Harmonic Analysis and Convexity

Institute for Computational and Experimental Research in Mathematics (ICERM)

September 7, 2022 - December 9, 2022
Wednesday, September 7, 2022
Harmonic Analysis and Convexity
  • 9:00 am - 3:00 pm EDT
    Check In
    11th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Welcome
    11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, September 8, 2022
Harmonic Analysis and Convexity
  • 10:00 - 10:05 am EDT
    Rotem Assouline Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:05 - 10:10 am EDT
    Effrosyni Chasioti Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:10 - 10:15 am EDT
    Manuel Fernandez Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:15 - 10:20 am EDT
    Paul Simanjuntak Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:20 - 10:25 am EDT
    Maud Szusterman Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:25 - 10:30 am EDT
    Weiyan (Claire) Huang Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:30 - 10:35 am EDT
    Dylan Langharst Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:35 - 10:40 am EDT
    Jacopo Ulivelli Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 10:40 - 10:45 am EDT
    Bartłomiej Zawalski Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
  • 1:00 - 1:10 pm EDT
    Fushuai (Black) Jiang Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 1:10 - 1:20 pm EDT
    Fabian Mussnig Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 1:20 - 1:30 pm EDT
    Michael Roysdon Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 1:30 - 1:40 pm EDT
    Nimita Shinde Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 1:40 - 1:50 pm EDT
    Manasa Vempati Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 1:50 - 2:00 pm EDT
    Nathan Wagner Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 2:00 - 2:10 pm EDT
    Hoanan Zhang Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 2:20 - 2:30 pm EDT
    Alexandros Eskenazis Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 2:30 - 2:40 pm EDT
    Kasia Wyczesany Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 2:40 - 2:50 pm EDT
    Sudan Xing Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 2:50 - 3:00 pm EDT
    Andrew Yarmola Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 3:00 - 3:10 pm EDT
    Shixuan Zhang Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 3:10 - 3:20 pm EDT
    Orli Herscovici Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 3:20 - 3:30 pm EDT
    Alex McDonald Introduction
    Lightning Talks - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, September 9, 2022
Harmonic Analysis and Convexity
  • 10:00 - 11:00 am EDT
    Grad Student/Postdoc Meeting with ICERM Directorate
    Meeting - 11th Floor Conference Room
  • 2:00 - 3:00 pm EDT
    Organizer Meeting with ICERM Directorate
    Meeting - 11th Floor Conference Room
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, September 12, 2022
  • 9:50 - 10:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Session Chair
    • Brendan Hassett, ICERM/Brown University
  • 10:00 - 10:45 am EDT
    Introduction to computer assisted proofs in analysis and PDE (Part 1)
    11th Floor Lecture Hall
    • Speaker
    • Javier Gomez Serrano, Brown University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 11:00 am - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:45 pm EDT
    Bellman function and convexity (Part 1)
    11th Floor Lecture Hall
    • Speaker
    • Sergei Treil, Brown University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Uniqueness Questions in Convexity: Floating bodies and others. (Part 1)
    11th Floor Lecture Hall
    • Speaker
    • Dmitry Ryabogin, Kent State University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 5:00 - 6:30 pm EDT
    Welcome Reception
    Reception - Ground Floor - Hemenway's Patio
Tuesday, September 13, 2022
  • 9:00 - 9:45 am EDT
    Introduction to computer assisted proofs in analysis and PDE (Part 2)
    11th Floor Lecture Hall
    • Speaker
    • Javier Gomez Serrano, Brown University
    • Session Chair
    • Irina Holmes Fay, Texas A&M University
  • 10:15 - 11:00 am EDT
    Volume and Duality (Part 1)
    11th Floor Lecture Hall
    • Speaker
    • Artem Zvavitch, Kent State University
    • Session Chair
    • Irina Holmes Fay, Texas A&M University
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:45 pm EDT
    Uniqueness Questions in Convexity: Floating bodies and others. (Part 2)
    11th Floor Lecture Hall
    • Speaker
    • Dmitry Ryabogin, Kent State University
    • Session Chair
    • Irina Holmes Fay, Texas A&M University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, September 14, 2022
  • 9:00 - 9:45 am EDT
    Bellman function and convexity (Part 2)
    11th Floor Lecture Hall
    • Speaker
    • Sergei Treil, Brown University
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
  • 10:15 - 11:00 am EDT
    Introduction to computer assisted proofs in analysis and PDE (Part 3)
    11th Floor Lecture Hall
    • Speaker
    • Javier Gomez Serrano, Brown University
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
  • 11:45 am - 12:30 pm EDT
    Volume and Duality (Part 2)
    11th Floor Lecture Hall
    • Speaker
    • Artem Zvavitch, Kent State University
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
  • 12:45 - 2:30 pm EDT
    Lunch/Free Time
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, September 15, 2022
  • 9:00 - 9:45 am EDT
    Bellman function and convexity (Part 3)
    11th Floor Lecture Hall
    • Speaker
    • Sergei Treil, Brown University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 10:15 - 11:00 am EDT
    Volume and Duality (Part 3)
    11th Floor Lecture Hall
    • Speaker
    • Artem Zvavitch, Kent State University
    • Session Chair
    • Irina Holmes Fay, Texas A&M University
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:45 pm EDT
    Uniqueness Questions in Convexity: Floating bodies and others. (Part 3)
    11th Floor Lecture Hall
    • Speaker
    • Dmitry Ryabogin, Kent State University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, September 16, 2022
  • 9:00 - 9:45 am EDT
    Examples of harmonic analysis Bellman functions and why they are Bellman (Part 1)
    11th Floor Lecture Hall
    • Speaker
    • Alexander Volberg, Michigan State University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 10:15 - 11:00 am EDT
    Examples of harmonic analysis Bellman functions and why they are Bellman (Part 2)
    11th Floor Lecture Hall
    • Speaker
    • Alexander Volberg, Michigan State University
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:45 pm EDT
    Dyadic martingales and the hypercube: duality
    11th Floor Lecture Hall
    • Speaker
    • Paata Ivanishvili, University of California, Irvine
    • Session Chair
    • Artem Zvavitch, Kent State University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, September 19, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EDT
    Multilinear singular integrals and applications
    Seminar - 11th Floor Lecture Hall
    • Polona Durcik, Chapman University
    Abstract
    We give an overview of some recent results and open problems in the area of multilinear singular integrals and discuss their connection with questions on patterns in large subsets of the Euclidean space.
