Organizing Committee
 Javier Gomez Serrano
Brown University  Irina Holmes Fay
Texas A&M University  Bo'az Klartag
The Weizmann Institute of Science  Alexander Koldobskiy
University of MissouriColumbia  Sergei Treil
Brown University  Alexander Volberg
Michigan State University  Artem Zvavitch
Kent State University
Abstract
In recent years, the interaction between harmonic analysis and convex geometry has dramatically increased, which resulted in solutions to several longstanding problems. The program will bring together leading mathematicians in both areas, along with researchers working in related applied fields, for the firstever longterm joint program.
The main directions of the program will include: the Fourier approach to Geometric Tomography, the study of geometric properties of solids based on information about their sections and projections, Volume and Duality, Bellman technique for extremal problems of harmonic analysis, and various types of convexity of solutions of corresponding Hamilton–Jacobi–Bellman equation, as well as numerical computations and computerassisted proofs applied to the aforementioned problems. The computational part will cover theoretical aspects (optimal algorithms, and why they work) as well as more applied ones (implementation).
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Maria Alfonseca Cubero
North Dakota State UniversitySep 1330, 2022

Heshan Aravinda
University of FloridaSep 2628, 2022

Shiri ArtsteinAvidan
Tel Aviv UniversityOct 1721, 2022

Rotem Assouline
Weizmann Institute of ScienceSep 7Dec 10, 2022

Aidan Backus
Brown UniversitySep 7Dec 9, 2022

Alexander Barvinok
University of MichiganOct 1721, 2022

Sergey Bobkov
University of MinnesotaSep 22Oct 21, 2022

Simon Bortz
University of AlabamaNov 28Dec 2, 2022

Almut Burchard
University of TorontoSep 2630, 2022

Alan Chang
Princeton UniversityOct 1622, 2022

Effrosyni Chasioti
Kent State UniversitySep 7Dec 10, 2022

Michael Christ
UC BerkeleyNov 28Dec 2, 2022

Krzysztof Ciosmak
Fields Institute/University of TorontoOct 1721, 2022

Laura Cladek
Institute for Advanced StudyNov 28Dec 2, 2022

Andrea Colesanti
University of FlorenzeSep 2630, 2022

José Manuel Conde Alonso
Universidad Autónoma de MadridOct 922, 2022

Dario CorderoErausquin
Sorbonne UniversityOct 1721, 2022

Amalia Culiuc
Amherst CollegeSep 7Dec 9, 2022

Susanna Dann
Universidad de los AndesSep 8Dec 10, 2022

Francesco Di Plinio
Washington UniversityNov 19Dec 10, 2022

Ngoc Do
Missouri State universitySep 2630, 2022

Komla Domelevo
Universität WürzburgNov 28Dec 2, 2022

Hongjie Dong
Brown UniversitySep 7Dec 9, 2022

Xiaoyu Dong
University of MichiganOct 1721, 2022

Keiko Dow
D'Youville CollegeOct 1721, 2022

