## Programs & Events

##### Numerical PDEs: Analysis, Algorithms, and Data Challenges

Jan 29 - May 3, 2024

This Semester Program will bring together both leading experts and junior researchers to discuss the current state-of-the-art and emerging trends in computational PDEs. While there are scores of numerical methodologies designed for a wide variety of PDEs, the program will be designed around three workshops each centered around a specific theme: PDEs and Geometry, Nonlocal PDEs, and Numerical Analysis of Multiphysics problems. This grouping of topics embodies a broad representation of computational mathematics with each set possessing its own skill set of mathematical tools and viewpoints. Nonetheless, all workshops will have the common theme of using rigorous mathematical theory to develop and analyze the convergence and efficiency of numerical methods. The diversity of the workshop topics will bring together historically distinct groups of mathematicians to interact and facilitate new ideas and breakthroughs.

##### Organizing Committee

- Marta D'Elia
- Johnny Guzman
- Brittany Hamfeldt
- Michael Neilan
- Maxim Olshanskiy
- Sara Pollock
- Abner Salgado
- Valeria Simoncini

##### An ICERM Public Lecture: Mathematicians Helping Art Historians and Art Conservators

May 2, 2024

In recent years, mathematical algorithms have helped the art historians and art conservators putting together fragments of world-famous frescos by Andrea Mantegna classify certain paintings as “roll mates,” remove artifacts in preparation for a restoration campaign, and gain insight into the hidden paintings underneath visible ones.

This lecture will review these applications and give a glimpse into the mathematical aspects that make them possible.

##### Interacting Particle Systems: Analysis, Control, Learning and Computation

May 6 - 10, 2024

Systems of interacting particles or agents are studied across many scientific disciplines. They are used as effective models in a wide variety of sciences and applications, to represent the dynamics of particles in physics, cells in biology, people in urban mobility studies, but also, more abstractly in the context of mathematics, as sample particles in Monte Carlo simulations or parameters of neural networks in machine learning.

This workshop aims at bringing together researchers in analysis, computation, inference, control and applications, to facilitate cross-fertilization and collaborations.

##### Organizing Committee

- Jose Carrillo
- Katy Craig
- Massimo Fornasier
- Fei Lu
- Mauro Maggioni
- Kavita Ramanan

##### The Ceresa Cycle in Arithmetic and Geometry

May 13 - 17, 2024

In the 1980s, Ceresa exhibited one of the first naturally occurring examples of an algebraic cycle, the Ceresa cycle, which is in general homologically trivial but algebraically nontrivial. In the last few years, there has been a renewed interest in the Ceresa cycle, and other cycle classes associated to curves over arithmetically interesting fields, and their interactions with analytic, combinatorial, and arithmetic properties of those curves. We hope to capitalize on this momentum to bring together different communities of arithmetic geometers to fully explore explicit computations around the arithmetic and geometry of cycles when these various approaches are systematically combined.

##### Organizing Committee

- Daniel Corey
- Jordan Ellenberg
- Wanlin Li
- Daniel Litt
- Congling Qiu
- Padmavathi Srinivasan

##### 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

- Hoi Nguyen
- Oanh 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

##### 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

##### 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

##### 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