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, September 20, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EDT
    Professional Development: Job Applications in Academia
    Professional Development - 11th Floor Lecture Hall
  • 11:30 am - 12:30 pm EDT
    Postdoc/ Graduate Student tutorial: Intersection Bodies (Part 1)
    Tutorial - 10th Floor Classroom
    • Alexander Koldobskiy, University of Missouri-Columbia
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, September 21, 2022
Harmonic Analysis and Convexity
  • 10:30 - 11:15 am EDT
    Weighted Estimates for the Bergman Projection Using Sparse Domination
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
    • Nathan Wagner, Brown University
    Abstract
    The Bergman projection, or the orthogonal projection from L^2 to the Bergman space of square-integrable holomorphic functions on a given domain, is a fundamental operator in complex analysis. Although the Bergman projection is automatically bounded on L^2, it is non-trivial whether it extends to a bounded operator on L^p for 1<p<\infty, or on L^p spaces with respect to different measures (i.e. weighted inequalities). On the other hand, sparse domination is a recently developed powerful technique in harmonic analysis that has been useful in proving weighted inequalities with sharp constants. In this talk, we will sketch the ideas of how sparse domination-like ideas can be used to prove weighted inequalities for the Bergman projection on the unit ball.
  • 11:15 am - 12:00 pm EDT
    Generalizations of Berwald’s Inequality to Measures.
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
    • Dylan Langharst, Kent State University
    Abstract
    The inequality of Berwald is a reverse-Hölder like inequality for the p-th average of a concave function over a convex body in R^n . We prove Berwald’s inequality for averages of concave functions with respect to measures that have some concavity conditions, e.g. s-concave measures, s ∈ [−∞, 1/n]. As applications, we apply shown results to generalizations of the concepts of radial means bodies and the projection body of a convex body.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, September 22, 2022
Harmonic Analysis and Convexity
  • 11:30 am - 12:30 pm EDT
    Postdoc/ Graduate Student tutorial: Intersection Bodies (Part 2)
    Tutorial - 10th Floor Classroom
    • Alexander Koldobskiy, University of Missouri-Columbia
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, September 23, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EDT
    Sections of the Unit Cube
    Seminar - 11th Floor Lecture Hall
    • Mark Rudelson, University of Michigan
    Abstract
    Consider a section of an n-dimensional cube of unit volume by an (n-d)-dimensional affine hyperplane. If the distance from the hyperplane to the center of the cube is greater than 1/2, then the section can be empty. We will show that if this distance is 1/2 or less, then the volume of the section is uniformly bounded below by a constant independent of the dimension. This means that the minimal volume of a section undergoes a phase transition as the distance to the center of the cube increases, dropping from a constant level to zero. If time allows, we will discuss a similar phenomenon for sections by subspaces of smaller dimensions. Joint work with Hermann Koenig.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, September 26, 2022
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Session Chair
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:45 am EDT
    Haagerup's phase transition at polydisc slicing
    11th Floor Lecture Hall
    • Speaker
    • Tomasz Tkocz, Carnegie Mellon University
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
    Abstract
    We show a probabilistic extension of the Oleszkiewicz-Pełczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. Based on joint work with Chasapis and Singh.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    On the minimal dispersion on the cube
    11th Floor Lecture Hall
    • Speaker
    • Galyna Livshyts, Georgia Tech
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
    Abstract
    We discuss a randomized construction of a point configuration, which gives a bound for the minimal dispersion on the cube. The bound is close to optimal, and in some regime it is optimal for the Poisson point process. Joint work with Alexander Litvak.