Oliver Dragičević
University of LjubljanaNov 18Dec 3, 2022

Polona Durcik
Chapman UniversitySep 7Dec 9, 2022

Ronen Eldan
Weizmann Institute of ScienceOct 1721, 2022

Alexandros Eskenazis
University of CambridgeSep 3Dec 3, 2022

Dmitry Faifman
Tel Aviv UniversitySep 25Oct 1, 2022

Manuel Fernandez
Georgia Institute of TechnologySep 7Dec 9, 2022

Leonardo Ferrari
Université de NeuchâtelOct 1622, 2022

Valentia Fragkiadaki
Texas A&M UniversityNov 28Dec 2, 2022

Rupert Frank
LMU MunichNov 28Dec 2, 2022

Yuan Gao
Purdue UniversityOct 612, 2022

Eduardo GarciaJuarez
Universitat de BarcelonaOct 1721, 2022

Mohammad Ghomi
Georgia Institute of TechnologySep 2630, 2022

Ryan Gibara
University of CincinnatiOct 1721, 2022

Tainara Gobetti Borges
Brown UniversitySep 7Dec 9, 2022

Javier Gomez Serrano
Brown UniversitySep 7Dec 9, 2022

Maria (Masha) Gordina
University of ConnecticutOct 1721, 2022

Rachel Greenfeld
Institute for Advanced StudyOct 1721, 2022

Wyatt Gregory
University of Missouri  ColumbiaOct 1721, 2022

Julián Haddad
Universidade Federal de Minas GeraisSep 2630, 2022

Orli Herscovici
Georgia Institute of TechnologySep 11Oct 1, 2022

Irina Holmes Fay
Texas A&M UniversitySep 5Dec 9, 2022

Weiyan Huang
Washington University in St. LouisSep 10Dec 9, 2022

Han Huang
Georgia Institute of TechnologyOct 1721, 2022

Brice Huang
Massachusetts Institute of TechnologyOct 1721, 2022

Daniel Hug
Karlsruhe Institute of Technology (KIT)Sep 2630, 2022

Paata Ivanishvili
University of California, IrvineSep 7Dec 9, 2022

Ben Jaye
Georgia TechSep 7Dec 9, 2022

David Jerison
MITOct 1721, 2022

Fushuai Jiang
University of MarylandAug 20, 2022Jan 1, 2023

Bo'az Klartag
The Weizmann Institute of ScienceOct 1622, 2022

Alexander Koldobskiy
University of MissouriColumbiaSep 7Dec 9, 2022

Vjekoslav Kovač
University of ZagrebNov 28Dec 2, 2022

Marie Jose Kuffner
John Hopkins UniversityNov 28Dec 2, 2022

Gil Kur
Massachusetts Institute of Technology (MIT)Sep 7Dec 9, 2022

Sefika Kuzgun
University of RochesterOct 1721, 2022

Dylan Langharst
Kent State UniversitySep 7Dec 9, 2022

Rafał Latała
University of WarsawOct 1721, 2022

James Lee
University of WashingtonOct 1721, 2022

Joseph Lehec
Université ParisDauphineOct 1721, 2022

Brett Leroux
University of California, DavisOct 1721, 2022

Zane Li
University of WisconsinMadisonOct 1721, 2022

Elliott Lieb
Princeton UniversityNov 28Dec 2, 2022

Alexander Litvak
University of AlbertaSep 11Dec 3, 2022

Galyna Livshyts
Georgia TechSep 7Dec 9, 2022

Guozhen Lu
University of ConnecticutNov 28Dec 2, 2022

Monika Ludwig
Technische Universität WienSep 7Oct 1, 2022

Jose Ramon Madrid Padilla
UCLA  University of California Los AngelesOct 1721, 2022

