September 9  December 18, 2024
Organizers: Sergey Bobkov, Polona Durcik, Alexandros Eskenazis, Irina Holmes Fay, Paata Ivanisvili, Dor Minzer, and Alexander Volberg
Description: The trimester program aims to bring together experts, postdocs, and students in computer science and certain areas in mathematics (analysis, probability, and combinatorics) in order to learn about some challenging open problems recently raised in computer science, to use and invent necessary new tools and techniques in mathematics to solve these challenging problems, and vice versa to learn and further extend methods developed in computer science to develop new directions in mathematics motivated by questions in computer science. The core topics of the trimester program would be: learning theory, complexity of classical and quantum algorithms, vector valued functions on the hypercube, complex Hypercontractivity, polynomial inequalities on the hypercube, and discrete approximation theory on the hamming cube.
The duedate for application has expired and the application platform is closed.
PERSON 
AFFILIATION 
PERIOD OF STAY 
Gautam Aishwarya 
Technion  Israel Institute of Technology 
20.10.2024  18.12.2024 
Florent Baudier 
Texas A&M University 
06.10.2024  12.10.2024 
Lars Becker 
Universität Bonn 
09.09.2024  18.12.2024 
David Beltran 
Universitat de Valencia 
07.10.2024  19.10.2024 
Pierre Bizeul 
Technion 
03.11.2024  18.12.2024 
Sergey Bobkov 
University of Minnesota 
09.10.2024  18.12.2024 
Alexander Borichev 
Aix Marseille University 
17.10.2024  06.11.2024 
Xiaonan Chen 
University of California, Irvine 
03.11.2024  29.11.2024 
Valentina Ciccone 
Universität Bonn 
09.09.2024  18.12.2024 
Dario CorderoErausquin 
Sorbonne Université 
17.11.2024  22.11.2024 
Jaume de Dios Pont 
ETHZ 
12.10.2024  25.10.2024 
Oliver Dragičević 
University of Ljubljana 
02.11.2024  10.11.2024 
Devraj Duggal 
University of Minnesota 
13.09.2024  18.12.2024 
Polona Durcik 
Chapman University 
09.09.2024  18.10.202428.10.2024  18.12.2024 
Alexandros Eskenazis 
CNRS, Sorbonne Université 
09.09.2024  08.12.2024 
Francisco Escudero Gutiérrez 
Centrum Wiskunde & Informatica (CWI) and QuSoft 
15.09.2024  08.11.2024 
Yuval Filmus 
Technion  Israel Institute of Technology 
09.09.2024  22.09.202402.10.2024  27.10.2024 
Felipe Ferreira Goncalves 
IMPA 
03.11.2024  22.11.2024 
Miriam Gordin 
Princeton University 
10.09.2024  25.09.2024 
Marco Fraccaroli 
Basque Center for Applied Mathematics 
15.09.2024  18.10.2024 
Dmitry Grigoryev 
CNRS, Université de Lille 
09.09.2024  18.12.2024 
Kornélia Héra 
Universität Bonn 
07.10.2024  18.12.2024 
Tuomas Hytönen 
Aalto University 
15.09.2024  11.10.2024 
Alex Iosevich 
University of Rochester 
15.09.2024  28.09.2024 
Benjamin Jaye 
Georgia Tech 
30.11.2024  14.12.2024 
Nathan Keller 
Bar Ilan University 
09.09.2024  18.12.2024 
Guy Kindler 
The Hebrew University of Jerusalem 
09.09.2024  18.12.2024 
Ohad Klein 
The Hebrew University of Jerusalem 
03.11.2024  13.11.2024 
Egor Kosov 
Centre de Recerca Matemàtica 
18.11.2024  17.12.2024 
Vjekoslav Kovač 
University of Zagreb 
06.10.2024  11.10.2024 
Dmitrii Krachun 
Princeton University 
05.11.2024  09.11.2024 
Cosmas Kravaris 
Princeton University 
06.10.2024  19.10.2024 
Rafal Latala 
University of Warsaw 
09.09.2024  04.10.2024 
Noam Lifshitz 
The Hebrew University of Jerusalem 
09.09.2024  18.09.2024 
Galyna Livshyts 
Georgia Institute of Technology 
30.11.2024  14.12.2024 
Jose Ramon Madrid Padilla 
Virginia Polytechnic Institute and State University 
07.10.2024  15.10.2024 
Nathan Mehlhop 
Lousiana State University 
24.11.2024  18.12.2024 
James Melbourne 
Centro de Investigación en Matemáticas, A.C. 
