## Programs & Events

##### K3 Surfaces

Feb 14 - 17, 2024

The purpose of the workshop is to advance toward the goal of making information relating to families of K3 surfaces and their elliptic fibrations into the LMFDB. We expect to begin with families of Picard number 19, building on the previous week's work on Shimura curves, and entering at least the following information: Picard lattice, frame lattices, transcendental lattice, 2-neighbour relations, elliptic fibrations, singular projective model. For some of these, code exists or is currently under construction; for others, it will need to be developed.

The workshop will consist of a small group of mostly experienced people. We expect that most of the time will be spent writing code in small groups, with at least one meeting a day to make sure that we are all going in the same direction while avoiding duplication of effort.

##### Organizing Committee

- Noam Elkies
- Adam Logan
- John Voight

##### PDEs and Geometry: Numerical Aspects

Mar 11 - 15, 2024

The development and analysis of numerical methods for PDEs whose formulation or interpretation is derived from an underlying geometry is a persistent challenge in numerical analysis. Examples include PDEs posed on complicated manifolds or graphs, PDEs that describe interactions across complex interfaces, and equations derived from intrinsically geometric concepts such as curvature-driven flows or highly nonlinear Monge-Ampere equations arising in optimal transport. In recent years, these PDEs have gained significance in diverse areas such as machine learning, optical design problems, meteorology, medical imaging, and beyond. Hence, the development of numerical methods for this class of PDEs is poised to lead to breakthroughs for a wide range of timely problems. However, designing methods to accurately and efficiently solve these PDEs requires careful consideration of the interactions between discretization methods, the PDE operators, and the underlying geometric properties.

This... (more)

##### Organizing Committee

- Charlie Elliott
- Brittany Hamfeldt
- Michael Neilan
- Maxim Olshanskiy
- Axel Voigt

##### The Industrialization of SciML

Mar 23 - 24, 2024

Scientific Machine Learning (SciML) is a merger of computational sciences and data-driven machine learning, implemented in software as a set of abstractions to leverage existing domain knowledge and physics models within learning schemes and accelerated computing platforms. Only now are the component technologies becoming mature and integrated, with the purpose of providing robust and reliable ML that encodes domain knowledge and yields interpretable solutions in nearly all sciences at any scaleâ€”from particle physics and protein folding, to epidemiology and economics, to climate and astrophysics.

While recent years have shown immense research progress in accelerating classical physics solvers and discovering new governing laws for complex physical systems, SciML methods and applications fall short of real-world utility. Across all physical and life sciences the technical maturity and validations necessary are lacking, failing, or unknown to SciML research. In the context of... (more)

##### Organizing Committee

- Marta D'Elia
- George Karniadakis
- Alexander Lavin

##### Nonlocality: Challenges in Modeling and Simulation

Apr 15 - 19, 2024

This workshop focuses on the modeling, analysis, approximation, and applications of nonlocal equations, which have raised new challenges to mathematical modeling, numerical analysis, and their computational implementation. Recent applications include, but are not limited to: heat and mass diffusion, mechanics, pattern formation, image processing, self-organized dynamics, and population dispersal.

Invited speakers and participants will bring expertise from a wide range of related fields, including mathematical and numerical analysis of nonlocal and fractional equations, numerical methods and discretization schemes, multiscale modeling, adaptivity, machine learning, software implementation, peridynamics modeling of material failure and damage, nonlocal and fractional modeling of anomalous heat and mass diffusion, and several engineering and scientific applications in which nonlocal modeling is useful.

##### Organizing Committee

- Marta D'Elia
- Abner Salgado
- Pablo Seleson
- Xiaochuan Tian

##### An ICERM Public Lecture: Mathematicians Helping Art Historians and Art Conservators

May 2, 2024

In recent years, mathematical algorithms have helped the art historians and art conservators putting together fragments of world-famous frescos by Andrea Mantegna classify certain paintings as “roll mates,” remove artifacts in preparation for a restoration campaign, and gain insight into the hidden paintings underneath visible ones.

This lecture will review these applications and give a glimpse into the mathematical aspects that make them possible.

##### Interacting Particle Systems: Analysis, Control, Learning and Computation

May 6 - 10, 2024

Systems of interacting particles or agents are studied across many scientific disciplines. They are used as effective models in a wide variety of sciences and applications, to represent the dynamics of particles in physics, cells in biology, people in urban mobility studies, but also, more abstractly in the context of mathematics, as sample particles in Monte Carlo simulations or parameters of neural networks in machine learning.