Alex McDonald
The Ohio State UniversitySep 10Oct 29, 2022

Dan Mikulincer
MITOct 1721, 2022

Joseph Miller
University of Texas at AustinOct 1429, 2022

Stephanie Mui
New York UniversitySep 2630, 2022

Fabian Mussnig
TU WienSep 7Oct 4, 2022

Sergii Myroshnychenko
Lakehead UniversitySep 2630, 2022

Piotr Nayar
University of WarsawSep 2630, 2022

Jelani Nelson
UC BerkeleyOct 1721, 2022

Oanh Nguyen
Brown UniversityOct 1721, 2022

Diogo Oliveira e Silva
Instituto Superior TécnicoNov 28Dec 2, 2022

Adam Osękowski
University of WarsawNov 28Dec 2, 2022

Stefanie Petermichl
Université Paul SabatierNov 28Dec 2, 2022

Peter Pivovarov
University of MissouriSep 2630, 2022

Keith Promislow
Michigan State UniversityOct 1721, 2022

Eli Putterman
Tel Aviv UniversitySep 7Dec 10, 2022

Luis Rademacher
University of California, DavisSep 7Dec 9, 2022

Abba Ramadan
The university of AlabamaOct 1721, 2022

Kavita Ramanan
Brown UniversityOct 1721, 2022

Chase Reuter
North Dakota State UniversitySep 2630, 2022

Alexander Reznikov
Florida State UniversityNov 28Dec 2, 2022

Joris Roos
UMass LowellNov 28Dec 2, 2022

Liran Rotem
Technion  Israel Institute of TechnologyOct 822, 2022

Michael Roysdon
Tel Aviv UniversitySep 1Dec 10, 2022

Boris Rubin
Louisiana State UniversitySep 2630, 2022

Mark Rudelson
University of MichiganSep 7Dec 9, 2022

Dmitry Ryabogin
Kent State UniversitySep 7Dec 9, 2022

Carsten Schuett
CAU KielSep 7Dec 9, 2022

Richard Schwartz
Brown UniversitySep 7Dec 9, 2022

Vadim Semenov
NYUSep 2630, 2022; Oct 1721, 2022; Nov 28Dec 2, 2022

Yair Shenfeld
MITSep 2630, 2022

Nimita Shinde
IITBMonash Research AcademySep 1, 2022May 31, 2023

Paul Simanjuntak
University of Missouri  ColumbiaSep 6Dec 10, 2022

Joseph Slote
CaltechNov 28Dec 2, 2022

Mariana Smit Vega Garcia
Western Washington UniversityNov 28Dec 2, 2022

Susanna Spektor
Sheridan college institute of technologySep 2630, 2022

Alina Stancu
CONCORDIA UNIVERSITYSep 2630, 2022

Rui Sun
University of AlbertaSep 2630, 2022

Nike Sun
Massachusetts Institute of Technology and University of California, BerkeleyOct 1721, 2022

Brandon Sweeting
University of AlabamaNov 28Dec 2, 2022

Stanislaw Szarek
Case Western Reserve U.Oct 1721, 2022

Maud Szusterman
Université de ParisSep 7Dec 9, 2022

Kateryna Tatarko
University of WaterlooSep 7Nov 11, 2022

Krystal Taylor
The Ohio State UniversityNov 28Dec 2, 2022

Christoph Thiele
University of BonnNov 14Dec 26, 2022

Konstantin Tikhomirov
Carnegie Mellon UniversityOct 1721, 2022

Tomasz Tkocz
Carnegie Mellon UniversitySep 2630, 2022; Oct 1622, 2022

Sergei Treil
Brown UniversitySep 7Dec 9, 2022

Jacopo Ulivelli
La Sapienza, University of RomeSep 12Oct 26, 2022

Ramon van Handel
Princeton UniversityOct 1721, 2022

Dimitrios Vardakis
Michigan State UniversityOct 1522, 2022

Santosh Vempala
Georgia Tech College of ComputingOct 1921, 2022

Naga Manasa Vempati
Georgia Institute of TechnologyAug 31, 2022Jan 1, 2023

Rick Vitale
University of ConnecticutOct 1721, 2022

Alexander Volberg
Michigan State UniversitySep 15Dec 9, 2022

BeatriceHelen Vritsiou
University of AlbertaSep 2630, 2022

Nathan Wagner
Brown UniversitySep 7Dec 9, 2022

Ke Wang
Hong Kong University of Science and TechnologyOct 1721, 2022

Elisabeth Werner
Case Western Reserve UniversitySep 7Dec 9, 2022

Qiang Wu
University of IllinoisOct 1721, 2022

Kasia Wyczesany
Tel Aviv UniversitySep 1Dec 9, 2022

Sudan Xing
University of AlbertaSep 1Dec 30, 2022

Andrew Yarmola
Princeton UniversitySep 7Dec 9, 2022

Vladyslav Yaskin
University of AlbertaSep 11Dec 3, 2022

Pierre Youssef
New York University Abu DhabiOct 1422, 2022

Shuya Yu
University of DelawareOct 1721, 2022

Bartłomiej Zawalski
Polish Academy of SciencesSep 7Dec 9, 2022; Sep 25Nov 5, 2022

Haonan Zhang
IST AustriaSep 11Dec 3, 2022

Shixuan Zhang
Georgia Institute of TechnologySep 6, 2022May 5, 2023

Yiming Zhao
Syracuse UniversitySep 2630, 2022

Tianyi Zheng
UCSDOct 1721, 2022

Artem Zvavitch
Kent State UniversitySep 11Dec 3, 2022
Visit dates listed on the participant list may be tentative and subject to change without notice.
Semester Schedule
Wednesday, September 7, 2022
Harmonic Analysis and Convexity

9:00 am  3:00 pm EDTCheck In11th Floor Collaborative Space

3:00  3:30 pm EDTWelcome11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, September 8, 2022
Harmonic Analysis and Convexity

10:00  10:05 am EDTRotem Assouline IntroductionLightning Talks  11th Floor Lecture Hall

10:05  10:10 am EDTEffrosyni Chasioti IntroductionLightning Talks  11th Floor Lecture Hall

10:10  10:15 am EDTManuel Fernandez IntroductionLightning Talks  11th Floor Lecture Hall

10:15  10:20 am EDTPaul Simanjuntak IntroductionLightning Talks  11th Floor Lecture Hall

10:20  10:25 am EDTMaud Szusterman IntroductionLightning Talks  11th Floor Lecture Hall

