## Programs & Events

##### Advances in PDEs: Theory, Computation and Application to CFD

Aug 20 - 24, 2018

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)

##### Organizing Committee

- Alina Chertock
- Adi Ditkowski
- Anne Gelb
- Johnny Guzman
- Jan Hesthaven
- Yvon Maday
- Chi-Wang Shu
- Eitan Tadmor
- Jennifer Ryan

##### SageDays@ICERM: Combinatorics and Representation Theory

Jul 23 - 27, 2018

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, Khovanovâ€“Laudaâ€“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)

##### Organizing Committee

- Ben Salisbury
- Gabriel Feinberg
- Darij Grinberg
- Travis Scrimshaw

##### Computational Aspects of Time Dependent Electromagnetic Wave Problems in Complex Materials

Jun 25 - 29, 2018

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. In... (more)

##### Organizing Committee

- Vrushali Bokil
- Susan Hagness
- Shan Zhao
- Fengyan Li
- Fernando Teixeira
- Yingda Cheng

##### Fractional PDEs: Theory, Algorithms and Applications

Jun 18 - 22, 2018

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)

##### Organizing Committee

- Francesco Mainardi
- George Karniadakis
- Mark Meerschaert
- Hong Wang
- Jie Shen

##### Frame Theory and Exponential Bases

Jun 4 - 8, 2018

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)

##### Organizing Committee

- Mihalis Kolountzakis
- Alex Iosevich
- Shahaf Nitzan

##### Birational Geometry and Arithmetic

May 14 - 18, 2018

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.

##### Organizing Committee

- Asher Auel
- Yuri Tschinkel
- Marta Pieropan
- Anthony Varilly-Alvarado
- Sho Tanimoto

##### Pedestrian Dynamics: Modeling, Validation and Calibration

Aug 21 - 25, 2017

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 1950â€™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)

##### Organizing Committee

- Benedetto Piccoli
- Marie-Therese Wolfram
- Armin Seyfried
- Jose Antonio Carrillo
- Alethea Barbaro

##### Localized Kernel-Based Meshless Methods for Partial Differential Equations

Aug 7 - 11, 2017

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)

##### Organizing Committee

- Natasha Flyer
- Bengt Fornberg
- Elisabeth Larsson
- Greg Fasshauer
- Oleg Davydov

##### Women in Data Science and Mathematics Research Collaboration Workshop (WiSDM)

Jul 17 - 21, 2017

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)

##### Organizing Committee

- Emina Soljanin
- Ellen Gasparovic
- Sibel Tari
- Xu Wang
- Giseon Heo
- Regina Liu
- Kathryn Leonard
- Julie Mitchell
- Deanna Needell
- Carlotta Domeniconi
- Linda Ness

##### Robust Methods in Probability & Finance

Jun 19 - 23, 2017

On financial markets one never observes the same data twice; market configurations are subject to change across time. This poses some specific challenges to inference, prediction, and optimal control in financial contexts. Classically, strong model assumptions are needed, while current research aims at methods which are robust with respect to model misspecification. This issue lies at the heart of the envisaged workshops, and the program of the workshops will reflect recent developments in this direction.

The last decade saw a rise of robust methods in probability and finance resulting in new numerical and theoretical challenges. Interestingly, these challenges bring together methodologies from PDEs, probability, stochastic analysis, and control theory. Mathematically speaking, robustness typically translates into nonlinearity showing up as a defining feature. Examples in this direction are nonlinear expectations, nonlinear PDEs, and H-infinity optimal stochastic control. Finance has... (more)

##### Organizing Committee

- Tomasz Bielecki
- Eva Lutkebohmert-Holtz
- Philipp Harms
- Marcel Nutz
- Patrick Dondl
- Thorsten Schmidt

##### Probabilistic Scientific Computing: Statistical inference approaches to numerical analysis and algorithm design

Jun 5 - 9, 2017

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)

##### Organizing Committee

- George Karniadakis
- Philipp Hennig
- Michael Osborne
- Houman Owhadi
- Paris Perdikaris

##### Current Developments in Mathematical Fluid Dynamics: Regularity, Instabilities, and Turbulence

Jan 24 - 27, 2017

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)

##### Organizing Committee

- Peter Constantin
- Vlad Vicol
- NataĊĦa Pavlovic