Forward simulations of the propagation and scattering of transient electromagnetic (EM) waves in complex media are important in a variety of applications, such as radar, environmental and medical imaging, noninvasive detection of cancerous tumors, design of engineered composites such as metamaterials, communication and computation, and global climate assessment, among others. These applications involve multiple spatial and temporal scales, complex geometries, spatial and temporal heterogeneities, and stochastic effects at small scales.

Biological tissues are complex media with inhomogeneous and frequency dependent (dispersive) properties. Analyses of EM wave interactions with biological media is fundamental in many medical applications, such as noninvasive diagnosis techniques, and for advancing the quality of medical imaging in general. Characterization of EM wave interaction with natural media is of great importance for environmental remote sensing and global climate assessment.... (more)

Fractional partial differential equations (FPDEs) are emerging as a powerful tool for modeling challenging multiscale phenomena including overlapping microscopic and macroscopic scales. Compared to integer-order PDEs, the fractional order of the derivatives in FPDEs may be a function of space and time or even a distribution, opening up great opportunities for modeling and simulation of multi-physics phenomena, e.g. seamless transition from wave propagation to diffusion, or from local to non-local dynamics. In addition, data-driven fractional differential operators may be constructed to fit data from a particular experiment or specific phenomenon, including the effect of uncertainties. FPDEs lead to a paradigm shift, according to which data-driven fractional operators may be constructed to model a specific phenomenon instead of the current practice of tweaking free parameters that multiply pre-set integer-order differential operators. This workshop will cover all these areas, including... (more)

The problem of decomposing a function into a sum of simply structured functions is a classical area of research in Analysis. Exciting recent progress, e.g. the solution to the Kadison-Singer problem, results about exponential frames and Riesz bases in various settings, and results about orthogonal exponential bases for convex polytopes, has re-energized discussion in this area, opened new directions for study, and turned it into an even more active and fruitful area for research. The goal of this workshop is to discuss such new developments in this area. In particular, the workshop will focus on problems regarding exponential systems in weighted spaces and the Fuglede conjecture. Related settings will also be of interest, for example: (i) Systems of vectors obtained by translating, translating and modulating, or translating and dilating a single function over the line; (ii) Sampling and decomposition of functions in the finite dimensional setting; (iii) Sampling and interpolation of... (more)

Recent developments in the minimal model program in positive characteristic and birational geometry have found purchase within arithmetic geometry, e.g., around questions of exceptional sets involved in Manin's conjecture on points of bounded height. In turn, arithmetic perspectives afforded by Manin's conjecture are starting to shed light on the geometry of spaces of rational curves.

Our goal in this workshop is to bring together two camps of geometers (birational and arithmetic) who have had few opportunities to interact on a large scale. We plan to focus on the interplay between theoretical developments and explicit constructions, e.g., in the study of Cox rings of Fano varieties, rationality problems, Manin's conjecture.

The complex dynamical behavior of large pedestrian crowds has long fascinated researchers from various scientific fields. Academic studies began in earnest in the last century, starting with empirical observations in the early 1950’s and continuing with the development of models in the field of applied physics. In more recent years, applied mathematicians have become increasingly interested in the analytical aspects and computational challenges related to simulation of existing models. With ongoing technical development, more and more data such as pedestrian trajectories and velocities have become available, leading to new questions of calibration of the mathematical models.

Since the inception of the field of study, several scientific communities have been independently working on the challenge of describing and simulating pedestrian dynamics. While mathematicians have mainly focused on the modeling and analytical aspects, physicists have developed experimental setups and methods... (more)

This workshop will provide a platform for researchers working on localized kernel-based methods to present and discuss their latest developments, as well as the current theoretical and practical challenges in the field. These methods, such as radial basis function-generated finite differences (RBF-FD) or RBF-generated partition of unity methods (RBF-PUM), promise to develop into general-purpose meshless techniques for the numerical solution of partial differential equations that inherit the ease of implementation of the finite difference method, and yet potentially possess a greater ability than the finite element method to fit any geometry or adapt to singularities or other features of the solution.

