## Programs & Events

##### Vlasov Models in Kinetic Theory

Sep 19 - 23, 2011

Vlasov-type models deal with continua of particles where the electric charges dominate the collisions, so that the collisions are ignored. They occur in physical plasmas, including astrophysical plasmas and fusion reactors.

There are many examples of astrophysical plasmas of this type, such as the solar wind. When a fusion reactor is very hot, the relevant times scales are so short that collisions can be ignored. Vlasov theory also models systems where the dominant force is gravity, such as clusters of stars or galaxies.

##### Organizing Committee

- Pierre Degond
- Francis Filbet
- Robert Glassey
- Jingmei Qiu
- Gerhard Rein

##### AWM Anniversary Conference at Brown University

Sep 17 - 18, 2011

40 Years and Counting: 2011 is the 40th anniversary of the Association for Women in Mathematics (AWM). With this conference, AWM continues to celebrate the progress of women in mathematical professions and to recognize individual achievements. Join us this fall on the Brown University campus in historic Providence, RI.

##### Organizing Committee

- Georgia Benkart
- Kristin Lauter
- Jill Pipher

##### Kinetic Theory and Computation

Sep 7 - Dec 9, 2011

Kinetic theory plays a central role in many areas of mathematical physics, from nanoscales to continuum mechanics. It is an indispensable tool in the mathematical description of applications in physical and social sciences, from its origin in dilute gases, to wide applications such as semi-conductors, polymers, cells, plasma, galaxies, traffic networking, and swarming. The number of particles is typically more than 10^{20}.

On the one hand, kinetic models provide more detailed and accurate description of regimes where hydrodynamic equations are either invalid or simply not available. On the other hand, because modern computers are still inadequate in simulating the molecular or even quantum dynamics in emerging industrial needs in micro- and nanotechnology, kinetic equations provide models that can capture important features of microscopic or quantum phenomena with a manageable computational cost. Kinetic theory is at the core of multiscale modeling, which connects fundamental... (more)

##### Organizing Committee

- Jose Blanchet
- Francis Filbet
- Irene Gamba
- Yan Guo
- Chi-Wang Shu
- Walter Strauss

##### 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

##### Brown University SUMS Conference

Mar 5, 2011

The Brown University Symposium for Undergraduates in the Mathematical Sciences (SUMS) has been held annually since 2002. The symposium's goal is to foster greater undergraduate interest and scholarship in mathematics by demonstrating the ubiquity of mathematics throughout the sciences. The conference also provides an environment in which motivated undergraduates can come together to share their own work and learn from distinguished faculty and researchers from around the country.