This workshop aims at bringing together researchers in analysis, computation, inference, control and applications, to facilitate cross-fertilization and collaborations.

##### Organizing Committee

- Jose Carrillo
- Katy Craig
- Massimo Fornasier
- Fei Lu
- Mauro Maggioni
- Kavita Ramanan

##### The Ceresa Cycle in Arithmetic and Geometry

May 13 - 17, 2024

In the 1980s, Ceresa exhibited one of the first naturally occurring examples of an algebraic cycle, the Ceresa cycle, which is in general homologically trivial but algebraically nontrivial. In the last few years, there has been a renewed interest in the Ceresa cycle, and other cycle classes associated to curves over arithmetically interesting fields, and their interactions with analytic, combinatorial, and arithmetic properties of those curves. We hope to capitalize on this momentum to bring together different communities of arithmetic geometers to fully explore explicit computations around the arithmetic and geometry of cycles when these various approaches are systematically combined.

##### Organizing Committee

- Daniel Corey
- Jordan Ellenberg
- Wanlin Li
- Daniel Litt
- Congling Qiu
- Padmavathi Srinivasan

##### Random Matrices and Applications

May 20 - 22, 2024

This workshop focuses on the role of random matrices in data science, machine learning, and theoretical computer science.

Playing a significant role in modern data science, random matrices provide an elegant way to represent both (a) the data and (b) the way we process it. To give an example of (a), the classical model of high-dimensional data is a set of points drawn from a certain distribution in a high-dimensional space which can be represented as a random matrix. An even more natural example is that most data in practice is noisy, so it can be represented as a deterministic matrix plus a random noise, which is a random matrix with a non-zero mean. An example of (b) is data compression, which can be realized by applying a random matrix of smaller sizes to the data in (a), thereby reducing its dimensions. Another example is data completion, where we need to reconstruct data (in the form of a matrix) from a random sub-matrix, given that the original matrix satisfies certain... (more)

##### Organizing Committee

- Hoi Nguyen
- Oanh Nguyen
- Konstantin Tikhomirov
- Roman Vershynin
- Van Vu

##### Recent Progress on Optimal Point Distributions and Related Fields

Jun 3 - 7, 2024

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)

##### Organizing Committee

- Dmitriy Bilyk
- Xuemei Chen
- Emily King
- Dustin Mixon
- Kasso Okoudjou

##### Summer@ICERM 2024: Mathematical Models to Predict, Prepare, and Prevent

Jun 10 - Aug 2, 2024

Mathematical modeling allows researchers to address questions and test hypotheses that may not be feasible to study otherwise. The Summer@ICERM 2024 faculty advisors will present a variety of research projects centered around approaches to using mathematical modeling for making predictions and determining associated preparations and necessary preventions in the fields of epidemiology, precision nutrition, and sports analytics. Faculty will guide the development of appropriate models and computational tools that can aid in answering fundamental questions in these fields.

During the eight-week program, students will be introduced to the research topics through interactive lectures. Afterward, students will work on their projects in assigned groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily; give regular talks about their findings; attend mini-courses, guest talks, and professional development seminars; and practice coding.... (more)

##### Organizing Committee

- Amanda Harsy Ramsay
- Adam Schultze
- Brittany Stephenson
- Cara Sulyok

##### Roots of Unity

Jun 10 - 14, 2024

The transition to independent learning and research is a crucial and often jarring point in every graduate student's career. This transition is even more difficult for students from marginalized groups, who often have smaller support systems and may face an actively unsupportive environment at their institution. The goal of this workshop is to support, mentor, and guide students at this crucial stage in their career.

During the workshop, mentors will guide the student participants through the (often very daunting!) experience of trying to read a paper without being an expert in the area. The participants will be broken into small working groups, each focused on a recent paper in their area of interest. Each group will be assisted throughout the week by mentors, both early career mathematicians (late stage graduate students or postdocs) and faculty members. The topics covered in this workshop will be Number Theory, Combinatorics, Commutative Algebra, and Geometry/Topology.

The... (more)

##### Organizing Committee

- Christine Berkesch
- Michelle Manes
- Priyam Patel
- Candice Price
- Bianca Viray

##### Queer in Computational and Applied Mathematics (QCAM)

Jun 24 - 28, 2024

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)

##### Organizing Committee

- Rowan Barker-Clarke
- Rustum Choksi
- Alexander Hoover
- Hermie Monterde
- Michael Robert
- Colton Sawyer
- Becca Thomases