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)

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)

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)

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)

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.

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.

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, they continue 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

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)

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)