13.09.2024  23.11.2024 
Manor Mendel 
Open University of Israel 

Kristina Oganesyan 
University of Ghent 
24.11.2024  18.12.2024 
Krzysztof Oleszkiewicz 
University of Warsaw 
09.09.2024  30.09.2024 
Diogo Oliveira e Silva 
Instituto Superior Técnico Lisboa 
09.09.2024  18.12.2024 
Emma Pollard 
Boise State University 
09.09.2024  06.12.2024 
Cyril Roberto 
Univesrité Paris Nanterre 
26.10.2024  09.11.2024 
Joris Roos 
University of Massachusetts Lowell 
09.09.2024  07.12.2024 
Miquel Saucedo 
Universitat Autònoma de Barcelona 
09.09.2024  18.12.2024 
Gideon Schechtman 
Weizmann Institute of Science 
06.10.2024  31.10.2024 
Rocco Servedio 
Columbia University 
22.09.2024  12.10.2024 
Lenka Slavíkóva 
Charles University 
06.10.2024  19.10.2024 
Joseph Slote 
California Institute of Technology 
02.10.2024  05.12.2024 
Rajula Srivastava 
Universität Bonn 
09.09.2024  18.12.2024 
Lauritz Streck 
University of Cambridge 
06.10.2024  29.11.2024 
Maude Szusterman 
Tel Aviv University 
15.09.2024  15.12.2024 
Sergey Tikhonov 
ICREA and CRM 
29.09.2024  12.10.202417.11.2024  30.11.2024 
Tomasz Tkocz 
Carnegie Mellon University 
17.11.2024  23.11.2024 
Gennady Uratsev 
University of Arkansas 
06.10.2024  18.12.2024 
Akanksha Vishwakarma Roos 
selfaffiliated 
17.11.2024  30.11.2024 
Alexander Volberg 
Michigan State University 
09.09.2024  18.12.2024 
Bruno Volzone  Politecnico di Milano 
10.10.2024  10.11.2024 
Blazej Wróbel 
Polish Academy of Sciences 
06.10.2024  16.10.2024 
Kenwen Wu 
University of California, Berkeley 
03.11.2024  16.11.2024 
Xudong Wu 
Nanjing University 
03.11.2024  29.11.2024 
Xinyuan Xie 
University of Califronia, Irvine 
15.09.2024  18.12.2024 
Quanhua Xu 
Université de FrancheComté 
07.10.2024 12.10.2024 
Haonan Zhang 
University of South Carolina 
04.10.2024  03.11.2024 
PERSON 
AFFILIATION 
PERIOD OF STAY 
Luis Eduardo Aceves González Lars Becker Valentina Ciccone Devraj Duggal Polona Durcik Francisco Escudero Gutiérrez Alexandros Eskenazis Yuval Filmus Marco Fraccaroli Li Gao Cristian Andres Gonzalez Riquelme Miriam Gordin Tuomas Hytönen Alex Iosevich Guy Kindler Rafal Latala Yongjin Lee Zane Li Noam Lifshitz James Melbourne Siddharth Mulherkar Giuseppe Negro Krzysztof Oleszkiewicz Diogo Oliveira e Silva Emma Pollard Joris Roos Miquel Saucedo Shobu Shiraki Joseph Slote Maud Szusterman Alexander Volberg Xinyuan Xie 
Texas A&M University Universität Bonn Universität Bonn University of MinnesotaTwin Cities Chapman University Centrum Wiskunde & Informatica (CWI) and QuSoft CNRS, Sorbonne Université Technion – Israel Institute of Technology BCAM  Basque Center for Applied Mathematics Wuhan University Instituto Superior Tecnico, Universidade de Lisboa Princeton University Aalto University University of Rochester The Hebrew University of Jerusalem University of Warsaw University of Illinois UrbanaChampaign North Carolina State University Hebrew university of Jerusalem Centro de Investigación en Matemáticas, A.C. University of California, Los Angeles Instituto Superior Técnico University of Warsaw Instituto Superior Técnico Boise State University University of Massachusetts Lowell Universitat Autònoma de Barcelona Instituto Superior Técnico California Institute of Technology Tel Aviv University Michigan State University University of California, Irvine 




PERSON 
AFFILIATION 
PERIOD OF STAY 
Luis Eduardo Aceves González

Texas A&M University







PERSON 
AFFILIATION 
PERIOD OF STAY 
Radoslaw Adamczak

University of Warsaw





PERSON 
AFFILIATION 
PERIOD OF STAY 
Gautam Aishwarya

Technion  Israel Institute of Technology





Thursday, October 31, 2024  from 2:45 to 4:00 pm