10:25  10:30 am EDTWeiyan (Claire) Huang IntroductionLightning Talks  11th Floor Lecture Hall

10:30  10:35 am EDTDylan Langharst IntroductionLightning Talks  11th Floor Lecture Hall

10:35  10:40 am EDTJacopo Ulivelli IntroductionLightning Talks  11th Floor Lecture Hall

10:40  10:45 am EDTBartłomiej Zawalski IntroductionLightning Talks  11th Floor Lecture Hall

11:30 am  1:00 pm EDTLunch/Free Time

1:00  1:10 pm EDTFushuai (Black) Jiang IntroductionLightning Talks  11th Floor Lecture Hall

1:10  1:20 pm EDTFabian Mussnig IntroductionLightning Talks  11th Floor Lecture Hall

1:20  1:30 pm EDTMichael Roysdon IntroductionLightning Talks  11th Floor Lecture Hall

1:30  1:40 pm EDTNimita Shinde IntroductionLightning Talks  11th Floor Lecture Hall

1:40  1:50 pm EDTManasa Vempati IntroductionLightning Talks  11th Floor Lecture Hall

1:50  2:00 pm EDTNathan Wagner IntroductionLightning Talks  11th Floor Lecture Hall

2:00  2:10 pm EDTHoanan Zhang IntroductionLightning Talks  11th Floor Lecture Hall

2:20  2:30 pm EDTAlexandros Eskenazis IntroductionLightning Talks  11th Floor Lecture Hall

2:30  2:40 pm EDTKasia Wyczesany IntroductionLightning Talks  11th Floor Lecture Hall

2:40  2:50 pm EDTSudan Xing IntroductionLightning Talks  11th Floor Lecture Hall

2:50  3:00 pm EDTAndrew Yarmola IntroductionLightning Talks  11th Floor Lecture Hall

3:00  3:10 pm EDTShixuan Zhang IntroductionLightning Talks  11th Floor Lecture Hall

3:10  3:20 pm EDTOrli Herscovici IntroductionLightning Talks  11th Floor Lecture Hall

3:20  3:30 pm EDTAlex McDonald IntroductionLightning Talks  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, September 9, 2022
Harmonic Analysis and Convexity

10:00  11:00 am EDTGrad Student/Postdoc Meeting with ICERM DirectorateMeeting  11th Floor Conference Room

2:00  3:00 pm EDTOrganizer Meeting with ICERM DirectorateMeeting  11th Floor Conference Room

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, September 12, 2022

9:50  10:00 am EDTWelcome11th Floor Lecture Hall
 Session Chair
 Brendan Hassett, ICERM/Brown University

10:00  10:45 am EDTIntroduction 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 EDTLunch/Free Time

2:00  2:45 pm EDTBellman 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTUniqueness 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 EDTWelcome ReceptionReception  Ground Floor  Hemenway's Patio
Tuesday, September 13, 2022

9:00  9:45 am EDTIntroduction 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 EDTVolume 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 EDTLunch/Free Time

2:00  2:45 pm EDTUniqueness 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 EDTCoffee Break11th Floor Collaborative Space
Wednesday, September 14, 2022

9:00  9:45 am EDTBellman function and convexity (Part 2)11th Floor Lecture Hall
 Speaker
 Sergei Treil, Brown University
 Session Chair
 Alexander Koldobskiy, University of MissouriColumbia

10:15  11:00 am EDTIntroduction 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 MissouriColumbia

11:45 am  12:30 pm EDTVolume and Duality (Part 2)11th Floor Lecture Hall
 Speaker
 Artem Zvavitch, Kent State University
 Session Chair
 Alexander Koldobskiy, University of MissouriColumbia

12:45  2:30 pm EDTLunch/Free Time

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, September 15, 2022

9:00  9:45 am EDTBellman 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 EDTVolume 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 EDTLunch/Free Time

2:00  2:45 pm EDTUniqueness 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 EDTCoffee Break11th Floor Collaborative Space
Friday, September 16, 2022

9:00  9:45 am EDTExamples 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 EDTExamples 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 EDTLunch/Free Time

2:00  2:45 pm EDTDyadic martingales and the hypercube: duality11th Floor Lecture Hall
 Speaker
 Paata Ivanishvili, University of California, Irvine
 Session Chair
 Artem Zvavitch, Kent State University

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, September 19, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm EDTMultilinear singular integrals and applicationsSeminar  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 EDTCoffee Break11th Floor Collaborative Space
Tuesday, September 20, 2022
Harmonic Analysis and Convexity

