakota State University, Fargo, ND, USA

    Topic: Solutions to the 5th and 8th Busemann-Petty problems near the ball

    Abstract: In this talk we apply classical harmonic analysis tools, such as singular integrals and maximal functions, to two Busemann-Petty problems.

    Video of the talk

    Whiteboard of the talk

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

    Tselil Schramm, Stanford University, Palo Alto, CA, USA

    Topic: Computational Barriers to Estimation from Low-Degree Polynomials

    One fundamental goal of high-dimensional statistics is to detect and recover structure from noisy data. But even for simple settings (e.g. a planted low-rank matrix perturbed by noise), the computational complexity of estimation is sometimes poorly understood. A growing body of work studies low-degree polynomials as a proxy for computational complexity: it has been demonstrated in various settings that low-degree polynomials of the data can match the statistical performance of the best known polynomial-time algorithms for detection. But prior work has failed to address settings in which there is a "detection-recovery gap" and detection is qualitatively easier than recovery. In this talk, I'll describe a recent result in which we extend the method of low-degree polynomials to address recovery problems. As applications, we resolve (in the low-degree framework) open problems about the computational complexity of recovery for the planted submatrix and planted dense subgraph problems. Based on joint work with Alex Wein.

    Video of the talk

    Whiteboard of the talk

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

    No seminar: this conference intersects with the seminar time.

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

    No seminar: this conference intersects with the seminar time.

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

    Karoly Boroczky, Central European University, Budapest, Hungary

    Topic: Stability of the Prekopa-Leindler inequality and the unconditional Logarithmic Brunn-Minkowski Inequality

    Abstract: Recent results about the stability of the Prekopa-Leinder inequality (with Apratim De in the log-concave case, and with Alessio Figalli and Joao Goncalves in general) are discussed. As a consequence, stability of the Logarithmic Brunn-Minkowski Inequality under symmetries of a Coxeter group is obtained.

    Video of the talk

    Whiteboard of the talk

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

    Semyon Alesker, Tel Aviv University, Tel Aviv, Israel

    Topic: New inequalities for mixed volumes of convex bodies and valuations theory

    Abstract: I will present a few new inequalities for mixed volumes of general convex bodies. In a special case they can be considered as a new isoperimetric property of Euclidean ball in R^n. The inequalities are consequences of a recent result of J. Kotrbaty on Hodge-Riemann type inequalities on the space of translation invariant valuations on convex sets.

    Video of the talk

  • Tuesday, April 13, 2021, 10:30AM (New York, NY time)

    Vishesh Jain, Stanford University, Palo Alto, CA, USA

    Topic: Singularity of discrete random matrices

    Abstract: Let $M_n$ be an $n\times n$ random matrix whose entries are i.i.d copies of a discrete random variable $\xi$. It has been conjectured that the dominant reason for the singularity of $M_n$ is the event that a row or column of $M_n$ is zero, or that two rows or columns of $M_n$ coincide (up to a sign). I will discuss recent work, joint with Ashwin Sah (MIT) and Mehtaab Sawhney (MIT), towards the resolution of this conjecture.

    Video of the talk

    Slides of the talk

  • Tuesday, April 20, 2021, 11:30AM (New York, NY time)

    Anindya De, University of Pennsilvania

    Topic: Convex influences and a quantitative Gaussian correlation inequality.

    Abstract: The Gaussian correlation inequality (GCI), proven by Royen in 2014, states that any two centrally symmetric convex sets (say K and L) in the Gaussian space are positively correlated. We will prove a new quantitative version of the GCI which gives a lower bound on this correlation based on the "common influential directions" of K and L. This can be seen as a Gaussian space analogue of Talagrand's well known correlation inequality for monotone functions. To obtain this inequality, we propose a new approach, based on analysis of Littlewood type polynomials, which gives a recipe to transfer qualitative correlation inequalities into quantitative correlation inequalities. En route, we also give a new notion of influences for convex symmetric sets over the Gaussian space which has many of the properties of influences from Boolean functions over the discrete cube. Much remains to be explored, in particular, about this new notion of influences for convex sets. Based on joint work with Shivam Nadimpalli and Rocco Servedio.