  • 11:30 am - 12:15 pm EDT
    From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry
    11th Floor Lecture Hall
    • Speaker
    • Peter Pivovarov, University of Missouri
    • Session Chair
    • Alexander Koldobskiy, University of Missouri-Columbia
    Abstract
    I will discuss a family of affine isoperimetric inequalities for bodies that interpolate between intersection bodies and dual Lp centroid bodies. The focus will be a common framework for the Busemann intersection inequality and the Lutwak--Zhang inequality. The approach depends on new empirical versions of these inequalities. Based on joint work with R. Adamczak, G. Paouris and P. Simanjuntak.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Shortest closed curve to inspect a sphere
    11th Floor Lecture Hall
    • Speaker
    • Mohammad Ghomi, Georgia Institute of Technology
    • Session Chair
    • Kateryna Tatarko, University of Waterloo
    Abstract
    We show that in Euclidean 3-space any closed curve which contains the unit sphere in its convex hull has length at least 4pi, and characterize the case of equality, which settles a conjecture of Zalgaller. Furthermore, we establish an estimate for the higher dimensional version of this problem by Nazarov, which is sharp up to a multiplicative constant. Finally we discuss connections with sphere packing problems, and other optimization questions for convex hull of space curves. This is joint work with James Wenk.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Dual curvature measures for log-concave functions
    11th Floor Lecture Hall
    • Speaker
    • Yiming Zhao, Syracuse University
    • Session Chair
    • Kateryna Tatarko, University of Waterloo
    Abstract
    Dual curvature measures for convex bodies were introduced by Huang-Lutwak-Yang-Zhang in 2016. In this talk, we will discuss how this can be naturally extended to the set of log-concave functions. We will also discuss the Minkowski problem for these measures. This is joint work with Yong Huang, Jiaqian Liu, and Dongmeng Xi.
  • 5:00 - 6:30 pm EDT
    Reception
    10th Floor Collaborative Space
Tuesday, September 27, 2022
  • 9:00 - 9:45 am EDT
    TBA
    11th Floor Lecture Hall
    • Virtual Speaker
    • Sergii Myroshnychenko, Lakehead University
    • Session Chair
    • Dmitry Ryabogin, Kent State University
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Full Field Photoacoustic Tomography with Variable Sound Speed
    11th Floor Lecture Hall
    • Speaker
    • Ngoc Do, Missouri State university
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT, the measured data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique provide the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known for the full field PAT problem. I will discuss the mathematical foundations of the latter problem for variable sound speed and its uniqueness, stability, and exact inversion method using time-reversal. Our results demonstrate the suitability of both the full field approach and the proposed time-reversal technique for high resolution photoacoustic imaging.
  • 11:30 - 11:40 am EDT
    Smooth selection of convex sets
    Lightning Talks - 11th Floor Lecture Hall
    • Speaker
    • Fushuai Jiang, University of Maryland
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    We consider a generalization of the classical Whitney extension problem. Let $E\subset \mathbb{R}^n$ be a compact set and let $K(x) \subset \mathbb{R}^d$ be a convex set for each $x \in E$. I will describe a procedure to determine whether or not there exists a $C^m$ selection of $K$, i.e., if there exists $\phi \in C^m(\mathbb{R}^n, \mathbb{R}^d)$ such that $\phi(x)\in K(x)$ for every $x \in E$. This is based on the joint work with Kevin Luli and Kevin O'Neill.
  • 11:40 - 11:50 am EDT
    Measure Theoretic Minkowski's Existence Theorem
    Lightning Talks - 11th Floor Lecture Hall
    • Speaker
    • Dylan Langharst, Kent State University
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    The Brunn-Minkowski Theory has seen several generalizations over the past century. Many of the core ideas have been generalized to measures. With the goal of framing these generalizations as a measure theoretic Brunn-Minkowski theory, we prove the Minkowski existence theorem for a large class of Borel measures with density, denoted by $\Lambda^\prime$: for $\nu$ a finite, even Borel measure on the unit sphere and $\mu\in\Lambda^\prime$, there exists a symmetric convex body $K$ such that $$d\nu(u)=c_{\mu,K}dS_{\mu,K}(u),$$ where $c_{\mu,K}$ is a quantity that depends on $\mu$ and $K$ and $dS_{\mu,K}(u)$ is the surface area-measure of $K$ with respect to $\mu$. Examples of measures in $\Lambda^\prime$ are homogeneous measures (with $c_{\mu,K}=1$) and probability measures with continuous densities (e.g. the Gaussian measure).
  • 11:50 am - 12:00 pm EDT
    Harmonic analysis and geometric configurations in fractals
    Lightning Talks - 11th Floor Lecture Hall
    • Speaker
    • Alex McDonald, The Ohio State University
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    An active area of research is to determine when a set of sufficient Hausdorff dimension contains finite point configurations of some geometric type. In this talk, I will discuss how techniques from harmonic analysis are used to study such problems.
  • 12:00 - 12:10 pm EDT
    Valuations on convex functions with compact domain
    Lightning Talks - 11th Floor Lecture Hall
    • Speaker
    • Jacopo Ulivelli, La Sapienza, University of Rome
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    We provide a Homogenous decomposition Theorem for continuous and translation invariant valuations on convex functions with compact domain. As a consequence of an extension argument, these valuations are the same for super coercive convex functions, a case settled by Colesanti, Ludwig and Mussnig. Joint work with Jonas Knoerr.
