Dual Trimester Program: "Boolean Analysis in Computer Science"

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.

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
• Pandelis Dodos
• Michael Dymond
• Yuval Filmus
• Rachel Greenfeld
• James R. Lee
• Noam Lifshitz
• Manor Mendel
• Dan Mikulincer
• Assaf Naor
• Stefanie Petermichl
• Justin Salez
• Alex Samorodnitsky
• Błaźej Wróbel 
• 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
• Yuval Filmus
• Hamed Hatami
• Pooya Hatami
• Dmitry Krachun
• Noam Lifshitz
• Dan Mikulencer
• Shivam Nadimpalli

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:

• Tim Austin
• Thomas Courtade
• Rachel Greenfeld
• James Melbourne
• Chandra Nair
• Piotr Nayar
• Igal Sason
• Lisa Sauermann
• Joseph Slote
• Noah Stevens-Davidowitz
• Prasad Tetali
• 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.