## Programs & Events

##### Computational Geometric Topology in Arrangement Theory

Jul 6 - 10, 2015

This workshop will bring together mathematicians working on combinatorial, geometric and topological properties of arrangements. In addition to fundamental open problems in the area, we will emphasize connections to tropical geometry, configuration spaces, and applications (coding theory, statistical economics, topological robotics), building bridges between those working on different aspects of the area. The main aim of the workshop is to discuss computational issues that arise in studying topological and combinatorial invariants of arrangements.

The workshop will be comprised of two main activities: A series of short courses by leading experts and research or expository talks. The short courses will be aimed at a broad audience; in particular they will be appropriate for advanced graduate students and early career mathematicians. In addition to theory, talks will highlight computational aspects of the problems, and the state of the art on the main open conjectures in the field. We... (more)

##### Organizing Committee

- Nero Budur
- Graham Denham
- Anca Daniela Macinic
- Daniel Matei
- Laurentiu Maxim
- Hal Schenck
- Max Wakefield

##### Integrability in Mechanics and Geometry: Theory and Computations

Jun 1 - 5, 2015

This workshop focuses on topics at the interface of classical mechanics, differential geometry, and computer experiments. The directions of current research to be explored at the workshop include the study of invariants and complete integrability of geometrically motivated differential equations (in particular, vehicle motion, tire track geometry, and smoke ring equations), sub-Riemannian geometry, geometric control, nonholonomic systems (such as e.g. bicycle stability and nonholonomic methods in billiard problems), computational methods in mechanics and dynamics (including geometric integrators, biological applications, etc.).

The goal of the workshop is to explore broad applications of the mechanical approach to geometry and geometric one to classical mechanics, to foster interaction between researchers in the above areas, with a view of finding new domains for applications of these fertile ideas.

##### Organizing Committee

- Annalisa Calini
- Boris Khesin
- Gloria Mari-Beffa
- Vadim Zharnitsky

##### Mathematics of Lattices and Cybersecurity

Apr 21 - 24, 2015

Lattices are abstractly very simple objects, yet their concrete realizations contain beautifully intricate problems that are stubbornly difficult even in low dimensions. For example, our present day understandings of densest lattice packings and reduction theory are still plagued with large gaps.

In the 1970's and 1980's lattices entered the world of cryptography as tools used to break certain crypto systems, particularly those based on the subset sum problem, and since the 1990's they have become increasingly important in the building of other types of crypto systems (thanks to the difficulty in the underlying mathematics). Their significance has recently been bolstered by average-case complexity bounds and their present resistance to quantum computing attacks.

Currently the theory of lattices is a lively research topic among mathematicians, computer scientists, and experts in cybersecurity. However, to this date, there has been little to no interaction between these communities.... (more)

##### Organizing Committee

- Jeffrey Hoffstein
- Stephen Miller
- Ramarathnam Venkatesan

##### 11th DIMACS Implementation Challenge in Collaboration with ICERM

Dec 4 - 5, 2014

The DIMACS Implementation Challenges address questions of determining realistic algorithm performance where worst case analysis is overly pessimistic and probabilistic models are too unrealistic: experimentation can provide guides to realistic algorithm performance where analysis fails.

The 11th Implementation Challenge is dedicated to the study of Steiner Tree problems (broadly defined), bringing together research in both theory and practice. Broadly speaking, the goal of a Steiner Tree problem is to find the cheapest way of connecting a set of objects. In most common variants, these objects are either points in a metric space or a subset of the vertices of a network, and the goal is to find a tree that connects all of them.

The main aim of the challenge is to create a reproducible picture of the state-of-the-art in Steiner Tree problems. Phases 1 and 2 of this challenge - the collection and improvement of testbeds and algorithm development and evaluation - began in June 2013.... (more)

##### Organizing Committee

- David Johnson
- Thorsten Koch
- Renato Werneck
- Martin Zachariasen

##### Mathematics of Data Analysis in Cybersecurity

Oct 22 - 24, 2014

The goal of this workshop is to bring mathematicians and cybersecurity practitioners together to outline the key challenges in the mathematics of cybersecurity data analysis. The expected outcome of the workshop will be a roadmap for investment in specific mathematical topics that will directly impact the advancement of the science of cybersecurity.

Mathematicians have long been involved in information security through cryptography, and thus algebra and number theory. But modern cyber security is a much larger field, and the perspectives and methodologies of other parts of the mathematical sciences have been only rarely been brought to bear. Given the complexity and dynamics of cyberspace it is essential to have a formal scientific basis for the field of cybersecurity. Indeed, a variety of sources have called for the creation of a "science of cybersecurity", and mathematical methods should play a critical role in such a science.

The purpose of this workshop is to bring together... (more)

##### Organizing Committee

- Edoardo Airoldi
- Paul Barford
- Henry Cohn
- John Harer
- John Johnson
- Mauro Maggioni
- Jill Pipher

##### Integrability and Cluster Algebras: Geometry and Combinatorics

Aug 25 - 29, 2014

This workshop focuses on certain kinds of discrete dynamical systems that are integrable and have interpretations in terms of cluster algebras. Some such systems, like the pentagram map and the octahedral recurrence, are motivated by concrete algebraic constructions (taking determinants) or geometric constructions based on specific configurations of points and lines in the projective plane. The systems of interest in this workshop have connections to Poisson and symplectic geometry, classical integrable PDE such as the KdV and Boussinesq equations and also to cluster algebras. The aim of the workshop is to explore geometric, algebraic, and computational facets of these systems, with a view towards uncovering new phenomena and unifying the work to date.