9:30  10:30 am EDTProfessional Development: Job Applications in AcademiaProfessional Development  11th Floor Lecture Hall

11:30 am  12:30 pm EDTPostdoc/ Graduate Student tutorial: Intersection Bodies (Part 1)Tutorial  10th Floor Classroom
 Alexander Koldobskiy, University of MissouriColumbia

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, September 21, 2022
Harmonic Analysis and Convexity

10:30  11:15 am EDTWeighted Estimates for the Bergman Projection Using Sparse DominationPost 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 squareintegrable 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 nontrivial 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 dominationlike ideas can be used to prove weighted inequalities for the Bergman projection on the unit ball.

11:15 am  12:00 pm EDTGeneralizations 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 reverseHölder like inequality for the pth 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. sconcave 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 EDTCoffee Break11th Floor Collaborative Space
Thursday, September 22, 2022
Harmonic Analysis and Convexity

11:30 am  12:30 pm EDTPostdoc/ Graduate Student tutorial: Intersection Bodies (Part 2)Tutorial  10th Floor Classroom
 Alexander Koldobskiy, University of MissouriColumbia

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, September 23, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm EDTSections of the Unit CubeSeminar  11th Floor Lecture Hall
 Mark Rudelson, University of Michigan
Abstract
Consider a section of an ndimensional cube of unit volume by an (nd)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 EDTCoffee Break11th Floor Collaborative Space
Monday, September 26, 2022

8:50  9:00 am EDTWelcome11th Floor Lecture Hall
 Session Chair
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am EDTHaagerup's phase transition at polydisc slicing11th Floor Lecture Hall
 Speaker
 Tomasz Tkocz, Carnegie Mellon University
 Session Chair
 Alexander Koldobskiy, University of MissouriColumbia
Abstract
We show a probabilistic extension of the OleszkiewiczPełczyński polydisc slicing result. The Haageruptype phase transition occurs exactly when the pnorm recovers volume, in contrast to the real case. Based on joint work with Chasapis and Singh.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTOn the minimal dispersion on the cube11th Floor Lecture Hall
 Speaker
 Galyna Livshyts, Georgia Tech
 Session Chair
 Alexander Koldobskiy, University of MissouriColumbia
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 EDTFrom intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry11th Floor Lecture Hall
 Speaker
 Peter Pivovarov, University of Missouri
 Session Chair
 Alexander Koldobskiy, University of MissouriColumbia
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 LutwakZhang 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 EDTLunch/Free Time

2:30  3:15 pm EDTShortest closed curve to inspect a sphere11th Floor Lecture Hall
 Speaker
 Mohammad Ghomi, Georgia Institute of Technology
 Session Chair
 Kateryna Tatarko, University of Waterloo
Abstract
We show that in Euclidean 3space 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTDual curvature measures for logconcave functions11th 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 HuangLutwakYangZhang in 2016. In this talk, we will discuss how this can be naturally extended to the set of logconcave 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 EDTReception10th Floor Collaborative Space
Tuesday, September 27, 2022

9:00  9:45 am EDTTBA11th Floor Lecture Hall
 Virtual Speaker
 Sergii Myroshnychenko, Lakehead University
 Session Chair
 Dmitry Ryabogin, Kent State University

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTFull Field Photoacoustic Tomography with Variable Sound Speed11th Floor Lecture Hall
 Speaker
 Ngoc Do, Missouri State university
 Session Chair
 Dmitry Ryabogin, Kent State University
Abstract
Photoacoustic tomography (PAT) is a noninvasive 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 timedependent signals measured on an observation surface. In contrast, the measured data from the recently invented fullfield 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 timereversal. Our results demonstrate the suitability of both the full field approach and the proposed timereversal technique for high resolution photoacoustic imaging.