Title: Counting Lattice Points in Ellipsoids and the Central Limit Theorem for Quadratic Forms
Abstract: In this talk we review classical results on lattice point counting problems for ellipsoids and describe in dimensions five and larger some older and recent results on explicit error bounds. We outline their relation to corresponding errors estimates in the multivariate central limit theorem in Probability and the importance of gap principles for bounding Fourier integrals.
Tuesday, October 29, 2024  from 2:45 to 4:00 pm
Title: Testing monotonicity from quantum data
Abstract: This talk is about testing properties of Boolean functions from data, where it turns out quantum algorithms can have dramatic speedups. We will focus on monotonicity testing. Here, a classical algorithm given access only to uniformly random samples (x,f(x)) requires at least 2^Ω(sqrt(n)) samples to test if f is monotone. On the other hand, we will describe a quantum algorithm for monotonicity testing that requires only poly(n) quantum data, in the form of socalled function states: sum_x x,f(x) ⟩. We will also prove an n^3/2 lower bound for such quantum algorithms via a careful analysis of certain matrix ensembles. This is one of the first works to consider such lower bound arguments, and we welcome discussion and improvements to our techniques.  Based on joint work with Matthias Caro and Preksha Naik.
Thursday, October 24, 2024  from 2:15 to 3:30 pm
Title: The zero distribution for Taylor series with random and pseudorandom coefficients
Abstract: We study the local distribution of zeros of Taylor series for different classes of coefficients: random ones (independent, stationary, arithmetic random) and pseudorandom ones (exponentialpolynomial, RudinShapiro, ThueMorse).
Tuesday, October 22, 2024  from 2:45 to 4:00 pm
Title: Query lower bounds for logconcave sampling
Abstract: A central step in the implementation of probabilistic algorithms is that of sampling from known, complicated probability distributions: Given the density of a random variable (for example, as a blackbox function that one can query) generate samples from a random variable that has a distribution "similar enough" to the given one. Significant effort has been devoted to designing more and more efficient algorithms, ranging from relatively simple algorithms, such as rejection sampling, to increasingly sophisticated such as Langevin or diffusion based models. In this talk we will focus on the converse question: Finding universal complexity lower bounds that no algorithm can beat. We will do so in the case when the logdensity is a strictly concave smooth function. In this case we will be able to construct tight bounds in low dimension using a modification of Perron's sprouting construction for Kakeya sets. Based on joint work with Sinho Chewi, Jerry Li, Chen Lu and Shyam Narayanan.
Thursday, October 17, 2024  from 2:45 to 4:00 pm
Title: Global maximizers for spherical restriction
Abstract: We prove that constant functions are the unique realvalued maximizers for all L^2L^{2n} adjoint Fourier restriction inequalities on the unit sphere S^{d1}\subset R^d, d \in {3,4,5,6,7}, where n\geq 3 is an integer. The proof uses tools from probability theory, Lie theory, functional analysis, and the theory of special functions. It also relies on general solutions of the underlying EulerLagrange equation being smooth, a fact of independent interest which we discuss. We further show that complexvalued maximizers coincide with nonnegative maximizers multiplied by the character e^{i\xi\cdot\omega}, for some \xi, thereby extending previous work of Christ & Shao (2012) to arbitrary dimensions d\geq 2 and general even exponents.