##### Organizing Committee

- Vladimir Fock
- Max Glick
- Olga Kravchenko
- Sophie Morier-Genoud
- Valentin Ovsienko
- Richard Schwartz

##### Combinatorial Link Homology Theories, Braids, and Contact Geometry

Aug 4 - 8, 2014

This workshop will focus on recent advances in combinatorial link homology theories (e.g., Heegaard-Floer homology and Khovanov homology), especially as they apply to questions about braids and, more generally, mapping class groups of surfaces. There will be short mini-courses on

- Combinatorial knot Floer homology, with applications to contact geometry,
- Braid foliations and the Jones conjecture,
- Nielsen-Thurston theory, and
- Garside theory and a linear order on the braid group,

As the main goal of the workshop is to facilitate... (more)

##### Organizing Committee

- John Baldwin
- Joshua Greene
- Julia Grigsby
- Keiko Kawamuro
- Dan Margalit

##### Challenges in 21st Century Experimental Mathematical Computation

Jul 21 - 25, 2014

Over the past 25 years, experimental mathematics has developed as an important additional arrow in the mathematical quiver. Many mathematical scientists now use powerful symbolic, numeric and graphic (sometimes abbreviated "SNAG") computing environments in their research, in a remarkable departure from tradition. While these tools collectively are quite effective, challenges remain in numerous areas, including: (a) rapid, high-precision computation of special functions and their derivatives; (b) user-customizable symbolic computing; (c) graphical computing; (d) data-intensive computing; and (e) large-scale computing on parallel and GPU architectures (including algorithm and software design for such systems).

This workshop will convene mathematical and computer scientists who create or exploit these tools, together with computational tool developers and commercial vendors of mathematical software, to exchange approaches and extend the state of the art in the field, both in the design... (more)

##### Organizing Committee

- David Bailey
- Jonathan Borwein
- Olga Caprotti
- Ursula Martin
- Bruno Salvy
- Michela Taufer

##### Computational Nonlinear Algebra

Jun 2 - 6, 2014

Over the last two decades, algebraic and numerical techniques for nonlinear problems have begun a steady and relentless transition from mostly academic constructions, to widely used tools across the mathematical sciences, engineering and industrial applications. The workshop will bring together participants from many diverse fields including computer vision, cryptography, optimization and control, partial differential equations, robotics, and quantum computation, with the common interest in nonlinear algebraic computations. The main goal is to assess the state of the art, to stimulate further progress, and to accelerate developments by bringing together these diverse communities and have them share computational challenges and successes.

##### Organizing Committee

- Greg Blekherman
- Lek-Heng Lim
- Pablo Parrilo
- Andrew Sommese
- Rekha Thomas

##### Robust Discretization and Fast Solvers for Computable Multi-Physics Models

May 12 - 16, 2014

Most systems targeted by mathematical modeling in modern science and engineering are fundamentally multi-physical and multi-scale in nature. As such, they involve solving complex coupled, generally nonlinear, systems of partial differential equations (PDEs) built from subsystems of PDEs that mathematically model very different physical processes, often at very different scales.

Recent advances in high-performance computer hardware and advanced numerical algorithms have made it feasible to construct realistic mathematical models and to build corresponding numerical simulation software for these types of complex multi-physics/multi-scale problems. However, developing robust, efficient, and practical numerical algorithms for such simulation software that are capable of tackling these complex mathematical models is still extremely challenging in a number of fundamental ways. For example, we do not yet have robust methods that can handle strong coupling between different physics and/or... (more)

##### Organizing Committee

- Franco Brezzi
- Jan Hesthaven
- Michael Holst
- Jinchao Xu

##### From the Clinic to Partial Differential Equations and Back: Emerging challenges for Cardiovascular Mathematics

Jan 20 - 24, 2014

Mathematical models have been giving remarkable contributions in advancing knowledge and supporting decisions in several branches of medicine.

Some progress in applying predictive mathematical tools has been made, for example: surgical planning of the Total Cavopulmonary Connection in cardiac pediatrics is, in some hospitals, based on extensive numerical simulation. However, despite the significance, the impact of predictive modeling in the routine medical treatment falls behind.

The ultimate goal of this workshop is to foster collaboration between mathematicians and medical doctors on modeling cardiovascular system. The workshop is organized into two lines that reflect the special format of the workshop: (a) "Core topics" are up-to-date research areas in mathematics and scientific computing that still present several open exciting challenges, which can require developing new numerical models, computational approaches and validation techniques; (b) "New challenges" are a set of... (more)

##### Organizing Committee

- Pablo Blanco
- Leopold Grinberg
- John Oshinski
- Anne Robertson
- W. Robert Taylor
- Alessandro Veneziani

##### Issues in Solving the Boltzmann Equation for Aerospace Applications

Jun 3 - 7, 2013

Being central to gas dynamics, the Boltzmann equation describes gas flows at the microscopic level in regimes from free molecular to continuum. Its descriptive power makes it indispensable for predicting non-continuum phenomena in gases when experimental data is limited or not available. The Boltzmann equation is used in a wide range of applications, from external aerodynamics and thruster plume flows to vacuum facilities and microscale devices. Accurate solution of the Boltzmann equation for modeling gas flows arising in aerospace applications continues to be a challenge. Existing numerical capabilities fall short of capturing the complexities of engineering design. Reasons for this range from the absence of mathematical models that capture the physics properly to higher dimensionality of kinetic models and the resulting high cost of computations to the failure of mathematical theories to handle complex geometries of real life applications.

The goal of this workshop is to facilitate... (more)

##### Organizing Committee

- Alexander Alekseenko
- Jose Camberos
- Irene Gamba
- Sergey Gimelshein
- Prakash Vedula
- Ingrid Wysong