## Programs & Events

##### Random Matrices and Applications

May 20 - 22, 2024

This workshop focuses on the role of random matrices in data science, machine learning, and theoretical computer science.

Playing a significant role in modern data science, random matrices provide an elegant way to represent both (a) the data and (b) the way we process it. To give an example of (a), the classical model of high-dimensional data is a set of points drawn from a certain distribution in a high-dimensional space which can be represented as a random matrix. An even more natural example is that most data in practice is noisy, so it can be represented as a deterministic matrix plus a random noise, which is a random matrix with a non-zero mean. An example of (b) is data compression, which can be realized by applying a random matrix of smaller sizes to the data in (a), thereby reducing its dimensions. Another example is data completion, where we need to reconstruct data (in the form of a matrix) from a random sub-matrix, given that the original matrix satisfies certain... (more)

##### Organizing Committee

- Oanh Nguyen
- Hoi Nguyen
- Konstantin Tikhomirov
- Roman Vershynin
- Van Vu

##### Recent Progress on Optimal Point Distributions and Related Fields

Jun 3 - 7, 2024

Certain problems in mathematics, physics, and engineering are formulated as minimizing cost functions that take as input a set of points on a compact manifold. In applied and computational harmonic analysis one is usually interested in finding tight frames and equiangular tight frames, which are respectively minimizers of different cost functions. In quantum information theory, the study of SIC-POVMS is equivalent to the existence of a point configuration made of antipodal points on a complex sphere. There seems to be a phenomenon where highly symmetric configurations are optimizers and optimizers often exhibit (partial) symmetries. The theory of spherical designs in combinatorics and discrete geometry with applications in approximation theory in the form of cubature formulas is deeply related to point configurations and distributions. Training a neural network involves minimizing a cost function relating to the desired task; it was recently discovered that doing so often results in... (more)

##### Organizing Committee

- Dmitriy Bilyk
- Xuemei Chen
- Emily King
- Dustin Mixon
- Kasso Okoudjou

##### Roots of Unity

Jun 10 - 14, 2024

The transition to independent learning and research is a crucial and often jarring point in every graduate student's career. This transition is even more difficult for students from marginalized groups, who often have smaller support systems and may face an actively unsupportive environment at their institution. The goal of this workshop is to support, mentor, and guide students at this crucial stage in their career.

During the workshop, mentors will guide the student participants through the (often very daunting!) experience of trying to read a paper without being an expert in the area. The participants will be broken into small working groups, each focused on a recent paper in their area of interest. Each group will be assisted throughout the week by mentors, both early career mathematicians (late stage graduate students or postdocs) and faculty members. The topics covered in this workshop will be Number Theory, Combinatorics, Commutative Algebra, and Geometry/Topology.

The... (more)

##### Organizing Committee

- Christine Berkesch
- Michelle Manes
- Priyam Patel
- Candice Price
- Bianca Viray

##### Summer@ICERM 2024: Mathematical Models to Predict, Prepare, and Prevent

Jun 10 - Aug 2, 2024

Mathematical modeling allows researchers to address questions and test hypotheses that may not be feasible to study otherwise. The Summer@ICERM 2024 faculty advisors will present a variety of research projects centered around approaches to using mathematical modeling for making predictions and determining associated preparations and necessary preventions in the fields of epidemiology, precision nutrition, and sports analytics. Faculty will guide the development of appropriate models and computational tools that can aid in answering fundamental questions in these fields.

During the eight-week program, students will be introduced to the research topics through interactive lectures. Afterward, students will work on their projects in assigned groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily; give regular talks about their findings; attend mini-courses, guest talks, and professional development seminars; and practice coding.... (more)

##### Organizing Committee

- Amanda Harsy Ramsay
- Adam Schultze
- Brittany Stephenson
- Cara Sulyok

##### Queer in Computational and Applied Mathematics (QCAM)

Jun 24 - 28, 2024

The Queer in Computational and Applied Mathematics (QCAM) workshop will be the first workshop to celebrate research advances and foster stronger research networks of LGBTQIA+ mathematicians specializing in computational and applied mathematics. Goals of QCAM are to support LGBTQIA+ academics through mentoring and research opportunities, as well as providing a safe space for researchers across the subfields of computational and applied mathematics to connect, collaborate, and build support networks within the field. In addition, QCAM intends to address issues of diversity, equity, and inclusion in mathematics pertaining to LGBTQIA+ people, especially those with intersectional identities. This conference will be open to all and will ideally engage the wider mathematical audience of LGBTQIA+ allies to develop a community of support.

The scientific program will have invited speakers and contributed sessions that span the field of computational mathematics, with a planned focus on... (more)

##### Organizing Committee

- Rowan Barker-Clarke
- Rustum Choksi
- Alexander Hoover
- Hermie Monterde
- Michael Robert
- Colton Sawyer
- Becca Thomases

##### Solving the Boltzmann Equation for Neutrino Transport in Relativistic Astrophysics

Jul 8 - 12, 2024

The spectacular observation of gravitational waves from a binary neutron star merger by the LIGO-Virgo Collaboration (GW170817), and a successful follow-up campaign by nearly every electromagnetic telescope ushered in this new era of multi-messenger astrophysics. Much of the understanding of such events arises from numerical modeling. An important part of this modeling is the inclusion in simulations of neutrino transport, as described by Boltzmann's equation. Because of inherent computational resource limits and given the high cost of the transport equations and the complexity of neutrino-matter interactions, there is a trade-off between computational cost and physical realism in all simulations. This workshop covers various approaches to solving the neutrino transport problem in compact object mergers and core-collapse supernovae, including Monte Carlo methods, moment truncation schemes, and other techniques.

