## Programs & Events

##### Real Algebraic Geometry and Optimization

Oct 15 - 19, 2018

This workshop will focus on techniques and structures in real algebraic geometry and optimization, including computational tools for semi-algebraic sets, semidefinite programming techniques for polynomial optimization, and applications of these tools to problems in computer vision. Real algebraic geometry provides powerful tools to analyze the behavior of optimization problems, the geometry of feasible sets, and to develop new relaxations for hard non-convex problems. On the other hand, numerical solvers for semidefinite programs have led to new fast algorithms in real algebraic geometry. Algebraic methods over the real numbers are essential for many real-world applications. This workshop aims to explore the cutting edge of techniques in real algebraic geometry and convex optimization as well as applications of these tools to problems in computer vision and other information sciences.

##### Organizing Committee

- Greg Blekherman
- Didier Henrion
- Pablo Parrilo
- Rekha Thomas
- Cynthia Vinzant

##### Core Computational Methods

Sep 17 - 21, 2018

This workshop will focus on core algorithms in the three crucial areas in nonlinear algebra: numerical algebraic geometry, symbolic computation, and combinatorial methods. There have been tremendous advances in algorithms in these areas. As applications become more sophisticated, and require more computing resources, the basic algorithms and implementations need to step up to match the demand from applications. This workshop will bring together experts to exchange ideas on new algorithms that are needed and on improvement of existing ones. It will incite collaboration on hybrid algorithms involving computational methods from the three areas. Examples of open problems to be addressed include: certification of numerical methods, and combining numerical, symbolic and combinatorial methods to allow a much larger reach for decomposition algorithms.

##### Organizing Committee

- Wolfram Decker
- Jesús De Loera
- Andrew Sommese
- Mike Stillman

##### Nonlinear Algebra Bootcamp

Sep 5 - 12, 2018

The primary goal of this opening workshop is to expose program participants to many of the methods and software packages relevant to this program. There will be introductory lectures and ample time for experimentation with methods and software under the tutelage of area experts and software developers.

##### Organizing Committee

- Jonathan Hauenstein
- Frank Sottile
- Cynthia Vinzant
- Dan Bates
- Anton Leykin
- Mike Stillman

##### 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

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

##### 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
- Salvatore Torquato
- Achill Schürmann
- 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

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

##### 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
- Arno Kuijlaars
- Peter Grabner
- Doug Hardin

##### 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

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

##### Recent Advances in Seismic Modeling and Inversion: From Analysis to Applications

Nov 6 - 10, 2017

This workshop will bring together academic and industrial researchers with the goal of addressing some of the key challenges in the analysis of seismic inverse problems, with emphases on reconstruction, big data and fast algorithms. We aim to facilitate interactions among scientists addressing all aspects of these problems, from analysts addressing such questions as stability and uniqueness through geophysicists developing new acquisition systems and applying cutting-edge ideas to field data sets. The workshop will place particular emphasis on fast algorithms that address the unique big-data requirements of seismic imaging from the reservoir to whole-Earth scale.

Specific topics will include analysis of seismic inverse problems leading to reconstruction (iterative or direct) from finite data; emerging acquisition technologies; uncertainty quantification; big-data simulation; inversion and model reduction, including compressed sensing; fast solvers in frequency and time; anisotropy;... (more)

##### Organizing Committee

- Lexing Ying
- Vladimir Druskin
- Alison Malcolm
- Maarten de Hoop
- Alexander Vasilyevich Mamonov

##### Advances in model reduction for large-scale forward and inverse scattering problems

Nov 3, 2017

Model order reduction is a wide topic in computational mathematics that is generally used to approximate the response of complex systems. A recent development in this field is concerned with using reduced order models for solving efficiently and accurately inverse problems for partial differential equations. Such reduced order models are called data driven, because they are constructed from data interpolation conditions. Moreover, they are designed to respect the physics of the problem, such as loss of resolution away from the surface of measurements in diffusive inverse problems and causality conditions in inverse problems for the wave equation. This workshop will be focused on this novel approach to inversion, with particular emphasis on applications to inverse scattering problems arising in seismic imaging. The workshop will also celebrate the work of Dr. Vladimir Druskin, who has been making outstanding contributions to this field.

##### Organizing Committee

- Mikhail Zaslavsky
- Shari Moskow
- Alexander Vasilyevich Mamonov
- Liliana Borcea

##### Mathematical and Computational Aspects of Radar Imaging

Oct 16 - 20, 2017

This workshop will bring together mathematicians and radar practitioners to address a variety of issues at the forefront of mathematical and computational research in radar imaging. Some of the topics planned include shadow analysis and exploitation, interferometry, polarimetry, micro-Doppler analysis, through-the-wall imaging, noise radar, compressive sensing, inverse synthetic-aperture radar, moving target identification, quantum radar, multi-sensor radar systems, waveform design, synthetic-aperture radiometry, passive sensing, tracking, automatic target recognition, over-the-horizon radar, ground-penetrating radar, and Fourier integral operators in radar imaging.

##### Organizing Committee

- Margaret Cheney
- Eric Mokole
- Armin Doerry
- Frank Robey

##### Waves and Imaging in Random Media

Sep 25 - 29, 2017

Wave propagation and imaging in complex media is an interdisciplinary area in applied mathematics, with roots in hyperbolic partial differential equations, probability theory, statistics, optimization, and numerical analysis. It has a wide range of applications, including not only radar and seismic reconstruction but also many others, such as laser beam propagation through clouds, light propagation through the atmosphere in astronomy, secure communications in scattering media, medical imaging, and nondestructive testing of materials.

This workshop will present some of the latest advances in this area including wave propagation with time-dependent perturbations, source and reflector imaging in random media with sensor arrays, applications of random matrix theory for detection and imaging, imaging with cross correlation techniques, imaging with opportunistic or noise sources, applications of compressed sensing for imaging of sparse scenes, super-resolution in imaging, waves in novel... (more)

##### Organizing Committee

- Josselin Garnier
- Chrysoula Tsogka
- Kui Ren