## Programs & Events

##### 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

##### Geometry of Materials, Packings and Rigid Frameworks

Jan 29 - May 2, 2025

Given an incidence structure, one may model a variety of geometric problems. This Semester Program will revolve around two fundamental examples and their applications to modern challenges in the study, analysis, and design of materials. (1) Packings and patterns of circles where the underlying combinatorics are mixed with advanced geometric concepts and strong links are made to discrete differential geometry. (2) The rigidity and flexibility of bar-joint structures where real algebraic geometry is intertwined with sparse graph theory and matroidal techniques. A prime objective of the program is to advance the applicability of these topics to fundamental applications, most notably in statistical physics and materials science.

The program will integrate diverse fields of discrete mathematics, geometry, theoretical computer science, mathematical biology, and statistical and soft matter physics. Various workshops will be designed to attract both theoretical and applied practitioners and... (more)

##### Organizing Committee

- Alexander Bobenko
- John Bowers
- Philip Bowers
- Robert Connelly
- Steven Gortler
- Miranda Holmes-Cerfon
- Sabetta Matsumoto
- Anthony Nixon
- Meera Sitharam

##### Circle Packings, Minimal Surfaces, and Discrete Differential Geometry

Feb 10 - 14, 2025

This workshop brings together researchers from three distinct streams of mathematics: the classical rigidity theory of bar-joint and tensegrity frameworks in combinatorics and discrete geometry; the theory of generalized circle packing that arose from the study of 3-manifolds in geometric topology, extending to sphere packing and jamming; and discrete differential geometry. A scattering of results in recent years has started to forge connections among these fields.

Since the discovery that circle packings from triangulations could be used as a scheme for approximating the Riemann mapping of a simply connected proper domain in the plane to the unit disk, the theory of circle packing has enjoyed enormous development and has found widespread theoretical and practical applications. In the theoretical realm, circle packing provides a discrete analytic function theory that is faithful to its continuous cousin and it is closely associated with studies of hyperbolic and projective polyhedra.... (more)

##### Organizing Committee

- Alexander Bobenko
- Philip Bowers
- John Bowers
- Steven Gortler
- Meera Sitharam

##### Matroids, Rigidity, and Algebraic Statistics

Mar 17 - 21, 2025

This workshop will be centered on recent advances in graph rigidity and interactions between rigidity, algebraic statistics, and matroid theory. Three major advances are the recent resolution of the matroid maximality conjecture, the newly developed link to maximum likelihood estimation in Gaussian graphical models, and the recent positive resolution of Lovasz and Yemini's connectivity conjecture for generic rigidity. The workshop will showcase a diverse sample of current work addressing fundamental problems in graph rigidity, algebraic matroids, and algebraic statistics.

##### Organizing Committee

- Robert Connelly
- Elizabeth Gross
- Tibor Jordán
- Anthony Nixon
- Shin-ichi Tanigawa

##### Geometry of Materials

Apr 7 - 11, 2025

The geometric arrangement of a materialâ€™s constituents plays an important role in governing its behaviour. Concepts from discrete mathematics to describe these geometric arrangements, including notions of rigidity and flexibility, can bring fundamental insight into how a material might respond to stress, be designed, be reconfigured, etc. This workshop aims to build connections between the field of mathematical rigidity theory, and other areas of applied mathematics, science and engineering where such ideas might be used.

Rigidity and flexibility form a dichotomy: either a systemâ€™s constraints allow for a non-trivial deformation under an external load or they donâ€™t. However, there is a long history, dating to before the Industrial Revolution, of designing mechanisms by starting from a system that has the minimal number of constraints required for rigidity and then removing one of them. One degree of freedom mechanisms obtained this way are a rich class. In recent years, there... (more)

##### Organizing Committee

- Zeyuan He
- Matthias Himmelmann
- Miranda Holmes-Cerfon
- Sabetta Matsumoto
- Ileana Streinu
- Louis Theran

##### 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