## Programs & Events

##### Opening Event: Harmonic Analysis and Convexity

Sep 12 - 16, 2022

The interaction between harmonic analysis and convex geometry has been strong for a long time. However, in recent years new methods were developed that caused a steep rise in productivity of this cooperation. This workshop will include series of lectures introducing the participants to Fourier methods in geometric tomography, Bellman techniques for extremal problems of harmonic analysis, volume and duality, and computational aspects of the subject.

##### Harmonic Analysis Methods in Geometric Tomography

Sep 26 - 30, 2022

Geometric tomography is the area of Mathematics dealing with the retrieval of information about solid objects based on the size of their sections or projections, or other lower dimensional data. Results from this area often find real-world applications in science and engineering.

In recent years geometric tomography has seen a rapid period of growth due to many exciting developments in harmonic analysis. The goal of the present workshop is to bring together specialists in geometric tomography, harmonic analysis, and related areas to discuss important advances and share new ideas.

##### Organizing Committee

- Maria Alfonseca-Cubero
- Dmitry Ryabogin
- Vladyslav Yaskin
- Artem Zvavitch

##### Probabilistic Methods in Geometry and Analysis

Oct 17 - 21, 2022

Probabilistic methods have long played an important role in various areas of geometry and analysis. Notable applications of probabilistic methods appear, for example, in geometric functional analysis, in harmonic analysis, and in discrete mathematics. Conversely, mathematical phenomena of fundamentally geometric and analytic origin, such as the concentration of measure phenomenon, play a central role in modern probability theory. Novel interactions between probability, geometry and analysis continue to drive important innovations in these fields.

The aim of this workshop is to bring together a diverse range of experts from probability, geometry, and analysis, in order to promote further dialogue between these fields and to catalyze the creation of new interactions.

##### Organizing Committee

- Shiri Artstein-Avidan
- Ronen Eldan
- Bo'az Klartag
- Mark Rudelson
- Ramon van Handel

##### Extremal Problems in Harmonic Analysis, Convexity, and Bellman Functions

Nov 28 - Dec 2, 2022

Extremal problems in harmonic analysis recently acquired prominence in questions ranging from optimizers in Fourier restriction results to sharp geometric inequalities to sharp estimates of various singular operators of Calderón–Zygmund type. Sharp inequalities and their stability versions reveal new connections between harmonic analysis, geometric measure theory, additive combinatorics, and stochastic optimal control. There are many examples of sharp estimates by stochastic control approach and the use of special types of convexity and Monge–Ampére equation. There are interesting examples of using the computational tools in proving sharp geometric inequalities for martingales and on Hamming cube and for Fourier restriction inequalities.

##### Organizing Committee

- Irina Holmes Fay
- Alexander Volberg

##### Current Themes of Discrete Optimization: Boot-camp for early-career researchers

Jan 30 - Feb 3, 2023

Discrete optimization is a vibrant area of computational mathematics devoted to efficiently finding optimal solutions among a finite or countable set of possible feasible solutions.

This Boot-camp will be the opening event of the semester and it aims to attract young researchers to this topic.The four mini courses, presented by four speakers known for high-quality exposition, will cover various subjects such as new advances in approximation algorithms, mixed integer non-linear programming, algebraic techniques in optimization and applications to social sciences. The event provides a taste of the many methods and hot topics to be discussed during the semester. The event will also include a poster session to allow graduate students to present their work and other community building activities.

##### Organizing Committee

- Jesús De Loera
- Antoine Deza
- Marcia Fampa
- Volker Kaibel
- Jon Lee
- Laura Sanità

##### Discrete Optimization: Mathematics, Algorithms, and Computation

Jan 30 - May 5, 2023

Discrete optimization is a vibrant area of computational mathematics devoted to efficiently finding optimal solutions among a finite or countable set of possible feasible solutions.

A famous and classical example of a problem in discrete optimization is the *traveling salesperson problem*: For given cities and distances of traveling from one city to another, we seek to find the shortest route that visits each city once and returns to the starting city. Discrete optimization problems naturally arise in many kinds of applications including bioinformatics, telecommunications network design, airline scheduling, circuit design, and efficient resource allocation. The field also connects to a variety of areas in mathematics, computer science, and data analytics including approximation algorithms, convex and tropical geometry, number theory, real algebraic geometry, parameterized complexity theory, quantum computing, machine learning, and mathematical logic.

The semester program... (more)

##### Organizing Committee

- Jesús De Loera
- Antoine Deza
- Marcia Fampa
- Volker Kaibel
- Jon Lee
- Laura Sanità

##### Linear and Non-Linear Mixed Integer Optimization

Feb 27 - Mar 3, 2023

Mixed-Integer Linear Optimization has been an important topic in optimization theory and applications since the 1960s. As a mathematical subject, it is a rich combination of aspects of geometry, algebra, number theory, and combinatorics. The interplay between the mathematics, modeling, and algorithmics makes it a deep and fascinating subject of applied mathematics, which has had an enormous impact on real-world applications. But many physical systems have nonlinear aspects and further discrete design aspects. So we are naturally led to the paradigm of Mixed-Integer Non-Linear Optimization. But the mathematics and effective algorithmics of this subject are far more daunting than the linear case, and so there is a focus on broad sub-classes where results from the linear world can be lifted up. Furthermore, effective modeling techniques are much more subtle and are intertwined with state-of-the-art algorithmics and software which are rapidly evolving.

This workshop focuses on the latest... (more)

##### Organizing Committee

- Pietro Belotti
- Marcia Fampa
- Fatma Kılınç-Karzan
- Jon Lee
- Nick Sahinidis
- Yuan Zhou

##### Combinatorics and Optimization

Mar 27 - 31, 2023

Combinatorial optimization is an active research field in mathematics, with an immense range of applications. This workshop will bring together researchers and leading experts interested in the mathematical foundations of combinatorial optimization algorithms to discuss new tools and methods, in particular regarding the use of algebraic, analytical, and geometric techniques. Special emphasis will be given on polyhedral methods, since they are at the core of several groundbreaking combinatorial optimization results developed in recent years.

##### Organizing Committee

- Jesús De Loera
- Antoine Deza
- Volker Kaibel
- Britta Peis
- Laura Sanità
- Mohit Singh

##### Trends in Computational Discrete Optimization

Apr 24 - 28, 2023

The aim of this workshop is to discuss many exciting recent developments on the computational side of discrete optimization. The workshop has three main themes. The first theme is that of commercial and academic/open-source solvers that have allowed the solution of very large-scale problems, and of recent developments in exact solvers that have allowed for proofs of results in logic, knot theory, and combinatorics. The second theme is the interaction between optimization and machine learning: these two areas complement each other in several ways. The third theme is quantum computing and unconventional computing architectures: quantum computing has been used to tackle combinatorial optimization problems, and quantum algorithms exist for other related optimization problems such as linear and semidefinite relaxations.

##### Organizing Committee

- Amitabh Basu
- Antoine Deza
- Swati Gupta
- Volker Kaibel
- Giacomo Nannicini
- Sebastian Pokutta
- David Williamson

##### Dynamics, Rigidity and Arithmetic in Hyperbolic Geometry

May 15 - 19, 2023

Coming Soon!

##### Organizing Committee

- David Fisher
- Dubi Kelmer
- Hee Oh
- Alan Reid

##### Mathematical and Scientific Machine Learning

Jun 5 - 9, 2023

Coming Soon!