## Programs & Events

##### 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

##### 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

##### 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

##### 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

##### 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