Tuesday, October 15, 2024  from 2:45 to 4:00 pm
Title: The L^p theory for outer measure spaces
Abstract: The theory of L^p spaces for outer measures, or outer L^p spaces, was introduced by Do and Thiele, as tool in the proof of estimate for multilinear forms arising in the context of harmonic analysis (CalderónZygmund theory, timefrequency analysis). To this end, they developed the theory in the direction of the interpolation properties of the spaces, such as Hölder’s inequality and Marcinkiewicz interpolation. However, the outer L^p spaces can be defined in a broader generality of settings, for example extending the classical notion of mixed L^p spaces on the Cartesian product of measure spaces. In this talk we expose further developments in the theory of the outer L^p spaces, focusing on their Banach space properties, such as Fubini’s theorem, Köthe duality, and Minkowski’s inequality.
Thursday, October 3, 2024  from 2:45 to 4:00 pm
Title: Bounded functions with small tails are Juntas
Abstract: There seems to be some recent interest in structural results concerning functions whose Fourier transform is mostly supported on `lowdegrees' while their range is restricted to a specific set. This is at least partly motivated by applications to Theoretical Computer Science. In this talk I will go over a notsorecent result with this theme, which shows that a function f over the discrete hypercube whose Fourier representation is `mostly' of low degree and which obtains values in the (continuous) segment [1,1] must be close to a junta, namely it can be approximated by only looking at a constant number of inputcoordinates. The proof goes by showing a largedeviation lower bound for low degree functions that uses some tricks that may be of interest. If time permits I may also talk about some improvements to our result made by O’Donnell and Zhao. Joint work with Irit Dinur, Ehud Friedgut, and Ryan O'Donnell.
Tuesday, October 1, 2024  from 2:45 to 4:00 pm
Title: Weighted inequalities for the Fourier transform
Abstract: In this talk we discuss inequalities for the Fourier transform between weighted Lebesgue spaces and their connection with an interpolation technique due to Calderón.
Thursday, September 26, 2024  from 2:45 to 4:00 pm
Title: On the spectral norm of Rademacher matrices
Abstract: We will discuss twosided nonasymptotic bounds for the mean spectral norm of nonhomogenous weighted Rademacher matrices. We will present a lower bound and show that it may be reversed up to log log log n factor for arbitrary n×n Rademacher matrices. Moreover, the triple logarithm may be eliminated for matrices with 0,1coefficients.
Tuesday, September 24, 2024  from 2:45 to 4 pm
Title: On Spherical Covariance Representations
Abstract: We first motivate the study of covariance representations by surveying preceding results in the Gaussian space. Their spherical counterparts are then derived thereby allowing applications to the spherical concentration phenomenon. The applications include second order concentration inequalities. The talk is based on joint work with Sergey Bobkov.
Thursday, September 12, 2024  from 2:45 to 4:00 pm
Title: On the asymptotics of the optimal constants in the KhinchineKahane inequality
Abstract: Let us consider a sequence of indepenedent symmetric +/1 random variables, often called the Rademacher system. A linear combination of these random variables is a real random variable called a (weighted) Rademacher sum. There are also vectorvalued Rademacher sums, in which the real coefficients in the linear combination are replaced by vectors from some normed linear space. Rademacher sums, both real and vectorvalued, have been studied for more than 100 years now. In the talk, classical moment inequalities for Rademacher sums will be described, going back to Khinchine (1923) and Kahane (1964), as well as some more recent results.