11:30  11:40 am EDTSmooth selection of convex setsLightning 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 EDTMeasure Theoretic Minkowski's Existence TheoremLightning Talks  11th Floor Lecture Hall
 Speaker
 Dylan Langharst, Kent State University
 Session Chair
 Dmitry Ryabogin, Kent State University
Abstract
The BrunnMinkowski 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 BrunnMinkowski 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 areameasure 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 EDTHarmonic analysis and geometric configurations in fractalsLightning 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 EDTValuations on convex functions with compact domainLightning 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 EDTOn Gaussian projection type inequalitiesLightning 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\'olyaSzeg\"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 EDTLunch/Free Time

2:30  3:15 pm EDTQuasianalyticity and support in geometric tomography11th 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 quasianalytictype 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTCurvature measures and soap bubbles beyond convexity11th 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 KorevaarRos (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 nonconvex and nonsmooth setting. Thus we obtain characterization results for finite unions of Wulff shapes (bubbling) within the class of meanconvex sets or even for general sets with positive reach. Several related results are established. They include the extension of the classical SteinerWeyl 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 HeintzeKarcher inequality. (Based on joint work with Mario Santilli)
Wednesday, September 28, 2022

9:00  9:45 am EDTOn the L^p dual Minkowski problem for −1 < p < 011th 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 EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTInequalities for L_p Steiner coefficients11th 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 fdivergences of the cone measures of the convex body and its polar, namely the KullbackLeibler divergence and the Renyidivergence. Based on joint work with Kateryna Tatarko.

11:30 am  12:15 pm EDTRandomized Petty projection inequality11th Floor Lecture Hall
 Speaker
 Kateryna Tatarko, University of Waterloo
 Session Chair
 Monika Ludwig, Technische Universität Wien

12:25  12:30 pm EDTGroup Photo11th Floor Lecture Hall

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTInfinitesimal characterizations of ellipsoids or balls11th 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTThe Discrete Gauss Image problem11th 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 Minkowskitype 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 EDTThe extremals of Stanley's inequalities for partially ordered sets11th Floor Lecture Hall
 Speaker
 Yair Shenfeld, MIT
 Session Chair
 Elisabeth Werner, Case Western Reserve University
Abstract
The presence of logconcave 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 AlexandrovFenchel inequality), he proved that sequences which count the number of linear extensions of posets are logconcave. 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 EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTFractional polar projection bodies11th 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 EDTMean oscillation bounds on geometric rearrangements11th 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 EDTLunch/Free Time

2:30  3:15 pm EDTFunctional Intrinsic Volumes11th 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTTBA11th 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 EDTTBA11th Floor Lecture Hall
 Virtual Speaker
 BeatriceHelen Vritsiou, University of Alberta
 Session Chair
 Maria Alfonseca Cubero, North Dakota State University

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTExpansion of random 0/1 polytopes11th 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 EDTThe approximation of almost time and bandlimited functions by their expansion in some orthogonal polynomials bases11th 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 bandlimited 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 EDTLunch/Free Time

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 3, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm EDTMultiscale analysis of Jordan curvesSeminar  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 EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 4, 2022
Harmonic Analysis and Convexity

9:30  10:30 am EDTProfessional Development: Ethics IProfessional Development  11th Floor Lecture Hall

10:30  10:35 am EDTGraduate Student/Postdoc Group PhotoGroup Photo  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 5, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, October 6, 2022
Harmonic Analysis and Convexity

1:30  2:15 pm EDTOn LpBrunnMinkowski type and Lpisoperimetric type inequalities for measuresPost 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 LpMinkowski 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 LpBrunnMinkowski inequality to the setting of all measurable sets. In this talk, I will present a functional extension of their LpMinkowski convex combination— the Lp,s–supremal convolution and the LpBMI for measurable sets to the class of Borel measures on R n having 1 s concave densities, with s ≥ 0. Moreover, the LpBMI for product measures with quasiconcave 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 EDTCurvature of graphs and a discrete notion of logconcavityPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Eli Putterman, Tel Aviv University
Abstract
The utility of logconcavity in asymptotic geometric analyis is wellknown. One very fruitful perspective on this condition is provided by the formalism of Γcalculus due to Bakry and Émery, according to which logconcave 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 logconcavity on graphs. As an application, we show that the Poincaré constant of a logconcave 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 EDTCoffee Break11th Floor Collaborative Space
Friday, October 7, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm EDTSemester Program SeminarSeminar  11th Floor Lecture Hall
 Irina Holmes Fay, Texas A&M University

12:00  12:15 pm EDTSemester Program Group PhotoGroup Photo  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 11, 2022
Harmonic Analysis and Convexity

9:30  10:30 am EDTProfessional Development: Ethics IIProfessional Development  11th Floor Lecture Hall

3:30  4:00 pm EDTAda Lovelace Day Coffee BreakCoffee Break  11th Floor Collaborative Space
Wednesday, October 12, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm EDTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:00  4:00 pm EDTBalanced 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 FourierWalsh expansions. In this talk, we study an Lpinequality of Naor relating certain truncations of said FourierWalsh 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 Lpestimates 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 EDTCoffee Break11th Floor Collaborative Space
Thursday, October 13, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 14, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm EDTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 17, 2022