    Video of the talk

    Slides of the talk

  • Tuesday, April 27, 2021, 10:30AM (New York, NY time)

    Almut Burchard, University of Toronto, Canada

    Topic: On isodiametric capacitor problems related to aggregation

    Abstract: I will describe recent work with Rustum Choksi and Elias Hess-Childs on the strong-attraction limit of a class of non-local shape optimization problems, which serve as toy models for the formation of flocks. In these models, a cloud of particles arranges itself according to forces between pairs of particles that depend on their distance: Neighboring particles repel each other, while at long distance the force is attractive. In the strong-attraction limit, the shape optimization problem amounts to maximizing the capacity of a body, subject to a diameter constraint. Clearly, maximizers are bodies of constant width --- but what is their shape?

    Video of the talk

  • Tuesday, May 4, 2021, 10:30AM (New York, NY time)

    Gregory Wyatt, University of Missouri, Columbia, MO, USA (talk 1, 20 minutes)

    Topic: Inequalities for the Derivatives of the Radon Transform on Convex Bodies

    Abstract: It has been shown that the sup-norm of the Radon transform of a probability density defined on an origin-symmetric convex body of volume 1 is bounded from below by a positive constant that depends only on the dimension. Using Fourier analysis, we extend this estimate to the derivatives of the Radon transform. We also provide a comparison theorem for these derivatives.

    Video of the talk

    Slides of the talk

    Sudan Xing, University of Alberta, Canada (talk 2, 20 minutes)

    Topic: The general dual-polar Orlicz-Minkowski problem

    Abstract: In this talk, the general dual-polar Orlicz-Minkowski problem will be presented, which is polar" to the recently initiated general dual Orlicz-Minkowski problem and dual" to the newly proposed polar Orlicz-Minkowski problem. In particular, the existence, continuity and uniqueness of the solutions for the general dual-polar Orlicz-Minkowski problem will be presented. This talk is based on a joint work with Professors Deping Ye and Baocheng Zhu.

    Video of the talk

    Slides of the talk

  • Tuesday, May 11, 2021, 10:30AM (New York, NY time)

    Sang Woo Ryoo, Princeton University, NJ, USA

    Topic: A sharp form of Assouad's embedding theorem for Carnot groups

    Abstract: Assouad's embedding theorem, which embeds snowflakes of doubling metric spaces into Euclidean spaces, has recently been sharpened in many different aspects. Following the work of Tao, which establishes an optimal Assouad embedding theorem for the Heisenberg group, we establish it for general Carnot groups. One main tool is a Nash--Moser type iteration scheme developed by Tao, which we extend into the setting of Carnot groups. The other tool, which is the main novelty of this paper, is a certain orthonormal basis extension theorem in the setting of general doubling metric spaces. We anticipate that this latter tool could be used for other applications.

  • Tuesday, May 18, 2021, 10:30AM (New York, NY time)

    Maria Angeles Hernandez Cifre, Universidad de Murcia, Spain

    Topic: On the roots of polynomials with log-convex coefficients

    Abstract: In the spirit of the work developed for the Steiner polynomial of convex bodies, we investigate geometric properties of the roots of a general family of n-th degree polynomials closely related to that of dual Steiner polynomials of star bodies, deriving, as a consequence, further properties for the roots of the latter. We study the structure of the set of roots of such polynomials, showing that it is a closed convex cone in the upper half-plane, which covers its interior when n tends to infinity, and giving its precise description for every natural n\geq 2. This is a joint work with J. Yepes-Nicols and M. Trraga.

  • Tuesday, May 25, 2021, 11:30AM (New York, NY time)

    Alexander Litvak, University of Alberta, AB, Canada

    Topic: TBA

    Abstract: TBA

  • Tuesday, June 1, 2021, 10:30AM (New York, NY time)

    Ronen Eldan, Weizmann Institute of Science, Rehovot, Israel

    Topic: TBA

    Abstract: TBA

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

    Boaz Slomka, The Open University of Israel, Raanana, Israel

    Topic: Discrete variants of Brunn-Minkowski type inequalities

    Abstract: I will discuss a family of discrete Brunn-Minkowski type inequalities. As particular cases, this family includes the four functions theorem of Ahlswede and Daykin, a result due to Klartag and Lehec, and other variants, both known and new, Two proofs will be outlined, the first is an elementary short proof and the second is a transport proof which extends a result due to Gozlan, Roberto, Samson and Tetali, and which implies stronger entropic versions of our inequalities. Partly based on joint work with Diana Halikias and Boaz Klartag

  • Tuesday, June 15, 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, June 22, 2021, 10:30AM (New York, NY time)

    TBA, TBA

    Topic: TBA

    Abstract: TBA