## Programs & Events

##### 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 SchrÃ¶dinger 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 = âˆ’âˆ†+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 SchrÃ¶dinger operators, H = âˆ’âˆ† + 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 â€œdistorted 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

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

##### 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 Hamiltonâ€“Jacobiâ€“Bellman 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

##### 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 parametrizedÂ differential equations. Through the approximation of high-dimensional features with low-dimensional representations, ROM consists ofÂ 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 hasÂ the potential to substantially improve the efficiency of current simulation-based techniques.

While ROM hasÂ seen considerable success in numerous applications, it continues to attract active research and development. This workshop showcases emerging frontiers in ROMÂ 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
- Misha Kilmer
- Fengyan Li
- Akil Narayan

##### 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

##### 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

##### 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

##### 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

##### Algebraic Points on Curves

Jun 23 - 27, 2025

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

##### Organizing Committee

- Abbey Bourdon
- Robert Lemke Oliver
- Ari Shnidman
- Isabel Vogt
- David Zureick-Brown

##### LMFDB, Computation, and Number Theory (LuCaNT) 2025

Jul 7 - 11, 2025

This will be a one-week conference broadly focused on the topics of the LMFDB (http://lmfdb.org), mathematical databases, computation, and number theory. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.

The field of mathematical databases has emerged as an important area of research at the intersection of computer science and mathematics. It seeks to address questions that arise when organizing, storing, and providing access to mathematical knowledge in a structured manner. These databases are intended to be easily searchable and navigable, providing researchers, educators, and students with a convenient way to access mathematical content. There are many challenges in developing and maintaining mathematical databases, ranging from... (more)

##### Organizing Committee

- John Jones
- Jennifer Paulhus
- Andrew Sutherland
- John Voight

##### Innovative and Efficient Strategies for Stiff Differential Equations

Jul 21 - 25, 2025

A Â universal source of difficulty in the numerical solution of differential equations is stiffness,Â which may stem from multi-scale dynamics and means that straightforward explicit discretizations are very inefficient. Consequently, choosing how to deal with stiffness (usually through the selection of the time discretization method) is often the most impactful decision made while solving these problems; it can be the difference between complete intractability and rapid solution.

The most prominent and well-known effect of stiffness is its impact on numerical stability. Lesser-known but often equally important is the effect of order reduction, in which the convergence of the numerical solution is dramatically slowed compared to what classical numerical analysis would predict. Both of these issues can be dealt with through the use of implicit time discretizations. However, for large-scale applications (such as those coming from multi-dimensional PDE applications), such... (more)

##### Organizing Committee

- Sigal Gottlieb
- Zachary J Grant
- Jingwei Hu
- David Ketcheson