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)

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)

SageMath (sometimes Sage for short) is an open-source, general purpose mathematical software based on the Python programming language. It was created in 2005 by William Stein as a viable alternative to commercial software with an active and established community. SageMath has a broad library of functions useful to mathematicians in many fields, including combinatorics and representation theory. The welcoming and engaged community of users and contributors helps to create an environment of collaboration in both software development and mathematical research, leading to SageMath being cited in over 300 papers.

The study of the representation theories of certain algebras (e.g., Lie algebras, Hecke algebras, Khovanov–Lauda–Rouquier (KLR) algebras, quantum groups, etc.) also amounts to understanding the associated combinatorics. This has exposed deep connections between the associated representation theory and other areas of... (more)

Partial differential equations (PDEs) have long played crucial roles in the field of fluid dynamics. These PDE models, including Euler and Navier-Stokes equations for incompressible and compressible flows, kinetic equations for rarefied flows, and equations for more complex flows such as magneto-hydrodynamics flows, have motivated numerous studies from the theory of PDEs to the design and analysis of computational algorithms, and their implementation and application in computational fluid dynamics (CFD). This discipline is continually and dynamically evolving, constantly bringing forward new results in PDE theory, computation, and application to CFD, and also setting up the ground for generalizations to other related applications including electro-magnetics, fluid-structure interactions, cosmology, and computational electronics.

The aim of this workshop is to review the recent progress in the type of PDEs arising from fluid dynamics and other related physical areas, in terms of their... (more)

This symposium will highlight the progress in the mathematics of computation over the last few decades. The invited lectures will present historical surveys of important areas or overviews of topics of high current interest. Together they will provide a panoramic view of the most significant achievements in the past quarter century in computational mathematics and also the most important current trends.

The year 2018 marks the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals of the American Mathematical Society and the oldest research journal devoted to computational mathematics. This symposium will commemorate the event with invited lectures and poster presentations that reflect the spectrum of research covered by Mathematics of Computation at this juncture of its illustrious history.

The first day of the symposium (November 1) is devoted to the discrete topics and the other two days (November 2-3) are devoted to continuous... (more)

The area of encrypted search focuses on the design and cryptanalysis of practical algorithms and systems that can search on end-to-end encrypted data. With encrypted search algorithms, data can remain encrypted even in use. As such, encrypted search algorithms have a wide array of applications including in data management, healthcare, cloud computing, mobile security, blockchains, and censorship- and surveillance-resistant systems.

Designing, planning, and operating many systems is challenging due to the possibility of high-impact rare events. A motivating application is the electricity power grid, whose operation can be significantly disrupted by rare weather events such as a severe storm or a polar vortex. This workshop will explore optimization and simulation approaches to designing, planning, and operating systems impacted by such events. Stochastic optimization is one approach for optimizing such systems, in which the uncertain outcomes are modeled with random variables. Rare and high-impact events provide a challenge for stochastic optimization because (1) it is difficult to estimate the likelihood of rare events, (2) estimates of expected values with outcomes that have very low probability but high cost are inherently unstable, and (3) the actual distribution of the random events is often not known. Alternatively, robust and distributionally robust optimization models attempt to identify a solution that is... (more)

Dehn surgery has played a central role in the development of low-dimensional topology since it was first introduced by Max Dehn in 1910. Its study has stimulated several fascinating techniques that incorporate ideas from across mathematics: hyperbolic geometry, representation varieties, combinatorics, sutured manifold theory, and Floer homology, to name a few. These tools have led to sensational progress in understanding problems about Dehn surgery and low-dimensional topology at large. Furthermore, they seem well-suited to attack the major open problems in the area, such as the Berge conjecture and the L-space conjecture.

The workshop will function as a graduate summer school. At its core, the school will feature a sequence of mini-courses delivered by a cast of leading experts and distinguished expositors. The courses will unveil Dehn surgery and this suite of techniques to the next generation of researchers in the area. The school will additionally feature guided problem sessions... (more)

The Women in Symplectic and Contact Geometry and Topology workshop (WiSCon) is a Research Collaboration Conference for Women (RCCW) in the fields of contact and symplectic geometry/topology and related areas of low-dimensional topology. The goal of this workshop is to bring together researchers at various career stages in these mathematical areas to collaborate in groups on projects designed and led by leaders in the field.

The mathematical fields of symplectic and contact geometry/topology, rooted in concepts from classical physics, have experienced huge growth in the past few decades. This growth has come in many forms, including multiple flavors of homology theories, symplectic embedding problems, techniques for regularizing spaces of pseudoholomorphic curves, and examples of mirror symmetry, to name a few. This workshop aims to generate research collaborations which build on the growing momentum in these topics, while fostering a network for the traditionally underrepresented... (more)

WiSDM 2019 is a research collaboration workshop targeted toward people working in data science and mathematics. This program will bring together researchers at all stages of their careers, from graduate students to senior researchers, to collaborate on problems in data science.

Data science is typically characterized as work at the intersection of mathematics, computer science, statistics, and an application domain. The scientific focus will be on cutting-edge problems in network analysis for gene detection, group dynamics, graph clustering, novel statistical and topological learning algorithms, tensor product decompositions, reconciliation of assurance of anonymity and privacy with utility measures for data transfer and analytics, as well as efficient and accurate completion, inference and fusion methods for large data and correlations.

Applications are now open. Applicants should rank their top 3 choices of projects in their personal statement. Project descriptions can be found... (more)

Mathematical modelers face a variety of challenges, including summarizing large data sets to understand and explore a system of interest, inferring the model parameters most accurate for describing a given data set, and assessing the goodness-of-fit between data sets. Computational topology provides a lens through which these challenges may be addressed. At the same time, just as topological techniques provide opportunities for modelers, the challenges that modelers face give rise to opportunities for applied topologists. For instance, topologists may develop techniques that make model predictions based on the topology of experimental or simulation data, that analyze time-varying data, or that turn model outputs into formats suitable for machine learning.

This workshop brings together the applied mathematical modeling and applied topology communities, aiming to give modelers exposure to topological techniques still not commonly used in their community, and to give topologists exposure... (more)

Liquid crystals (LCs) are classic examples of partially ordered materials that combine the fluidity of liquids with the long-range order of solids, and have great potential to enable new materials and technological devices. A variety of LC phases exist, e.g. nematics, smectics, cholesterics, with a rich range of behavior when subjected to external fields, curved boundaries, mechanical strain, etc. Recently, new systems came into focus, such as bent-core LC phases, twist-bend-modulated nematics, chromonics and polymer-stabilized blue phases, with more to be discovered.

Best known for applications in displays, LCs have recently been proposed for new applications in biology, nanoscience and beyond, such as biosensors, actuators, drug delivery, and bacterial control (related to active matter). Indeed, it is believed that the LC nature of DNA once enabled the mother of all applications, namely life itself. New numerical methods and scientific computation is needed to guide new theory and... (more)