  • 12:10 - 12:20 pm EDT
    On Gaussian projection type inequalities
    Lightning Talks - 11th Floor Lecture Hall
    • Speaker
    • Sudan Xing, University of Alberta
    • Session Chair
    • Dmitry Ryabogin, Kent State University
    Abstract
    We provide an overview of projection bodies in Gaussian probability space for sets of finite Gaussian perimeter and their corresponding applications in functions of Bounded variation space. On the one hand, we study the properties of Gaussian projection bodies for sets of finite Gaussian perimeter under Ehrhard symmetrization and establish a Gaussian projection type inequality. The inequality concludes that Ehrhard symmetrization contracts the Minkowski sum of the Gaussian projection bodies for set of finite Gaussian perimeter $E$ and its reflection $E^v$. On the other hand, we investigate the functional ``lifting" of Ehrhard symmetrization and establish the affine Gaussian P\'olya-Szeg\"o type inequalities in terms of the functional Ehrhard symmetrization. This is based on a joint work with Prof. Youjiang Lin.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Quasianalyticity and support in geometric tomography
    11th Floor Lecture Hall
    • Speaker
    • Dmitry Faifman, Tel Aviv University
    • Session Chair
    • Luis Rademacher, University of California, Davis
    Abstract
    Section and projection functions of convex bodies are not arbitrary functions; in fact, other than in dimension and codimension one, they span a rather small subspace of all functions on the grassmannian, which exhibits a quasianalytic-type property. This phenomenon holds for a class of integral operators on grassmannians, and more generally for certain representations of the general linear group. As corollaries, we will see sharper versions of Alexandrov's projections theorem, Funk's sections theorem, and Klain's injectivity theorem for even valuations.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Curvature measures and soap bubbles beyond convexity
    11th Floor Lecture Hall
    • Speaker
    • Daniel Hug, Karlsruhe Institute of Technology (KIT)
    • Session Chair
    • Luis Rademacher, University of California, Davis
    Abstract
    A fundamental result in differential geometry states that if a smooth hypersurface in a Euclidean space encloses a bounded domain and one of its mean curvature functions is constant, then it is a Euclidean sphere. This statement has been referred to as the soap bubble theorem. Major contributions are due to Alexandrov (1958) and Korevaar--Ros (1988). While the smoothness assumption is seemingly natural at first thought, based on the notion of curvatures measures of convex bodies Schneider (1979) established a characterization of Euclidean spheres among general convex bodies by requiring that one of the curvature measures is proportional to the boundary measure. We describe extensions in two directions: (1) The role of the Euclidean ball is taken by a nice gauge body (Wulff shape) and (2) the problem is studied in a non-convex and non-smooth setting. Thus we obtain characterization results for finite unions of Wulff shapes (bubbling) within the class of mean-convex sets or even for general sets with positive reach. Several related results are established. They include the extension of the classical Steiner--Weyl tube formula to arbitrary closed sets in a uniformly convex normed vector space, formulas for the derivative of the localized volume function of a compact set and general versions of the Heintze--Karcher inequality. (Based on joint work with Mario Santilli)
Wednesday, September 28, 2022
  • 9:00 - 9:45 am EDT
    On the L^p dual Minkowski problem for −1 < p < 0
    11th Floor Lecture Hall
    • Speaker
    • Stephanie Mui, New York University
    • Session Chair
    • Monika Ludwig, Technische Universität Wien
    Abstract
    The L^p dual curvature measure was introduced by Lutwak, Yang, and Zhang in 2018. The associated Minkowski problem, known as the L^p dual Minkowski problem, asks about the existence of a convex body with prescribed L^p dual curvature measure. This question unifies the previously disjoint L^p Minkowski problem with the dual Minkowski problem, two open questions in convex geometry. In this paper, we prove the existence of a solution to the L^p dual Minkowski problem for the case of q < p + 1, −1 < p < 0, and p≠q for even measures.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Inequalities for L_p Steiner coefficients
    11th Floor Lecture Hall
    • Speaker
    • Elisabeth Werner, Case Western Reserve University
    • Session Chair
    • Monika Ludwig, Technische Universität Wien
    Abstract
    We show isoperimetric inequalities for weighted L_p affine surface areas which appear in the recently established L_p Steiner formula of the L_p Brunn Minkowski theory. We show that they are related to f-divergences of the cone measures of the convex body and its polar, namely the Kullback-Leibler divergence and the Renyi-divergence. Based on joint work with Kateryna Tatarko.
