## Programs & Events

##### 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

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

##### Research Experiences for Undergraduate Faculty (REUF) at AIM, San Jose, CA

Jun 11 - 15, 2018

The American Institute of Mathematics (AIM), co-sponsored by ICERM, invites applications for the Research Experiences for Undergraduate Faculty (REUF) workshop to be held at AIM in San Jose, CA.

This workshop, sponsored by AIM, ICERM, and the National Science Foundation, is one in a series of annual REUF workshops that bring together leading research mathematicians with faculty at undergraduate institutions who are interested in involving their students in areas of active research. The workshop can also serve as a research renewal opportunity for faculty who want to re-engage in research or are considering a change of research area.

The goals of the workshop are to promote undergraduate research in undergraduate institutions, and to forge lasting research collaborations among the participating faculty. The majority of the workshop will be spent working on problems in small research groups, reporting on progress, and formulating plans for future work. In addition to the workshop... (more)

##### 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

- Alex Iosevich
- Mihalis Kolountzakis
- 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

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

##### Seminar on Stochastic Processes 2018

May 9 - 12, 2018

The Seminar on Stochastic Processes 2018 (SSP2018), will be held from May 9 through May 12, 2018 at Brown University, Providence, Rhode Island. From May 9 - 11 the meeting will take place at the Institute for Computational and Experimental Research in Mathematics (ICERM), and on May 12, the talks will take place at the main campus of Brown University.

The meeting is hosted by ICERM, the Division of Applied Mathematics and the Department of Mathematics at Brown University. It is supported by funds from the National Science Foundation and the Lefschetz Center for Dynamical Systems at the Division of Applied Mathematics at Brown University, and is co-sponsored by the Institute of Mathematical Statistics.

##### Computational Challenges in the Theory of Lattices

Apr 23 - 27, 2018

This workshop will focus on the computational aspects of the theory of Euclidean lattices and on their applications to other areas in mathematics and computer science. It will put emphasis on computational challenges on lattice problems that have recently arisen from unexpected connections to other domains such as algebraic topology, automorphic forms, or cryptography.

A major goal of this workshop is to bring together researchers from different areas, working with Euclidean lattices, and to facilitate their interactions.

Topics will include the reduction theory of lattices and its applications, Voronoi algorithms and their use to compute the cohomology of arithmetic groups, the classification of lattice genera and the computation of spaces of modular forms, the algorithmic aspects of lattice based cryptography, in particular the relationship between the security of cryptographic primitives and the hardness of lattice problems.

##### Organizing Committee

- Christopher Peikert
- Henry Cohn
- Renaud Coulangeon
- Akshay Venkatesh
- Christine Bachoc

##### Public Lecture: Crowd Computing: Scientific discoveries by protein-folding game players

Apr 11, 2018

Can the brainpower of humans worldwide be brought to bear on critical problems posed in computational biology, such as the structure determination of proteins and designing novel enzymes? Yes! Citizen scientists—most of whom have little or no prior biochemistry experience—have uncovered knowledge that eluded scientists for years. Players of the online protein folding video game Foldit have contributed to several scientific discoveries through gameplay. Rather than solving problems with a purely computational approach, combining humans and computers can provide a means for solving problems neither could solve alone.

##### Computation and Optimization of Energy, Packing, and Covering

Apr 9 - 13, 2018

The packing and covering of equal geometric shapes, such as spheres or convex polyhedra, are classical geometric optimization problems. They have a long mathematical tradition and were for instance part of Hilbert's famous twenty-three problems for the 20th century. Nevertheless, seemingly simple packing and covering problems are still extremely hard to solve and generally, far from a solution. Likewise, minimal energy problems for pair potentials, of which best-packing is a special case, have many such unresolved questions.

However, in recent years several new developments with computer assisted approaches have led to previously unexpected breakthrough results. These involve massive computer searches and techniques from numerical optimization, as well as the creation and application of new optimization techniques, such as specific semi-definite programming bounds. New techniques for computer assisted certified proofs allow one to obtain results that would otherwise have been... (more)

##### Organizing Committee

- Robert Womersley
- Achill Schürmann
- Salvatore Torquato
- Frank Vallentin

##### Fast Algorithms for Generating Static and Dynamically Changing Point Configurations

Mar 12 - 16, 2018

This workshop focuses on fast algorithms for the generation of high quality point configurations and meshes such as hierarchical schemes combined with energy or geometrical optimization techniques. Energy methods utilizing appropriate potentials for a prescribed density on a given manifold have been effective in generating point configurations with good covering and packing properties. These methods rely on efficient energy, gradient, and potential computations which can be achieved by hierarchical algorithms that model a system in a recursively compressed (low-rank or low-dimensional) form where information is transmitted non-locally on a hierarchical tree structure. Different aspects of this technique can be found in the classical FFT, multigrid, and fast multipole method (FMM), as well as the recently developed fast direct solvers, multilevel models in statistics, and convolutional neural networks in deep learning.

Fast generation of point configurations and meshes for dynamically... (more)

##### Organizing Committee

- Natasha Flyer
- Doug Hardin
- Edward Saff
- Adrianna Gillman
- Jingfang Huang

##### Public Lecture: Sleeping Beauty and Other Probability Conundrums

Feb 28, 2018

Probability puzzles are notoriously tricky, and the best ones continue to intrigue the public and confound philosophers. We'll examine some of these questions and try to determine whether they uncover real problems with the foundations of probability theory, or just challenges to our flawed human intuition.

##### Optimal and Random Point Configurations

Feb 26 - Mar 2, 2018

This workshop will focus on probabilistic and physical aspects of systems of interacting points: their statistical mechanics, phase transitions, and ground states. Such systems include random point processes arising in probability and statistical physics, such as random matrices, determinantal processes, zeros of random polynomials, disordered ground states, and hyperuniform systems as well as configurations satisfying a geometric or analytic optimality constraint. Special cases also involve disordered and ordered sphere packings and covering problems.

While systems of interacting particles, their free energy and crystallization properties have been studied for a long time in the statistical physics community, there has also been much activity recently, both in the random matrix community and probability communities and in the complex analysis community to understand the microscopic laws of eigenvalues of random matrices and points in beta-ensembles, as well as understanding and... (more)

##### Organizing Committee

- Sylvia Serfaty
- Peter Grabner
- Doug Hardin
- Arno Kuijlaars

##### Point Configurations in Geometry, Physics and Computer Science

Feb 1 - May 4, 2018

The arrangement of point configurations in metric spaces, whether deterministic or random, is a truly interdisciplinary topic of great interest in mathematics, physics and computer science. Mathematical aspects involve optimization, discretization of manifolds, best packing and cubature, among others. For physics, such configurations arise in the study of crystallization, point processes connected with random matrices, self-assembling materials, jammed states, hyperuniformity and phase transitions. For computer science, extremal point configurations play a fundamental role in coding and information theory, and lattice-based protocols in cryptography and related computational complexity issues are of growing importance. Furthermore, there has been recent and substantial progress on related age-old problems (such as the Kepler conjecture).

The investigation of the above topics often evolves from the development of efficient computational methods that enable extensive numerical... (more)

##### Organizing Committee

- Robert Womersley
- Sylvia Serfaty
- Peter Grabner
- Achill Schürmann
- Salvatore Torquato
- Henry Cohn
- Doug Hardin
- Edward Saff
- Christine Bachoc