# 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
###### Opening Event: Harmonic Analysis and Convexity
• 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
###### Opening Event: Harmonic Analysis and Convexity
• 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
###### Opening Event: Harmonic Analysis and Convexity
• 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
###### Opening Event: Harmonic Analysis and Convexity
• 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
###### Opening Event: Harmonic Analysis and Convexity
• 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
###### Harmonic Analysis Methods in Geometric Tomography
• 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
###### Harmonic Analysis Methods in Geometric Tomography
• 9:00 - 9:45 am EDT
TBA
11th Floor Lecture Hall
• Virtual Speaker
• 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
###### Harmonic Analysis Methods in Geometric Tomography
• 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
• 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
###### Harmonic Analysis Methods in Geometric Tomography
• 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
###### Harmonic Analysis Methods in Geometric Tomography
• 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
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
Coffee Break - 11th Floor Collaborative Space
##### Wednesday, October 12, 2022
###### Harmonic Analysis and Convexity
• 10:30 am - 12:00 pm EDT
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
###### 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
###### Probabilistic Methods in Geometry and Analysis
• 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
###### Probabilistic Methods in Geometry and Analysis
• 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
###### Probabilistic Methods in Geometry and Analysis
• 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
###### Probabilistic Methods in Geometry and Analysis
• 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
###### Probabilistic Methods in Geometry and Analysis
• 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
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
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
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
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
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
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).