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 due-date 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 Cordero-Erausquin |
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 |
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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 |
self-affiliated |
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 Franche-Comté |
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 Minnesota-Twin 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 Urbana-Champaign 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 |
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PERSON |
AFFILIATION |
PERIOD OF STAY |
Luis Eduardo Aceves González
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Texas A&M University
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PERSON |
AFFILIATION |
PERIOD OF STAY |
Radoslaw Adamczak
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University of Warsaw
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PERSON |
AFFILIATION |
PERIOD OF STAY |
Gautam Aishwarya
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Technion - Israel Institute of Technology
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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 so-called 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 pseudo-random coefficients
Abstract: We study the local distribution of zeros of Taylor series for different classes of coefficients: random ones (independent, stationary, arithmetic random) and pseudo-random ones (exponential-polynomial, Rudin-Shapiro, Thue-Morse).
Tuesday, October 22, 2024 - from 2:45 to 4:00 pm
Title: Query lower bounds for log-concave 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 black-box 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 log-density 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 real-valued maximizers for all L^2-L^{2n} adjoint Fourier restriction inequalities on the unit sphere S^{d-1}\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 Euler--Lagrange equation being smooth, a fact of independent interest which we discuss. We further show that complex-valued 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 (Calderón-Zygmund theory, time-frequency 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 `low-degrees' 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 not-so-recent 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 input-coordinates. The proof goes by showing a large-deviation 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 two-sided non-asymptotic 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 0,1-coefficients.
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 Khinchine-Kahane 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 vector-valued 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 vector-valued, 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 Bohnenblust-Hille 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, vector-valued 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 Stevens-Davidowitz
- 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.