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.


On Saturdays, the lectures start one hour later, that is at:

8:30am in Los-Angeles, CA
9:30am in Edmonton, AB
10:30am in Columbia MO; College Station, TX; Chicago, IL
11:30am in Kent, OH; Atlanta, GA; Montreal; New York, NY
12:30pm in Rio de Janeiro, Buenos Aires
4:30pm (16:30) in London
5:30pm (17:30) in Paris, Milan, Budapest, Vienna
6:30pm (18:30) in Tel Aviv.



Spring 2020: abstracts, slides, videos of the talks





Schedule Fall 2020:


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

    Bo Berndtsson, Chalmers University of Technology and the University of Goteborg, Sweden

    Topic: Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem

    Abstract: We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter. Time permitting, we will also comment on Nazarov's proof and estimates of Bergman kernels.

    Slides of the talk

    Video of the talk



  • Saturday, August 29, 11:30AM (New York, NY time)

    Marton Naszodi, Alfred Renyi Inst. of Math. and Eotvos Univ., Budapest, Hungary

    Topic: Some new quantitative Helly-type theorems

    Abstract: Quantitative Helly-type theorems were introduced by Bárány, Katchalski and Pach in 1982, who, among other results, showed the following. There is a constant C_d depending on the dimension d only, such that if the intersection of a finite family of convex bodies in R^d is of volume at most one, then the intersection of some subfamily of 2d members is of volume at most C_d. We consider colorful and fractional versions of this result.

    Slides of the talk

    Video of the talk



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

    Kateryna Tatarko, Texas A&M University, College Station, TX, USA and the University of Alberta, Canada

    Topic: On the unique determination of ellipsoids by dual intrinsic volumes

    Abstract: In this talk, we show that an ellipsoid is uniquely determined up to an isometry by its dual Steiner polynomial. We reduce this result to the moment problem, and as a by-product obtain an alternative proof of the analogous known result for classical Steiner polynomials in $R^3$. This is joint work with S. Myroshnychenko and V. Yaskin.

    Slides of the talk

    Video of the talk



  • Saturday, September 5, 11:30AM (New York, NY time)

    Adam Kashlak, University of Alberta, Edmonton, Canada

    Topic: Analytic Permutation Testing via Kahane--Khintchine Inequalities

    Abstract: The permutation test is a versatile type of exact nonparametric significance test that requires drastically fewer assumptions than similar parametric tests by considering the distribution of a test statistic over a discrete group of distributionally invariant transformations. The main downfall of the permutation test is the high computational cost of running such a test making this approach laborious for complex data and experimental designs and completely infeasible in any application requiring speedy results. We rectify this problem through application of Kahane--Khintchine-type inequalities under a weak dependence condition and thus propose a computation free permutation test---i.e. a permutation-less permutation test. This general framework is studied within both commutative and non-commutative Banach spaces. We further improve these Kahane-Khintchine-type bounds via a transformation based on the incomplete beta function and Talagrand's concentration inequality. For k-sample testing, we extend the theory presented for Rademacher sums to weakly dependent Rademacher chaoses making use of modified decoupling inequalities. We test this methodology on classic functional data sets including the Berkeley growth curves and the phoneme dataset. We also consider hypothesis testing on speech samples under two experimental designs: the Latin square and the complete randomized block design.

    Slides of the talk

    Video of the talk





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

    Grigory Ivanov, IST Austria, Austria, and MIPT, Moscow, Russia.

    Topic: Functional John-Löwner ellipsoids of a log-concave function

    Abstract: We extend the notion of the John ellipsoid (the largest volume ellipsoid contained within a convex body) to the setting of log-concave functions. For every s > 0, we define a class of log-concave functions derived from ellipsoids. For any log-concave function f, and any fixed s > 0, we consider functions belonging to this class and find the one with the largest integral under the condition that it is pointwise less than or equal to f. We show that it exists and is unique, and call it the John s-function of f. We give a characterization of this function similar to the one provided by John in his fundamental theorem. As an application, we obtain a quantitative Helly-type result about the integral of the pointwise minimum of a family of log-concave functions. Next, we will discuss the concept of duality for log-concave functions and extend the notion of the Löwner ellipsoid (the smallest volume ellipsoid containing a convex body) to the setting of log-concave functions. Time permitting, we will discuss the difference between the behavior of convex sets and log-concave functions concerning our problems. Based on joint works with Márton Naszódi and Igor Tsiutsiurupa.

    Slides of the talk

    Video of the talk



  • Saturday, September 12, 11:30AM (New York, NY time)

    Masha Gordina, University of Connecticut, Storrk, CT, USA

    Topic: Uniform doubling on SU(2) and beyond

    Abstract: Suppose G is a compact Lie group equipped with a left-invariant Riemannian metric. Such metrics usually form a finite-dimensional cone. The Riemannian volume measure corresponding to such a metric is the Haar measure of the group (up to a multiplicative constant). Because of compactness, each left-invariant metric g has the doubling property, that is, there exists a doubling constant D=D(G, g) such that the volume of the ball of radius 2r is at most D times the volume of the ball of radius r. We are concerned with the following question: does there exist a constant D(G) such that, for all left-invariant metrics g on G, the constant D(G, g) is bounded above by D(G)? This is what we call uniformly doubling. The conjecture is that any compact Lie group is uniformly doubling. The only cases for which the conjecture is known are Riemannian tori and the group SU(2). The talk will describe a number of analytic consequences of uniform doubling (in absence of curvature bounds) and our approach to proving uniform doubling on SU(2). The work in progress for U(2) might be mentioned as well. This is joint work with Nathaniel Eldredge (University Northern Colorado) and Laurent Saloff-Coste (Cornell University). Reference: Left-invariant geometries on SU(2) are uniformly doubling, GAFA 2018.

    Slides of the talk

    Video of the talk



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

    Santosh Vempala, Georgia Institute of Technology, Atlanta, GA, USA

    Topic: Reducing Isotropy to KLS: An n^3\psi^2 Volume Algorithm

    Abstract: Computing the volume of a convex body is an ancient problem whose study has led to many interesting mathematical developments. In the most general setting, the convex body is given only via a membership oracle. In this talk, we present a faster algorithm for isotropic transformation of an arbitrary convex body in R^n, with complexity n^3\psi^2, where \psi bounds the KLS constant for isotropic convex bodies. Together with the known bound of \psi = O(n^{1/4}) [2017] and the Cousins-Vempala n^3 volume algorithm for well-rounded convex bodies [2015], this gives an n^{3.5} volume algorithm for general convex bodies, the first improvement on the n^4 algorithm of Lovász-Vempala [2003]. A positive resolution of the KLS conjecture (\psi = O(1)) would imply an n^3 volume algorithm. No background on algorithms, KLS or ABC will be assumed for the talk. Joint work with He Jia, Aditi Laddha and Yin Tat Lee.


    Remark: a follow up talk with more details will take place at the Georgia Tech High Dimensional Seminar on Wednesday, September 16, at 3:15pm (NYC time). Zoom link here.

    Slides of the talk

    Video of the talk



  • Saturday, September 19, 11:30AM (New York, NY time)

    Ferenc Fodor, University of Szeged, Hungary

    Topic: Strengthened inequalities for the mean width and the $\ell$-norm

    Abstract: According to a result of Barthe the regular simplex maximizes the mean width of convex bodies whose John ellipsoid is the Euclidean unit ball. This is equivalent to the fact that the regular simplex maximizes the $\ell$-norm of convex bodies whose L\"owner ellipsoid is the Euclidean unit ball. The reverse statement that the regular simplex minimizes the mean width of convex bodies whose L\"owner ellipsoid is the Euclidean unit ball is also true as proved by Schmuckenschl\"ager. In this talk we prove strengthened stability versions of these results and some related stability statements for the convex hull of the support of centered isotropic measures on the unit sphere. This is joint work with K\'aroly J. B\"or\"oczky (Budapest, Hungary) and Daniel Hug (Karlsruhe, Germany).



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

    Dan Mikulincer, Weizmann Institute of Science, Rehovot, Israel

    Topic: Stability of Stein kernels, moment maps and invariant measures

    Abstract: Suppose that \mu is some nice measure on a Euclidean space. We can associate it with several different constructions of interest: Stein kernels, arising from Stein's theory, the moment map, which is of a more geometric flavour and a particular choice of a stochastic process for which \mu is the invariant measure. We will discuss the connections between these different objects and show that they are stable with respect to the original measure. That is, a small perturbation to either construction will yield a new measure which is close to \mu. Joint work with Max Fathi.



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

    Konstantin Tikhomirov, Georgia Tech, Atlanta, GA, USA

    Topic: TBA

    Abstract: TBA.



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

    Paata Ivanisvili, North Carolina State University, NC, USA

    Topic: Enflo's problem

    Abstract: A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. I will speak about the joint work with Ramon van Handel and Sasha Volberg where we prove that Rademacher and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the Hamming cube.



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

    Keith Ball, University of Warwick, UK

    Topic: Rational approximations to the zeta function

    Abstract: I will describe the construction of a sequence of rational functions with rational coefficients that converge to the zeta function. These approximations extend and make precise the spectral interpretations of the Riemann zeros found by Connes and by Berry and Keating.



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

    Naomi Feldheim, Bar Ilan University, Israel

    Topic: TBA

    Abstract: TBA



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

    Rafal Latala, University of Warsaw, Poland

    Topic: TBA

    Abstract: TBA



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

    Michael Roysdon, Tel Aviv University, Israel

    Topic: L_p-Borell-Brascamp-Lieb type inequalities

    Abstract: (joint work with Sudan Xing) Many recent advances in the $L_p$-Brunn-Minkowski theory have been made in recent years; of particular interest, the L_p-BM conjecture has been shown to be true for p \geq 1-c(n) for some sufficiently small constant c(n) depending on the dimension. The goal of this talk is to introduce a functional counterpart of the $L_p$-Minkowski operations and to establish related Brascamp-Lieb inequalities. In particular, the following result is mentioned, which generalizes a result of Bobkov-Colesanti-Fragala: Let $p \geq 1$, $t \in (0,1)$, $\gamma \leq 1$, and $\alpha \geq -\gamma$. Suppose that $\phi$ is a monotone $\alpha$-concave functional acting on the class of Borel subsets of $\R^n$. Then, for any triple of Borel measurable functions $f,g,h: R^n \to \R_+$ satisfying a reasonable concavity condition, one has that \tilde{\phi}(h) \geq ((1-t) \tilde{\phi}(f)^{\beta} + t \tilde{\phi}(g)^{\beta]^{1/beta}, \beta = (p\alpha\gamma)/(\alpha+\gamma), and $\tilde{\phi}$ denotes the extension of $\phi$ to the functions f,g,h. Related $L_p$-BM inequalities for s-concave measures and isoperimetric type inequalities will be mentioned provided there's sufficient time.

    Jesús Yepes Nicolás, Universidad de Murcia, Spain

    Topic: TBA

    Abstract: TBA



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

    Dima Faifman, Tel Aviv University, Israel

    Topic: TBA

    Abstract: TBA



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

    Mark Sellke, Stanford University, Palo Alto, CA, USA

    Topic: Chasing Convex Bodies

    Abstract: I will explain the chasing convex bodies problem posed by Friedman and Linial in 1991. In this problem, an online player receives a request sequence K_1,...,K_T of convex sets in d dimensional space and moves his position online into each requested set. The player's movement cost is the length of the resulting path. Chasing convex bodies asks if there is an online algorithm with cost competitive against the offline optimal path. This is both an interesting metrical task system and (equivalent to) a competitive analysis view on online convex optimization. This problem has recently been solved twice. The first solution gives a 2^{O(d)} competitive algorithm while the second gives a nearly optimal min(d,sqrt(d*log(T))) competitive algorithm for T requests. The latter result is based on the Steiner point, which is the exact optimal solution to a related geometric problem called Lipschitz selection and dates from 1840. In the talk, I will briefly outline the first solution and fully explain the second. Partially based on joint works with Sébastien Bubeck, Bo'az Klartag, Yin Tat Lee, and Yuanzhi Li.



  • Saturday, November 21, 10:30AM (New York, NY time)

    Kasia Wyczesany, Tel Aviv University, Israel

    Topic: TBA

    Abstract: TBA



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

    Pierre Youssef, NYU Abu Dhabi, United Arab Emirates

    Topic: TBA

    Abstract: TBA



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

    María de los Ángeles Alfonseca-Cubero, North Dakota State University, Fargo, ND, USA

    Topic: TBA

    Abstract: TBA



  • Saturday, December 5, 11:30AM (New York, NY time)

    Susanna Spektor, Sheridan College, Toronto, ON, Canada

    Topic: TBA

    Abstract: TBA.



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

    Emanuel Milman, Technion, Haifa, Israel

    Topic: TBA

    Abstract: TBA



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

    Shay Sadovsky, Tel Aviv University, Israel

    Topic: TBA

    Abstract: TBA







    Schedule Spring 2021:


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

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

    Topic: TBA

    Abstract: TBA



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

    Fanny Augieri, Université Paris Diderot, Paris, France

    Topic: TBA

    Abstract: TBA






    Organizers: