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 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)

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)

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)

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.

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.

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.

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 scale—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)

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)

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.

It is practically rare that a natural phenomenon or engineering problem can be accurately described by a single law of physics. The striking diversity of rules of life forces scientists to continuously increase the complexity of models to address the ever-growing requirements for their prediction capabilities. It remains a formidable challenge to derive and analyze numerical methods which are universal enough to handle complex multiphysics problems with the same ease and efficiency as traditional methods do for textbook PDEs.

The workshop will focus on recent trends in the field of numerical methods for multiphysics problems that include the development of monolithic approaches, structure preserving discretizations, geometrically unfitted methods, data-driven techniques, and modern algebraic methods for the resulting linear and nonlinear discrete systems. The topics of interest include models and discretizations for fluid - elastic structure interaction, non-Newtonian fluids, phase... (more)