Programs & Events
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-Carrión
- Francois Foucart
- Steven Liebling
- Carlos Palenzuela
- Lorenzo Pareschi
- David Radice
![Image for "Solving the Boltzmann Equation for Neutrino Transport in Relativistic Astrophysics"](https://app.icerm.brown.edu/img/468_image.jpg)
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
![Image for "Braids Reunion Workshop"](https://app.icerm.brown.edu/img/489_image.jpg)
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
![Image for "Empowering a Diverse Computational Mathematics Research Community"](https://app.icerm.brown.edu/img/465_image.jpg)
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
![Image for "Simulating Extreme Spacetimes with SpEC and SpECTRE"](https://app.icerm.brown.edu/img/467_image.jpg)
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
![Image for "Spectral Analysis of Schrödinger Operators"](https://app.icerm.brown.edu/img/490_image.png)
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
![Image for "Discrete Optimization: Mathematics, Algorithms, and Computation"](https://app.icerm.brown.edu/img/492_image.jpeg)
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, the discovery of new phenomena, and many new intriguing open questions. These connections were studied during the Fall 2022 Harmonic Analysis and Convexity Semester Program at ICERM. 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; the Bellman technique for extremal problems in harmonic analysis; convexity of solutions to HamiltonâJacobiâBellman equations; as well as numerical computations and computer-assisted proofs. The workshop will explore the use of computational methods for theoretical aspects, including optimal algorithms, as well as practical... (more)
Organizing Committee
- Javier Gomez Serrano
- Irina Holmes Fay
- Alexander Koldobskiy
- Sergei Treil
- Alexander Volberg
- Artem Zvavitch
![Image for "Harmonic Analysis and Convexity"](https://app.icerm.brown.edu/img/499_image.jpg)
Computational Learning for Model Reduction
Jan 6 - 10, 2025
Reduced order modeling (ROM) has become an important tool in computational science for accelerating model-based simulations, including those governed by parametrized differential equations. Through the approximation of high-dimensional features with low-dimensional representations, ROM consists of proven strategies that build accurate emulators for the field or response of computationally expensive high-fidelity models using only a fraction of the simulation cost. In forward prediction or outer loop design and optimization, ROM has the potential to substantially improve the efficiency of current simulation-based techniques.
While ROM has seen considerable success in numerous applications, it continues to attract active research and development. This workshop showcases emerging frontiers in ROM by bringing together researchers whose core interests lie in model reduction and approximation theory, but who have also explored and developed novel methods that utilize various aspects of... (more)
Organizing Committee
- Yanlai Chen
- Sigal Gottlieb
- Serkan Gugercin
- Fengyan Li
- Akil Narayan
![Image for "Computational Learning for Model Reduction"](https://app.icerm.brown.edu/img/528_image.png)
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
![Image for "Women in Mathematical Computational Biology"](https://app.icerm.brown.edu/img/518_image.jpg)
Patterns, Dynamics, and Data in Complex Systems
Jan 21 - 24, 2025
The study of pattern formation in biological, ecological, physical, and social systems involves a rich interplay between theory, modeling, and computation. Analytical approaches using the theory of dynamical systems and partial differential equations have made powerful contributions to our understanding of nonlinear waves and patterns, yet many open questions remain in the study of higher-dimensional patterns and complex spatiotemporal behaviors. These analytical tools go hand-in-hand with computational methods, including numerical continuation and agent-based simulations. Together these approaches also complement empirical techniques, particularly in studies of biological pattern formation, leading to experimentally testable predictions and quantitative summaries of data.
In recent years, new opportunities have emerged for pattern detection and identification in applications using data-scientific approaches. These applications include spiral waves in cardiac dynamics, vegetation... (more)
Organizing Committee
- Paul Carter
- Veronica Ciocanel
- Stephanie Dodson
- Anna Ghazaryan
- Alexandria Volkening
![Image for "Patterns, Dynamics, and Data in Complex Systems"](https://app.icerm.brown.edu/img/514_image.png)
Links in Dimensions 3 and 4
May 12 - 16, 2025
A topologist might hope that results in knot theory can always be extended to links. Decades of work in link theory show such extensions are not always straightforward and are, in fact, sometimes impossible. There are also properties and strategies unique to link theory. For all these reasons, link theory is a rich source of relationships to driving questions in the study of topology in dimensions 3 and 4. Among the most compelling are connections to 4-dimensional surgery, exotica in dimension 4, and the study of surfaces in 4-manifolds. Additionally, a vast number of open questions and unexplored topics remain within the confines of the theory in areas such as link concordance, link homotopy, and homology theories, including Heegaard Floer homology and Khovanov homology.
This workshop will bring together low-dimensional topologists of all backgrounds to further the general knowledge of link theory within the low-dimensional topology community, including techniques and tools used to... (more)
Organizing Committee
- Miriam Kuzbary
- Gage Martin
- Brendan Owens
- Ryan Stees
![Image for "Links in Dimensions 3 and 4"](https://app.icerm.brown.edu/img/532_image.png)
Scientific Machine Learning for Gravitational Wave Astronomy
Jun 2 - 6, 2025
The aim of this workshop is to bring together participants from computational mathematics and gravitational wave astronomy to tackle computational challenges in leveraging data-driven methods in key areas of gravitational wave data analysis in order to maximize the science output of the ongoing and upcoming observations. The areas of focus will be: (i) noise classification and detection, (ii) waveform modeling and uncertainty quantification, and (iii) source parameter and astrophysical population Bayesian inference.
The participants will develop and apply new mathematical and computational techniques including: (i) neural network classifiers for distinguishing signals from instrumental noise, (ii) generative machine learning models for simulating realizations of non-Gaussian and non-stationary stochastic processes, (iii) surrogate models including uncertainty quantification, (iv) stochastic sampling, neural posterior estimation leveraging deep neural networks with normalizing flows or... (more)
Organizing Committee
- Sarah Caudill
- Katerina Chatziioannou
- Maya Fishbach
- Brendan Keith
- Jess McIver
- Michael Puerrer
- Joshua Speagle
- Vijay Varma
![Image for "Scientific Machine Learning for Gravitational Wave Astronomy"](https://app.icerm.brown.edu/img/524_image.png)