  • 11:30 am - 12:15 pm EDT
    Randomized Petty projection inequality
    11th Floor Lecture Hall
    • Speaker
    • Kateryna Tatarko, University of Waterloo
    • Session Chair
    • Monika Ludwig, Technische Universität Wien
  • 12:25 - 12:30 pm EDT
    Group Photo
    11th Floor Lecture Hall
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Infinitesimal characterizations of ellipsoids or balls
    11th Floor Lecture Hall
    • Speaker
    • Alina Stancu, CONCORDIA UNIVERSITY
    • Session Chair
    • Carsten Schuett, CAU Kiel
    Abstract
    We will talk about close (say in Hausdorff metric) convex bodies constructions for which the homothety implies an ellipsoid or a ball. (joint work in progress)
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    The Discrete Gauss Image problem
    11th Floor Lecture Hall
    • Speaker
    • Vadim Semenov, NYU
    • Session Chair
    • Carsten Schuett, CAU Kiel
    Abstract
    The Gauss Image problem is a generalization to the question originally posed by Aleksandrov who studied the existence of the convex body with the prescribed Aleksandrov's integral curvature. A simple discrete case of the Gauss Image Problem can be formulated as follows: given a finite set of directions in Euclidian space and the same number of unit vectors, does there exist a convex polytope in this space containing the origin in its interior with vertices at given directions such that each normal cone at the vertex contains exactly one of the given vectors. In this talk, we are going to discuss the discrete Gauss Image Problem, and its relation to other Minkowski-type problems. Two different proofs of the problem are going to be addressed: A smooth proof based on transportation polytopes and a discrete proof based on Helly’s theorem. This work is based on the recent results of the author.
Thursday, September 29, 2022
  • 9:00 - 9:45 am EDT
    The extremals of Stanley's inequalities for partially ordered sets
    11th Floor Lecture Hall
    • Speaker
    • Yair Shenfeld, MIT
    • Session Chair
    • Elisabeth Werner, Case Western Reserve University
    Abstract
    The presence of log-concave sequences is prevalent in diverse areas of mathematics ranging from geometry to combinatorics. The ubiquity of such sequences is not completely understood but the last decade has witnessed major progress towards this goal. However, we know very little about the extremals of such sequences: If we have equality somewhere along the sequence, what can be said about the sequence itself? This question is related to optimal structures (e.g. the ball in the isoperimetric inequality) and it is a necessary step towards the improvement and stability of the inequalities themselves. I will talk about the extremals of such sequences coming from the theory of partially ordered sets (posets). R. Stanley showed in the 80's how to associate polytopes to posets and, using this correspondence (via the Alexandrov-Fenchel inequality), he proved that sequences which count the number of linear extensions of posets are log-concave. The extremals of these sequences were unknown however, with even conjectures lacking. I will explain the resolution of this problem and the complete characterization of the extremals. The extremals turn out to be complicated and rich structures which exhibit new phenomena depending on the geometry of the associated polytopes. Towards the resolution of this problem we developed new tools that shed brighter light on the relation between the geometry of polytopes and the combinatorics of partially ordered sets. Joint work with Zhao Yu Ma.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Fractional polar projection bodies
    11th Floor Lecture Hall
    • Speaker
    • Monika Ludwig, Technische Universität Wien
    • Session Chair
    • Elisabeth Werner, Case Western Reserve University
    Abstract
    Affine fractional isoperimetric inequalities are established that are stronger (and directly imply) the Euclidean fractional isoperimetric inequalities. These inequalities are fractional versions of the Petty projection inequality. Using the functional version of fractional polar projection bodies, affine fractional Sobolev inequalities are established that are stronger that the fractional Sobolev inequalities of Almgren and Lieb and imply (in the limit) the affine Sobolev inequality by Gaoyong Zhang. Joint work with Julián Haddad (Universidade Federal de Minas Gerais)
  • 11:30 am - 12:15 pm EDT
    Mean oscillation bounds on geometric rearrangements
    11th Floor Lecture Hall
    • Speaker
    • Almut Burchard, University of Toronto
    • Session Chair
    • Elisabeth Werner, Case Western Reserve University
    Abstract
    Symmetric decreasing rearrangement (when applicable) can reduce a geometric variational problem to a radial problem, where the unknown functions depend on the single variable |x|. Classical inequalities for perimeter, gradient norms, and convolution integrals indicate that symmetric decreasing rearrangement reduces the overall oscillation of functions. Less is known about its effect on the mean oscillation of a function. I will discuss recent result (w. Galia Dafni and Ryan Gibara) on inequalities and continuity properties. The question of sharp inequalities remains open.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Functional Intrinsic Volumes
    11th Floor Lecture Hall
    • Speaker
    • Fabian Mussnig, TU Wien
    • Session Chair
    • Susanna Dann, Universidad de los Andes
    Abstract
    We consider functional intrinsic volumes on convex functions. In many ways these objects behave similarly to the classical intrinsic volumes on convex bodies. However, we will also show where analogies fail. The presented results include characterizations, representations, integral geometry and inequalities and we will see that some classical results can be retrieved from the new ones. Joint work with Andrea Colesanti, Monika Ludwig and Jacopo Ulivelli.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Speaker
    • Alexander Litvak, University of Alberta
    • Session Chair
    • Susanna Dann, Universidad de los Andes
Friday, September 30, 2022
  • 9:00 - 9:45 am EDT
    TBA
    11th Floor Lecture Hall
    • Virtual Speaker
    • Beatrice-Helen Vritsiou, University of Alberta
    • Session Chair
    • Maria Alfonseca Cubero, North Dakota State University
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Expansion of random 0/1 polytopes
    11th Floor Lecture Hall
    • Speaker
    • Luis Rademacher, University of California, Davis
    • Session Chair
    • Maria Alfonseca Cubero, North Dakota State University
    Abstract
    This talk will be about a type of discrete isoperimetric inequality and uses projections of polytopes in a fundamental way. A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every 0/1 polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a 0/1 polytope in R^d is greater than 1 over some polynomial function of d. This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of a random 0/1 polytope in R^d is at least 1/12d with high probability. This is joint work with Brett Leroux.