##### Organizing Committee

- Isabel Cordero-Carrion
- Francois Foucart
- Steven Liebling
- Carlos Palenzuela
- Lorenzo Pareschi
- David Radice

##### Braids Reunion Workshop

Jul 15 - 19, 2024

This conference is intended to celebrate and amplify the mathematics of the Braids Semester Program at ICERM in 2022. The aim is to bring together mathematicians who participated in the program, or whose research interacts with its themes, for an event that will rekindle the interactions between fields that the subject of braid groups naturally stimulated during the semester. A central goal is to showcase work that resulted from the semester's activities, and a further goal is to incorporate new participants whose research has fruitful connections with researchers who were a part of the semester.

The workshop will have a variety of activities, with research talks, problem sessions, and dedicated work time for collaboration. Special emphasis will be placed on highlighting the work of early-career mathematicians and providing space to develop new collaborations.

##### Organizing Committee

- Matthew Hedden
- Matt Hogancamp
- Jonathan Johnson
- Miriam Kuzbary
- Nancy Scherich

##### Empowering a Diverse Computational Mathematics Research Community

Jul 22 - Aug 2, 2024

The goal of this two-week research and professional development workshop is to support the retention and success of junior and mid-career computational mathematicians who are from groups that are underrepresented in the field. Participants will forge strong collaborations in mentored research groups and engage in professional development via no-lead learning communities. The larger goal of the workshop is to form a positive, diverse community of researchers who are committed to supporting each otherâ€™s professional and scholarly growth.

In research teams led by experienced mentors, participants will be introduced to cutting-edge opportunities in numerical analysis and scientific computing, and will actively work on and contribute to a research project with their team. The supportive formal and informal mentoring will help participants grow their scientific and collaborative skills. In addition, the collaborative learning communities will provide the participants with a forum for... (more)

##### Organizing Committee

- Vrushali Bokil
- Sigal Gottlieb
- Fengyan Li
- Suzanne Weekes

##### Simulating Extreme Spacetimes with SpEC and SpECTRE

Aug 5 - 9, 2024

A new era of astronomical observation was announced in 2016 when the first-ever detection of gravitational waves from a binary black hole system occurred. Gravitational waves encode detailed information about the astrophysical systems they emerge from and complement what can be learned through traditional light-based observation.

Gravitational wave science requires high-fidelity numerical simulations of the expected merger events. The Simulating eXtreme Spacetimes (SXS) collaboration has managed the development of two distinct codes for this purpose: (i) the Spectral Einstein Code (SpEC) based on pseudospectral methods, and (ii) an open-source code SpECTRE, an hp-adaptive discontinuous Galerkin scheme that also includes a sub-cell finite volume scheme in regions of strong shock formation that is ideally suited for multi-scale, multi-physics problems. SpECTRE targets problems in multi-messenger astrophysics, including neutron star mergers, core-collapse supernovae, and gamma-ray... (more)

##### Organizing Committee

- Katerina Chatziioannou
- Nils Deppe
- Scott Field
- Lawrence Kidder
- Geoffrey Lovelace
- Mark Scheel
- Leo Stein
- Saul Teukolsky
- Nils Vu

##### GirlsGetMath@ICERM: Summer Math Camp for High School Students

Aug 12 - 16, 2024

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 2024.

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, fractals, matrices, vectors, and data science.

The goals of the program are:

- to show young adults that the study... (more)

##### Organizing Committee

- Amalia Culiuc
- Anarina Murillo

##### Spectral Analysis of Schrödinger Operators

Aug 19 - 23, 2024

The central theme of this workshop is the analysis and computation of SchrÃ¶dinger operators and applications to nonlinear problems in several areas of Mathematical Physics, Analysis of Partial Differential Equations, Quantum Chemistry, and more. The simplest, most basic example, of such an operator is of the form H = âˆ’âˆ†+V on an appropriate Hilbert space, and their Dirac analogues.

Many problems in Quantum Physics and Chemistry require a precise understanding of the spectra of SchrÃ¶dinger operators, H = âˆ’âˆ† + V, for various classes of potentials V (x), and in various regimes, especially in the semi-classical and adiabatic ones. The analysis entails determining eigenvalues and eigenvectors and more generally the evolution generated by H, the study of wave operators, and of the â€œdistorted Fourier transformâ€ and its mapping properties. All of these can be interpreted as diagonalization procedures which are especially delicate for non-selfadjoint operators that can arise as... (more)

##### Organizing Committee

- Jianfeng Lu
- Benoit Pausader
- Fabio Pusateri
- Wilhelm Schlag
- Israel Michael Sigal
- Ebru Toprak

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

Aug 26 - 30, 2024

This reunion workshop will bring together participants from ICERM's Spring 2023 Discrete Optimization Semester Program and researchers with related interests. Participants will discuss recent advances and catalyze new collaborations related to combinatorial optimization and mixed-integer linear and non-linear optimization.

The Spring 2023 Semester Program at ICERM explored unsolved fundamental questions in discrete optimization and connected areas of mathematics, computer science, and data analytics.

##### Organizing Committee

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