The aim of this reunion meeting is to bring together the participants from the Fall 2020 program “advances in computational relativity” to work in a focused way towards solving the most pressing mathematical modeling and numerical simulation issues facing the gravitational wave community, and cultivating new subfields within mathematics that focus on important, pressing issues related to gravitational waves as well as providing mathematicians with new questions and problems to explore.

The areas of focus will be: (i) mathematical and computational approaches for solving the source-free Einstein field equations (a nonlinear, coupled, hyperbolic-elliptic PDE system) including fundamental aspects of general relativity or alternative theories of gravity, (ii) mathematical and computational approaches for the Einstein field equations with matter and magnetic fields, as well as the multi-scale, multi-physics modeling challenges for such problems, and (iii) methods for the detection,... (more)

The Numerical Relativity community summer school aims to provide graduate students and postdocs with the tools needed to master and understand cutting-edge numerical relativity simulations. Our one-week lecture series is geared toward providing a comprehensive introduction to the numerical study of gravitational waves, relativistic fluids, and modified gravity. In addition, we hope to strengthen the ties between different code communities and plan hand-on sessions and hackathons to foster interaction amongst the participants. There will also be the opportunity for students and postdocs to interact with senior participants and lecturers of the ICERM workshop program.

As part of your application, please briefly answer the following questions in your personal statement:

1. How does your research involve numerical relativity, or how do you plan to involve numerical relativity in the future?
2. Do you have experience in computational physics and/or numerical relativity? Which,... (more)

GirlsGetMath@ICERM is a five-day non-residential mathematics program that is open to high schoolers, regardless of gender, who live in or near greater Rhode Island and who will be entering the 10th or 11th grade in the fall of 2022.

GirlsGetMath occurs in an encouraging environment that builds young students' confidence in math and science.

GirlsGetMath expands participants' understanding and knowledge of mathematics through computations and experimentations.

GirlsGetMath provides expert mathematical training and mentoring.

GirlsGetMath@ICERM encourages 20-25 high schoolers to explore topics such as cryptography, the mathematics of voting, image processing, prime numbers and factoring, and fractals.

The goals of the program are:

• to show young adults that the study of mathematics can be exciting,... (more)

In recent years, the interaction between harmonic analysis and convex geometry has dramatically increased, which resulted in solutions to several long-standing problems. The program will bring together leading mathematicians in both areas, along with researchers working in related applied fields, for the first-ever long-term 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 computer-assisted 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).

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.

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.

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.

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)

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.

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)