  • 11:30 am - 12:15 pm EDT
    The approximation of almost time- and band-limited functions by their expansion in some orthogonal polynomials bases
    11th Floor Lecture Hall
    • Speaker
    • Susanna Spektor, Sheridan college institute of technology
    • Session Chair
    • Maria Alfonseca Cubero, North Dakota State University
    Abstract
    In this joint work with Philippe Jaming and Abderrazek Karoui our aim is to investigate the quality of approximation of almost time- and almost band-limited functions by its expansion in two classical orthogonal polynomials bases: the Hermite basis and the ultraspherical polynomials bases (which include Legendre and Chebyshev bases as particular cases). This allows us to obtain the quality of approximation in the $L^2$ Sobolev space by these orthogonal polynomials bases. Also, we obtain the rate of the Legendre series expansion of the prolate spheroidal wave functions.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 3, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EDT
    Multi-scale analysis of Jordan curves
    Seminar - 11th Floor Lecture Hall
    • Virtual Speaker
    • Ben Jaye, Georgia Tech
    Abstract
    In this talk we will describe how one can detect regularity in Jordan curves through analysis of associated geometric square functions. We will particularly focus on the resolution of a conjecture of L. Carleson. Joint work with Xavier Tolsa and Michele Villa.
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 4, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EDT
    Professional Development: Ethics I
    Professional Development - 11th Floor Lecture Hall
  • 10:30 - 10:35 am EDT
    Graduate Student/Postdoc Group Photo
    Group Photo - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 5, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 6, 2022
Harmonic Analysis and Convexity
  • 1:30 - 2:15 pm EDT
    On Lp-Brunn-Minkowski type and Lp-isoperimetric type inequalities for measures
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
    • Sudan Xing, University of Alberta
    Abstract
    In 2011, Lutwak, Yang and Zhang extended the definition of the Lp-Minkowski convex combination (p ≥ 1) from convex bodies containing the origin in their interiors to all measurable subsets in R n , and as a consequence, extended the Lp-Brunn-Minkowski inequality to the setting of all measurable sets. In this talk, I will present a functional extension of their Lp-Minkowski convex combination— the Lp,s–supremal convolution and the Lp-BMI for measurable sets to the class of Borel measures on R n having 1 s -concave densities, with s ≥ 0. Moreover, the Lp-BMI for product measures with quasi-concave densities, Lp isoperimetric inequalities for general measures, etc, will also be provided under this new definition. This talk is based on a joint work with Dr. Michael Roysdon.
  • 2:30 - 3:15 pm EDT
    Curvature of graphs and a discrete notion of log-concavity
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
    • Eli Putterman, Tel Aviv University
    Abstract
    The utility of log-concavity in asymptotic geometric analyis is well-known. One very fruitful perspective on this condition is provided by the formalism of Γ-calculus due to Bakry and Émery, according to which log-concave measures are simply measures with "nonnegative curvature." In this talk, we will explain this formalism and propose a new method for extending it to the setting of graphs, which yields a replacement for the notion of log-concavity on graphs. As an application, we show that the Poincaré constant of a log-concave sequence decreases along the heat flow, which is a discrete variant of a previous result of Klartag and the speaker.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 7, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EDT
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
    • Irina Holmes Fay, Texas A&M University
  • 12:00 - 12:15 pm EDT
    Semester Program Group Photo
    Group Photo - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 11, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EDT
    Professional Development: Ethics II
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Ada Lovelace Day Coffee Break
    Coffee Break - 11th Floor Collaborative Space
Wednesday, October 12, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EDT
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:00 - 4:00 pm EDT
    Balanced Fourier truncations on the free group.
    Seminar - 11th Floor Lecture Hall
    • José Manuel Conde Alonso, Universidad Autónoma de Madrid
    Abstract
    Functions on the Hamming cube {-1,1}^n can be written as Fourier-Walsh expansions. In this talk, we study an Lp-inequality of Naor relating certain truncations of said Fourier-Walsh expansions, which happen to be conditional expectations, and discrete derivatives. The above result has deep connections with the theory of Lipschitz inclusions between Banach spaces, and it is proven using harmonic analysis tools. We shall investigate Lp-estimates for balanced averages of Fourier truncations in other group algebras, in terms of differential operators acting on them. Our prime example is the free group Fn. Our main inequality relates norms in Lp(LFn), the noncommutative Lp space associated with the group von Neumann algebra of Fn. For our balanced Fourier truncations, we will explore two natural options: conditional expectations and Hilbert transforms. We shall also discuss the right notion of discrete derivative in our group theoretic setting.