Video
September 16  20, 2024
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sergey Bobkov, Polona Durcik, Alexandros Eskenazis, Irina Holmes Fay, Paata Ivanisvili, Dor Minzer, and Alexander Volberg
Lecturers:
 Alexandros Eskenazis
 Yuval Filmus
 Alex Iosevich
 Noam Lifshitz
 Alexander Volberg
Description: The interaction between learning theory and harmonic analysis was emphasized by mathematics of quantum computing. One of the outstanding open problems in this area concerns the sharp estimates in BohnenblustHille inequality that generalizes a celebrated Littlewood’s lemma.
How to learn (with small error and with large probability) a complicated function or a very large matrix in a relatively small number of random (quantum) queries? Of course, there should be some Fourier type restrictions on a function (a matrix) to have a reasonable answer to this.
The “classical” way of learning (Boolean) functions comes from very sophisticated extensions of theorems of Kahn—Kalai—Linial type. In those results the interplay between maximal influence and heavy Fourier tails is the main technique. Maximal influence should be large if the `tail’ is small. However, recently another approach that is hinged on Bohnenblust—Hille inequality appeared. The school will cover the classical maximal influence approach to `probably approximately correct' (PAC) learning as well as the recent achievements using Bohnenblust—Hille inequality and its quantum counterpart.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this school, are eligible to attend this event.
October 7  11, 2024
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sergey Bobkov, Polona Durcik, Alexandros Eskenazis, Irina Holmes Fay, Paata Ivanisvili, Dor Minzer, and Alexander Volberg
Lecturers:
 Florent Baudier
 David Beltran
 Pandelis Dodos
 Polona Durcik
 Michael Dymond
 Yuval Filmus
 Li Gao
 Tuomas Hytönen
 Guy Kindler
 Vjekoslav Kovač
 Jose Ramon Madrid Padilla
 Stefanie Petermichl
 Joris Roos
 Justin Salez
 Rocco Servedio
 Lenka Slavíková
 Błażej Wróbel
 Quanhua Xu
 Haonan Zhang
Analytic questions of a discrete nature are ubiquitous in many areas of mathematics and theoretical computer science. The purpose of this conference is to bring together a diverse group of experts working, broadly, on Discrete Analysis with particular emphasis on questions having a geometric component. The topics will include Boolean analysis, vectorvalued harmonic analysis, metric embeddings, geometry of graphs and groups, and aspects of discrete probability and theoretical computer science.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.
November 4  8, 2024
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sergey Bobkov, Polona Durcik, Alexandros Eskenazis, Irina Holmes Fay, Paata Ivanisvili, Dor Minzer, Joseph Slote, and Alexander Volberg
Lecturers:
 Srinivasan Arunachalam
 Francisco Escudero Gutierrez
 Tom Gur (online)
 Hamed Hatami
 Pooya Hatami
 Ohad Klein
 Dmitry Krachun
 Avichai Marmor (online)
 Dan Mikulincer (online)
 Shivam Nadimpalli
 Joris Roos
 Ohad Sheinfeld
 Kewen Wu
Harmonic analysis on the hypercube has long found exciting applications in theoretical computer science, in areas as diverse as learning theory, voting theory, and computational complexity theory. And TCS has also inspired challenging new questions in analysis, often leading to new perspectives on familiar topics. Indeed, this connection is only deepening as quantum computing, machine learning, and other areas of TCS expand to spaces beyond the hypercube. Talks in this workshop will focus on such connections recently uncovered, techniques in use today, and conjectures old and new. We hope it can also be an invitation to the topic for a harmonic analysis audience, thanks to additional introductory talks scheduled.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.
November 18  22, 2024
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Sergey Bobkov, Polona Durcik, Alexandros Eskenazis, Steven Heilman, Irina Holmes Fay, Paata Ivanisvili, Dor Minzer, and Alexander Volberg
Lecturers:
 Thomas Courtade
 James Melbourne
 Chandra Nair
 Piotr Nayar
 Igal Sason
 Lisa Sauermann
 Joseph Slote
 Noah StevensDavidowitz
 Sergey Tikhonov
 Tomasz Tkocz
This workshop brings together leading experts in Boolean analysis, information theory, and lattices to explore the forefront of these disciplines through the talks and discussions about intriguing open problems, recent resolutions, and the evolution of innovative ideas, approaches, and techniques.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.