8:50  9:00 am EDTWelcome11th Floor Lecture Hall
 Session Chair
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am EDTUpper bounds for the Fisher information11th 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 EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTThe convex hull of space curves with totally positive torsion11th 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 ndimensional 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 EDTHow 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 EDTLunch/Free Time

2:30  3:15 pm EDTApproximation of convex bodies in Hausdorff distance by random polytopes11th 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTTBA11th Floor Lecture Hall
 Stanislaw Szarek, Case Western Reserve U.

5:00  6:30 pm EDTReception11th Floor Collaborative Space
Tuesday, October 18, 2022

9:00  9:45 am EDTTBA11th Floor Lecture Hall
 Kavita Ramanan, Brown University

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTTBA11th Floor Lecture Hall
 Jelani Nelson, UC Berkeley

11:30 am  12:15 pm EDTSpectral hypergraph sparsification via chaining11th Floor Lecture Hall
 James Lee, University of Washington
Abstract
Using aspects of Talagrand's generic chaining theory, we show how to construct spectral hypergraph epssparsifiers 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 EDTLunch/Free Time

2:30  3:15 pm EDTEmbedding the hypercube into dense bipartite graphs11th 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 EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTVolume growth of groups and random walks11th Floor Lecture Hall
 Tianyi Zheng, UCSD
Wednesday, October 19, 2022

9:00  9:45 am EDTRegularity for weighted convex isoperimetric problems11th Floor Lecture Hall
 Alexandros Eskenazis, University of Cambridge

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTAverage Case Analysis of Gaussian Elimination with Partial Pivoting11th 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 EDTTBA11th Floor Lecture Hall
 Alexander Litvak, University of Alberta

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTLimit laws and hypoellipticity11th 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 OnsagerMachlup 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 spacetime scaling property, Gaussianity, and spectral properties via Dirichlet forms in these settings. The OnsagerMachlup 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 (subRiemannian) setting. The talk is based on the joint work with Marco Carfagnini, Tai Melcher and Jing Wang.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTTBA11th Floor Lecture Hall
 Oanh Nguyen, Brown University
Thursday, October 20, 2022

9:00  9:45 am EDTTransportation of measures via Langevin flows11th 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, KnotheRosenblatt 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 EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTHorocyclic BrunnMinkowksi inequality11th Floor Lecture Hall
 Rotem Assouline, Weizmann Institute of Science

11:30 am  12:15 pm EDTThe estimate for the Dimensional BrunnMinkowski conjecture for all logconcave measures11th Floor Lecture Hall
 Galyna Livshyts, Georgia Tech
Abstract
We will show that for any even logconcave 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+(1t)L)^{c(n)}\geq t\mu(K)^{c(n)}+(1t)\mu(L)^{c(n)}, Where c(n)=n^{4o(1)}. This constitutes progress towards the Dimensional BrunnMinkowski conjecture.

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTBounding suprema of canonical processes via convex hull11th Floor Lecture Hall
 Rafał Latała, University of Warsaw

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTA Gaussian correlation inequality for p.s.h. functions11th Floor Lecture Hall
 Dario CorderoErausquin, Sorbonne University
Abstract
A positive correlation inequality is established for circularinvariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the OrnsteinUhlenbeck semigroup, and another natural semigroup associated to the Gaussian dbarLaplacian. Joint work with Franck Barthe.
Friday, October 21, 2022

9:00  9:45 am EDTA quick estimate for the volume of a polyhedron11th Floor Lecture Hall
 Virtual Speaker
 Alexander Barvinok, University of Michigan
Abstract
Let P be a bounded polyhedron, defined as the intersection of the nonnegative 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 EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTBourgain’s slicing problem and KLS isoperimetry up to polylog11th Floor Lecture Hall
 Joseph Lehec, Université ParisDauphine
Abstract
We prove that Bourgain’s hyperplane conjecture and the KannanLovaszSimonovits isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.

