## Programs & Events

##### Mathematical Aspects of P versus NP and its Variants

Aug 1 - 5, 2011

This workshop will bring together computer scientists and mathematicians to examine the P v. NP problem and its variants from the perspectives of algebra, geometry, and number theory, and to introduce the mathematical aspects of these questions to a larger audience. Diverse researchers working on different aspects of these problems will clarify connections between different approaches.

There will be two main topics: Analogues of P v. NP *(e.g., Valiant's conjectures, the Mulmuley-Sohoni Conjecture, the BSS model, and other computational models);* and Algebraic, Number Theoretic, and Geometric Aspects of P v. NP *(e.g., Holographic algorithms, characterizations of NP in terms of sheaf cohomology, sparse polynomials, and other arithmetic approaches).*

The workshop will emphasize the "work" aspect, so there will be few scheduled lectures, with extensive discussion periods, and follow-up lectures scheduled impromptu as needed.

##### Organizing Committee

- Saugata Basu
- Joseph Landsberg
- Joseph Maurice Rojas

##### Cluster Algebras and Statistical Physics

Aug 15 - 19, 2011

Cluster algebras are commutative algebras with a distinguished set of generators grouped into overlapping subsets of fixed cardinality; the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. These algebras were developed to explain the "Laurent phenomenon", in which certain a priori rational functions defined by these mutations turn out to always be Laurent polynomials. Cluster algebras encode a surprisingly widespread range of phenomena in settings as diverse as quiver representations, TeichmÃ¼ller theory, invariant theory, tropical calculus, Poisson geometry, and polyhedral combinatorics. This workshop will explore the connection between cluster algebras and various topics in statistical physics, including the dimer model on surfaces, integrable systems such as the KP equation, and certain dynamical systems (Y- and Q-systems) which play an important role in the theory of the thermodynamic Bethe... (more)

##### Organizing Committee

- Lauren Williams
- David Wilson

##### Synchronization-reducing and Communication-reducing Algorithms and Programming Models for Large-scale Simulations

Jan 9 - 13, 2012

As concurrency in scientific computing pushes beyond a million threads and performance of individual threads becomes less reliable for hardware-related reasons, attention of mathematicians, computer scientists, and supercomputer users and suppliers inevitably focuses on reducing communication and synchronization bottlenecks. Though convenient for succinctness, reproducibility, and stability, instruction ordering in contemporary codes is commonly overspecified. This workshop attempts to outline evolution of simulation codes from today's infra-petascale to the ultra-exascale and to encourage importation of ideas from other areas of computer science into numerical algorithms, new invention, and programming model generalization.

##### Organizing Committee

- David Keyes
- Matt Knepley
- Katherine Yelick

##### Heterostructured Nanocrystalline Materials

May 30 - Jun 1, 2012

The theme of this workshop is the computation, modeling, and mathematical analysis of heterostructured nanocrystalline materials. This includes quantum dots, nanowires, graphene, and grain boundaries. These various phenomena will be discussed in the context of modeling and computation on different scales ranging from density functional theory to continuum mechanics. The workshop will also address various techniques that allow one to combine models on different scales to yield efficient computational methods.

##### Organizing Committee

- Tim Schulze
- Vivek Shenoy
- Peter Smereka

##### NSF/CBMS Conference: Finite Element Exterior Calculus (FEEC)

Jun 11 - 15, 2012

FEEC is a recent advance in the mathematics of finite element methods that employs differential complexes to construct stable numerical schemes for several important types of application problems. It has aroused great interest because it both presents interesting mathematical problems and shows great potential for application in computational science and engineering. The concentrated sequence of lectures in this program will provide participants with an understanding of the mathematical tools required to fully grasp the concepts in FEEC. ICERM is pleased to host this NSF-CBMS Regional Research Conference.

Douglas Arnold will deliver 10 lectures, one in the morning and one in the afternoon of each day of the workshop. Richard Falk and Anil Hirani will both give one presentation.

Limited funding is available to support participants.

##### Organizing Committee

- Alan Demlow
- Johnny Guzman
- Dmitriy Leykekhman

##### Bridging Scales in Computational Polymer Chemistry

Aug 6 - 10, 2012

Many important advances in material and biomedical science will come from controlling the chemical properties and nanoscale morphology of polymer mixtures. Predicting the longtime continuum-level properties of such complex systems poses a canonical computational challenge due to the disparate length and time scales separating the molecular description from the macroscopic behavior, particularly the evolution of morphology. This workshop focuses on four overlapping approaches to bridging this gap: Accelerated Molecular Methods, Coarse-Graining of Molecular Dynamics, Computational Approaches to Self-Consistent Mean Field, and Coupled Molecular and Continuum-Variational models. The goal is to spur the development of hybrid computational methods with the capacity to identify and characterize the rare events and the driving forces which steer the systems towards equilibrium, and connect the burgeoning growth in parallel-computation techniques for particle-based systems with recently... (more)

##### Organizing Committee

- Andrew Christlieb
- Cecilia Clementi
- Keith Promislow
- Mark Tuckerman
- Zhengfu Xu

##### Reproducibility in Computational and Experimental Mathematics

Dec 10 - 14, 2012

In addition to advancing research and discovery in pure and applied mathematics, computation is pervasive across the sciences and now computational research results are more crucial than ever for public policy, risk management, and national security. Reproducibility of carefully documented experiments is a cornerstone of the scientific method, and yet is often lacking in computational mathematics, science, and engineering. Setting and achieving appropriate standards for reproducibility in computation poses a number of interesting technological and social challenges. The purpose of this workshop is to discuss aspects of reproducibility most relevant to the mathematical sciences among researchers from pure and applied mathematics from academics and other settings, together with interested parties from funding agencies, national laboratories, professional societies, and publishers. This will be a working workshop, with relatively few talks and dedicated time for breakout group discussions... (more)

##### Organizing Committee

- David Bailey
- Jonathan Borwein
- Randall LeVeque
- Bill Rider
- William Stein
- Victoria Stodden

##### 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

##### 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

##### 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

##### 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

##### 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