The numerical evidence collected in recent years by a rapidly growing community of researchers suggests that these methods combine numerical stability on irregular node layouts, high computational speed, high accuracy, easy local adaptive refinement, and excellent opportunities for... (more)

Research Collaboration Workshop for Women in Data Science and Mathematics (WiSDM). This program will bring together women at all stages of their careers, from graduate students to senior researchers, to collaborate on problems in data science. The scientific focus will be on cutting edge problems in the areas of predictive modeling, multi-scale representation and feature selection, statistical and topological learning, and related areas. Data science is a cross-disciplinary field relying on statistics, computer science and mathematics and driven by problems in many other disciplines. While data science has emerged as a prominent new field enrolls record numbers and attracts research talents from many scientific disciplines, the role of theoretical and applied mathematics has not been highly visible. Mathematics provides many structured representations that can be in the analysis of data arising from such diverse fields as geometric measure theory, classical analysis, computational... (more)

There is an urgent and unmet need to formally analyze, design, develop and deploy advanced methods and algorithms that can scale in statistical and computational efficiency to the size of modern data sets and the complexity of contemporary mathematical models. Addressing this need will require a holistic approach involving new foundational theory, algorithms, and programming language design.

The emerging research theme of Probabilistic Scientific Computing (PSC) or Probabilistic Numerics lies at the nexus of these overlapping directions. It aims to improve statistical quantification of uncertainty, improve computational efficiency, and build more effective and scalable numerical methods for statistical models by leveraging the natural correspondence between computation and inference.

The primary goal of the workshop is to introduce recent results and new directions in probabilistic scientific computing to the US research communities in statistics and machine learning, in numerical... (more)

The purpose of the topical workshop is to gather leading experts, postdoctoral scholars, and graduate students, to present exciting new developments in the field of mathematical fluid dynamics. The focus of the meeting will be placed on current research on regularity, instabilities, and the onset of turbulence in fluid flow, from a theoretical and from a computational perspective. Despite their long and fruitful history, to date these topics continue to enchant and inspire mathematicians, physicists, and computational scientists: in part due to their ubiquitous applications in areas from aeronautical engineering to medicine, and in part because the basic mathematical questions are still open. Among these are global in time existence of solutions to the equations describing motion of inviscid and viscous fluids in three spatial dimensions, and the conjectured relation between the phenomenological theories of turbulence and the statistical properties of solutions to the underlying... (more)

This workshop is a one-week program aimed at 20-25 researchers interested in the opportunity to shape the future of research on the mathematics of crime. Small teams will come together to work on real problems with real crime and policing data provided by the Providence Police Department. Five teams will be assembled, each with a technical advisor who will share their expertise and serve as an anchor point and leader for hands-on research that will take place over the course of the week. This will be a truly hands-on experience in which groups will spend time brainstorming mathematical methods and models to approach the problem at hand, analyzing data provided, and creating code to implement ideas as necessary. There will also be research presentations from the technical advisors throughout the week, as well as closing presentations by each team to present their ideas and progress at the end of the workshop. We fully anticipate that lasting collaborations will be formed, and that work... (more)

A moduli space parameterizes geometric objects with alike structures and encodes in itself the geometry of all possible families of such objects. This workshop will focus on three aspects of moduli spaces: Cycles, Geometric Invariant Theory, and Dynamics. One of our main goals is to synthesize the recent progress on moduli of abelian differentials on algebraic curves motivated by dynamics and in the GIT constructions of related moduli spaces, with the view towards better understanding of geometric cycles on these moduli spaces.

In many cases, computer programming and experiments are important tools to discover new phenomena, both in dynamics and in the study of cycles on moduli spaces. Hence many talks will emphasize computational and experimental aspects of these fields and the workshop will feature a computational problem session whose goal is to disseminate computational techniques and problems to a wider body of researchers.

An integral part of the workshop is a series of three... (more)

This workshop is concerned with sampling challenges, modeling and simulation for data-rich applications in high dimensions. It brings together mathematicians, statisticians and computational scientists to explore the interplay between computational applied mathematics and data science. On the agenda will be novel developments in the study of complex phenomena based on data-analytic techniques, such as efficient calculation of ergodic (long term) averages and statistical inference under a wide range of geometric, physical and analytical constraints.

In applied mathematics and computational science, in particular in molecular modeling, image analysis and geosciences, among others, many objects of interest are high-dimensional and stochastic, and a wide variety of techniques have been developed for sampling and approximating the quantities of interest. Similar issues arise in the area of data science and statistical modeling, where learning problems in the presence of high-dimensional... (more)