11:30 am  12:15 pm EDTA *Slightly* Improved Bound for the KLS Constant (or The Fashion Wars: LV vs Ldan)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 EDTLunch/Free Time

2:30  3:15 pm EDTTBA11th Floor Lecture Hall
 Dan Mikulincer, MIT
Abstract
TBA

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 24, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm EDTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, October 25, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, October 26, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm EDTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, October 27, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, October 28, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm EDTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, October 31, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm EDTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, November 1, 2022
Harmonic Analysis and Convexity

9:30  10:30 am EDTProfessional Development: HiringProfessional Development  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, November 2, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm EDTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, November 3, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, November 4, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm EDTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, November 7, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm ESTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, November 8, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, November 9, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm ESTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, November 10, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, November 11, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm ESTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, November 14, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm ESTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, November 15, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, November 16, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm ESTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, November 17, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, November 18, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm ESTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, November 21, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm ESTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, November 22, 2022
Harmonic Analysis and Convexity

9:30  10:30 am ESTProfessional Development: Papers and JournalsProfessional Development  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, November 23, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm ESTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, November 24, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, November 25, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, December 5, 2022
Harmonic Analysis and Convexity

3:00  4:00 pm ESTAnalysis SeminarSeminar  11th Floor Lecture Hall

4:00  4:30 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, December 6, 2022
Harmonic Analysis and Convexity

9:30  10:30 am ESTProfessional Development: Grant ProposalsProfessional Development  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, December 7, 2022
Harmonic Analysis and Convexity

10:30 am  12:00 pm ESTGraduate Student/Postdoc SeminarPost Doc/Graduate Student Seminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, December 8, 2022
Harmonic Analysis and Convexity

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, December 9, 2022
Harmonic Analysis and Convexity

11:00 am  12:00 pm ESTSemester Program SeminarSeminar  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC4).
All event times are listed in .
ICERM local time in Providence, RI is Eastern Daylight Time (UTC4). Would you like to switch back to ICERM time or choose a different custom timezone?
Your Visit to ICERM
 ICERM Facilities
 ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am  5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
 Traveling to ICERM
 ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. Indepth directions and transportation information are available on our travel page.
 Lodging/Housing
 Visiting ICERM for longer than a weeklong workshop? ICERM staff works with participants to locate accommodations that fit their needs. Since shortterm furnished housing is in very high demand, take advantage of the housing options ICERM may recommend. Contact housing@icerm.brown.edu for more details.
 Childcare/Schools
 Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
 Technology Resources
 Wireless internet access and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
 Accessibility
 To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
 Discrimination and Harassment Policy
 ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Brown University's "Code of Conduct", "Discrimination and Workplace Harassment Policy", "Sexual and Genderbased Misconduct Policy", and "Title IX Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director of Finance & Administration; they are the responsible employees at ICERM under this policy.
 Exploring Providence
 Providence's worldrenowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.
Visa Information
Contact visa@icerm.brown.edu for assistance.
 Need a US Visa?
 J1 visa requested via ICERM staff
 Eligible to be reimbursed
 B1 or Visa Waiver Business (WB) –if you already have either visa – contact ICERM staff for a visa specific invitation letter.
 Ineligible to be reimbursed
 B2 or Visa Waiver Tourist (WT)
 Already in the US?

F1 and J1 not sponsored by ICERM: obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.
H1B holders do not need letter of approval.
All other visas: alert ICERM staff immediately about your situation.
ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.
Financial Support
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
 ORCID iD
 As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
 Acceptable Costs

 1 roundtrip between your home institute and ICERM
 Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
 Ground Transportation to and from airports and ICERM.
 Unacceptable Costs

 Flights on nonU.S. or nonE.U. airlines
 Flights on U.K. airlines
 Seats in economy plus, business class, or first class
 Change ticket fees of any kind
 Multiuse bus passes
 Meals or incidentals
 Advance Approval Required

 Personal car travel to ICERM from outside New England
 Multipledestination plane ticket; does not include layovers to reach ICERM
 Arriving or departing from ICERM more than a day before or day after the program
 Multiple trips to ICERM
 Rental car to/from ICERM
 Flights on a Swiss, Japanese, or Australian airlines
 Arriving or departing from airport other than PVD/BOS or home institution's local airport
 2 oneway plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
 Travel Maximum Contributions

 New England: $250
 Other contiguous US: $750
 Asia & Oceania: $2,000
 All other locations: $1,500
 Note these rates were updated in Spring 2022 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
 Reimbursement Requests

Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
 Reimbursement Tips

 Scanned original receipts are required for all expenses
 Airfare receipt must show full itinerary and payment
 ICERM does not offer per diem or meal reimbursement
 Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
 Keep all documentation until you receive your reimbursement!
 Reimbursement Timing

6  8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.
 Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.