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 13, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 14, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EDT
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 17, 2022
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Session Chair
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:45 am EDT
    Upper bounds for the Fisher information
    11th Floor Lecture Hall
    • Sergey Bobkov, University of Minnesota
    Abstract
    We discuss upper bounds for the Fisher information in high dimensions in terms of the total variation and norms in Sobolev spaces.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The convex hull of space curves with totally positive torsion
    11th Floor Lecture Hall
    • Virtual Speaker
    • Paata Ivanishvili, University of California, Irvine
    Abstract
    Finding a simple description of a convex hull of a set K in n-dimensional Euclidean space is a basic problem in mathematics. When K has some additional geometric structures one may hope to give an explicit construction of its convex hull. A good starting point is when K is a space curve. In this talk I will describe convex hulls of space curves which have a "very" positive torsion. In particular, we obtain a parametric representation of the boundary of the convex hull, different formulas for their Euclidean volumes and the surface areas, and the solution to a general moment problem corresponding to such curves.
  • 11:30 am - 12:15 pm EDT
    How curved are level surfaces of eigenfunctions?
    11th Floor Lecture Hall
    • Virtual Speaker
    • David Jerison, MIT
    Abstract
    I will discuss several conjectures about level sets of eigenfunctions in convex domains.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Approximation of convex bodies in Hausdorff distance by random polytopes
    11th Floor Lecture Hall
    • Elisabeth Werner, Case Western Reserve University
    Abstract
    While there is extensive literature on approximation, deterministic as well as random, of general convex bodies in the symmetric difference metric, or other metrics coming from intrinsic volumes, very little is known for corresponding random results in the Hausdorff distance. For a polygon Q in the plane, the convex hull of n points chosen at random on the boundary of Q gives a random polygon Q_n. We determine the exact limiting behavior of the expected Hausdorff distance between Q and a random polygon Q_n as the number n of points chosen on the boundary of Q goes to infinity. Based on joint work with J. Prochno, C. Schuett and M. Sonnleitner.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Stanislaw Szarek, Case Western Reserve U.
  • 5:00 - 6:30 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, October 18, 2022
  • 9:00 - 9:45 am EDT
    TBA
    11th Floor Lecture Hall
    • Kavita Ramanan, Brown University
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    TBA
    11th Floor Lecture Hall
    • Jelani Nelson, UC Berkeley
  • 11:30 am - 12:15 pm EDT
    Spectral hypergraph sparsification via chaining
    11th Floor Lecture Hall
    • James Lee, University of Washington
    Abstract
    Using aspects of Talagrand's generic chaining theory, we show how to construct spectral hypergraph eps-sparsifiers with only O(eps^{-2} log(r) n log n) hyperedges, where n is the number of vertices and r is the rank of the hypergraph.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Embedding the hypercube into dense bipartite graphs
    11th Floor Lecture Hall
    • Konstantin Tikhomirov, Carnegie Mellon University
    Abstract
    A well known conjecture of Burr and Erdos asserts that the Ramsey number of the hypercube on 2^n vertices is of the order O(2^n). Motivated by this problem, we construct randomized embeddings of the hypercube into dense bipartite graphs and, as a corollary, show that the Ramsey number of the hypercube is of order O(2^{2n−cn}) for a universal constant c>0. This improves upon the previous best known bound O(2^{2n}), due to Conlon, Fox and Sudakov.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Volume growth of groups and random walks
    11th Floor Lecture Hall
    • Tianyi Zheng, UCSD
Wednesday, October 19, 2022
  • 9:00 - 9:45 am EDT
    Regularity for weighted convex isoperimetric problems
    11th Floor Lecture Hall
    • Alexandros Eskenazis, University of Cambridge
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Average Case Analysis of Gaussian Elimination with Partial Pivoting
    11th Floor Lecture Hall
    • Han Huang, Georgia Institute of Technology
    Abstract
    The Gaussian Elimination with Partial Pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for a typical square coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random n x n standard Gaussian coefficient matrix A, the growth factor of the Gaussian Elimination with Partial Pivoting is at most polynomially large in n with probability close to one. This implies that with high probability the number of bits of precision sufficient to solve Ax=b to m bits of accuracy using GEPP is m + O(log(n)), which improves an earlier estimate m + O( log^2 n) of Sankar, and which we conjecture to be optimal by the order of magnitude. We further provide tail estimates of the growth factor which can be used to support the empirical observation that GEPP is more stable than the Gaussian Elimination with no pivoting. This talk is based on a joint work with Konstantin Tikhomirov.
