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.

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.

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 other’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)

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)

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)

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 = −∆+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 = −∆ + 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 “distorted Fourier transform” 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)

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.

A fundamental challenge that spans nearly all areas of evolutionary biology is the development of effective techniques for analyzing the unprecedented amount of genomic data that has become readily available within the last decade. Such data present specific challenges for the area of phylogenetic inference, which is concerned with estimating the evolutionary relationships among collections of species, populations, or sequences. These challenges include development of evolutionary models that are sufficiently complex to be biologically realistic while remaining computationally tractable; deriving and implementing algorithms to efficiently estimate phylogenetic relationships that use models whose theoretical properties are well-understood and therefore interpretable; and devising ways to scale novel methodology developed to handle datasets that are increasingly large and complex.

This semester program brings together mathematicians, statisticians, computer scientists, and experimental... (more)

The program will explore different perspectives on uncertainty quantification, efficient simulation, and the analysis of complex stochastic systems. The topics covered will include exciting recent developments on efficient methods for approximating quasi-stationary distributions, simulation of equilibrium distributions, information divergences in sensitivity analysis of rare events, large deviations methods for efficient importance sampling, accelerated Monte Carlo via nonlinear PDE, and complex probabilistic models including reflected diffusions and high-dimensional dynamics arising in chemistry and physics.

Computational phylogenetic methods have become essential tools for understanding the evolutionary relationships that underlie much life science research. Motivated by biological questions and insights, built on a broad spectrum of mathematical and statistical ideas and approaches, and implemented through novel and sophisticated algorithmic design, their development draws from multiple fields. Bringing together researchers spanning disciplinary perspectives and techniques, this workshop will present a diverse sample of work addressing current challenges in phylogenetics, with an eye toward future progress.

The unprecedented amount of genomic data that has become readily available presents specific challenges for the area of phylogenetic inference, which is concerned with estimating the evolutionary relationships among collections of species, populations, or sequences. These challenges include development of evolutionary models that are sufficiently complex to be biologically realistic while remaining computationally tractable; deriving and implementing algorithms to efficiently estimate phylogenetic relationships that use models whose theoretical properties are well-understood and therefore interpretable; and devising ways to scale novel methodology developed to handle datasets that are increasingly large and complex.

This workshop focuses on statistical modeling and the scaling of phylogenetic methods. Topics will include modeling (e.g. multispecies coalescent model with extension to networks; diversification models) and inference with speed to scale to genomic datasets,... (more)