Programs & Events
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
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
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 otherâs 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
Spectral Analysis of Schrödinger Operators
Aug 19 - 23, 2024
The central theme of this workshop is the analysis and computation of Schrödinger 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 = ââ+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 Schrödinger operators, H = ââ + 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 âdistorted 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
The goal of this reunion meeting is to bring together the participants from the spring 2023 program “Discrete Optimization: Mathematics, Algorithms, and Computation” uniting experts in combinatorial optimization, mixed-integer linear and non-linear optimization, with the aim of having an environment to discuss the latest advances and to catalyze new collaborations.
Organizing Committee
- Jesús De Loera
- Antoine Deza
- Marcia Fampa
- Volker Kaibel
- Jon Lee
- Laura Sanità
Harmonic Analysis and Convexity
Dec 9 - 13, 2024
In recent years, there has been a significant increase in the interaction between harmonic analysis and convex geometry, leading to solutions for several longstanding open problems, discovery of new phenomena, as well as many new intriguing open questions. These connections were studied during the Fall 2022 ICERM semester on “Harmonic Analysis and Convexity”. The objective of this workshop is to revisit and review the results produced during the semester and the subsequent year.
The primary areas of focus for the workshop will encompass: The Fourier approach to Geometric Tomography; Volume and Duality; Bellman technique for extremal problems in harmonic analysis; Convexity of solutions to Hamilton–Jacobi–Bellman equations; as well as numerical computations and computer-assisted proofs: Exploring the use of computational methods for theoretical aspects, including optimal algorithms, as well as practical implementation.
Organizing Committee
- Javier Gomez Serrano
- Irina Holmes Fay
- Alexander Koldobskiy
- Sergei Treil
- Alexander Volberg
- Artem Zvavitch
Women in Mathematical Computational Biology
Jan 13 - 17, 2025
Biological systems are typically highly interconnected and complex. With technological advances, it is possible to collect massive amounts of data from these systems, but it is not always clear how to organize the information to draw conclusions and make predictions. In such cases, mathematical formulations are powerful tools allowing researchers to frame questions, explore patterns, and synthesize information. Augmenting and expanding computational algorithms, machine learning algorithms, and data science techniques is necessary to keep pace with the complexity of the models needed for predictive modeling. The interdisciplinary nature of mathematical biology requires a variety of skills and facilitating interaction among research groups and institutions is important to moving the discipline forward.
The workshop aims to build research collaboration among researchers in mathematical biology. Participants will spend a week making significant progress on a research project and foster... (more)
Organizing Committee
- Ashlee Ford Versypt
- Rebecca SEgal
- Suzanne Sindi