  • 11:30 am - 12:15 pm EDT
    TBA
    11th Floor Lecture Hall
    • Alexander Litvak, University of Alberta
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Limit laws and hypoellipticity
    11th Floor Lecture Hall
    • Maria (Masha) Gordina, University of Connecticut
    Abstract
    We will consider several classical problems for hypoelliptic diffusions and random walks: the large deviations principle (LDP), the small ball problem (SBP), Chung’s law of iterated logarithm (LIL), and finding the Onsager-Machlup functional. As two very different examples we will look at hypoelliptic Brownian motion and the corresponding random walk on the Heisenberg group, and the Kolmogorov diffusion. We will explore the role of space-time scaling property, Gaussianity, and spectral properties via Dirichlet forms in these settings. The Onsager-Machlup functional is used to describe the dynamics of a continuous stochastic process, and it is closely related to the SBP and LIL, as well as the rate functional in the LDP. Unlike in the elliptic (Riemannian) case we do not rely on the tools from differential geometry such as comparison theorems or curvature bounds as these are not always available in the hypoelliptic (sub-Riemannian) setting. The talk is based on the joint work with Marco Carfagnini, Tai Melcher and Jing Wang.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Oanh Nguyen, Brown University
Thursday, October 20, 2022
  • 9:00 - 9:45 am EDT
    Transportation of measures via Langevin flows
    11th Floor Lecture Hall
    • Yair Shenfeld, MIT
    Abstract
    A basic problem in probability theory and engineering is finding a way of representing a complicated probability measure as a simpler probability measure under some transformation. A desirable property of such transformations is that it is Lipschitz, since it allows for information from the simpler probability measure to be transferred to the complicated measure. While various transformations (optimal transport, Knothe-Rosenblatt rearrangement) exist, establishing their regularity is a difficult problem. In this talk, I will discuss the Lipschitz properties of the Langevin transport map which is constructed infinitesimally along the Langevin dynamics. I will show that this map is Lipschitz in many settings where no other Lipschitz transport maps are known to exist. I will conclude the talk by introducing a new connection between the Langevin transport map and renormalization groups methods from quantum and statistical field theories.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Horocyclic Brunn-Minkowksi inequality
    11th Floor Lecture Hall
    • Rotem Assouline, Weizmann Institute of Science
  • 11:30 am - 12:15 pm EDT
    The estimate for the Dimensional Brunn-Minkowski conjecture for all log-concave measures
    11th Floor Lecture Hall
    • Galyna Livshyts, Georgia Tech
    Abstract
    We will show that for any even log-concave measure \mu and any pair of symmetric convex sets K and L, and any t between 0 and 1, one has the inequality: \mu(tK+(1-t)L)^{c(n)}\geq t\mu(K)^{c(n)}+(1-t)\mu(L)^{c(n)}, Where c(n)=n^{-4-o(1)}. This constitutes progress towards the Dimensional Brunn-Minkowski conjecture.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Bounding suprema of canonical processes via convex hull
    11th Floor Lecture Hall
    • Rafał Latała, University of Warsaw
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    A Gaussian correlation inequality for p.s.h. functions
    11th Floor Lecture Hall
    • Dario Cordero-Erausquin, Sorbonne University
    Abstract
    A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural semigroup associated to the Gaussian dbar-Laplacian. Joint work with Franck Barthe.
Friday, October 21, 2022
  • 9:00 - 9:45 am EDT
    A quick estimate for the volume of a polyhedron
    11th Floor Lecture Hall
    • Virtual Speaker
    • Alexander Barvinok, University of Michigan
    Abstract
    Let P be a bounded polyhedron, defined as the intersection of the non-negative orthant in R^n and an affine subspace of codimension m. I present a simple and computationally efficient formula that approximates the volume of P within a factor c^m, where c > 0 is an absolute constant. This is joint work with Mark Rudelson.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Bourgain’s slicing problem and KLS isoperimetry up to polylog
    11th Floor Lecture Hall
    • Joseph Lehec, Université Paris-Dauphine
    Abstract
    We prove that Bourgain’s hyperplane conjecture and the Kannan-Lovasz-Simonovits isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.
  • 11:30 am - 12:15 pm EDT
    A *Slightly* Improved Bound for the KLS Constant (or The Fashion Wars: LV vs L-dan)
    11th Floor Lecture Hall
    • Santosh Vempala, Georgia Tech College of Computing
    Abstract
    We refine the recent breakthrough technique of Klartag and Lehec to obtain an improved polylogarithmic bound for the KLS constant.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    TBA
    11th Floor Lecture Hall
    • Dan Mikulincer, MIT
    Abstract
    TBA
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 24, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EDT
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, October 25, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, October 26, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EDT
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, October 27, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, October 28, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EDT
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, October 31, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EDT
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 1, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EDT
    Professional Development: Hiring
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 2, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EDT
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 3, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, November 4, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EDT
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, November 7, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EST
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 8, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 9, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EST
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 10, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, November 11, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EST
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, November 14, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EST
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 15, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 16, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EST
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 17, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, November 18, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EST
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, November 21, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EST
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, November 22, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EST
    Professional Development: Papers and Journals
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, November 23, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EST
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, November 24, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, November 25, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, December 5, 2022
Harmonic Analysis and Convexity
  • 3:00 - 4:00 pm EST
    Analysis Seminar
    Seminar - 11th Floor Lecture Hall
  • 4:00 - 4:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, December 6, 2022
Harmonic Analysis and Convexity
  • 9:30 - 10:30 am EST
    Professional Development: Grant Proposals
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, December 7, 2022
Harmonic Analysis and Convexity
  • 10:30 am - 12:00 pm EST
    Graduate Student/Postdoc Seminar
    Post Doc/Graduate Student Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, December 8, 2022
Harmonic Analysis and Convexity
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, December 9, 2022
Harmonic Analysis and Convexity
  • 11:00 am - 12:00 pm EST
    Semester Program Seminar
    Seminar - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .