This workshop will focus on recent advances in the study of geometric structures and their associated group representations. As well as featuring hyperbolic structures, the workshop will also consider more exotic structures, such as projective structures, complex hyperbolic and spherical CR-structures and locally homogeneous space-times. A related focus includes aspects of coarse or non-positively curved geometry such as Gromov hyperbolic spaces and CAT(0) complexes. We will explore the interaction between experimental evidence and rigorous proof.

The program focuses on the recent impact of computation and experiment on the study of the pure mathematics sides of topology, geometry, and dynamics. Specific areas include 3-dimensional topology, the study of locally symmetric spaces, low-dimensional dynamics, and geometric group theory. Included are areas where computation has not yet had an impact, but might do so in the near future.

This workshop, sponsored by AIM, ICERM, and the NSF, will introduce undergraduate faculty to research opportunities in several fields of mathematics that will equip them with the tools to mentor students in undergraduate research in mathematics. Lectures at the workshop will provide background information and introduce open problems. The majority of the workshop will be spent working on problems, reporting on progress, and formulating plans for future work.

The workshop will be hosted at ICERM.

Preference will be given to faculty who teach and advise substantial numbers of minority students.

If you would like to participate, please apply by filling out the on-line form no later than March 22, 2013. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to... (more)

Interested in discussing cutting edge research ideas with both peers and leaders in their field?

Interested in broadening your professional network across the mathematical sciences?

Interested in the opportunity to present your ideas and hear about funding opportunities from program officers?

The Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles,... (more)

Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.

Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.

Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.

Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.

The Summer@ICERM 2013 program is designed for a select group of 10-12 undergraduate scholars. Students will work in small groups of two or three, supervised by faculty advisors and aided by teaching assistants.

The faculty... (more)

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)

Recent years have seen a flurry of activity in the field of Weyl group multiple Dirichlet series. Surprising and unexpected connections between these multiple Dirichlet series and several different fields of mathematics have emerged. This workshop will survey recent results and set the stage for future developments which further interrelate analytic number theory, automorphic forms and combinatorial representation theory.

Particular focus will be given to applications of Weyl group multiple Dirichlet series to the following areas:

• Average value and nonvanishing results for families of L-functions
• Periods of automorphic forms
• Connections between characters sums over function fields and characters of affine root systems
• Metaplectic Casselman-Shalika formulae and deformations of the Weyl character formula

Schubert calculus is the modern approach to classical problems in enumerative algebraic geometry, specifically on flag varieties and their many generalizations. Crystals are combinatorial tools based on quantum groups which arise in the study of representations of Lie algebras. Whittaker functions are special functions on Lie groups or p-adic groups, for example GL(n,F) where F might be the real or complex numbers, or a p-adic field.

The area of intersection between these three topics is combinatorial representation theory. Common tools such as Demazure operators, the Bruhat partial order, and Macdonald polynomials appear in all three areas. Some connections between these three areas are quite new. This workshop will explore these connections.

Sage is a mathematics software system developed by and for the mathematics community, whose mission is to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Its wide span of features, in particular in number theory, combinatorics, and representation theory, together with its friendly community based development, fosters collaborations across disciplines, from the design and implementation of new computer exploration tools to research.

This workshop will bring together experienced Sage and Sage-Combinat developers and experts of multiple Dirichlet series and computational algebraic combinatorics. Like every workshop in the Sage Days series, it will welcome whoever wants to discover Sage, learn more about it, or contribute to it.

As the first meeting for the ICERM Semester... (more)

L-functions—vast generalizations of the Riemann zeta function— are fundamental objects of study in number theory. In the 1980's the idea emerged that it could be useful to tie together a family of related L-functions in one variable to create a "double Dirichlet series," which could be used to study the average behavior of the original family of L-functions. Double Dirichlet series soon became multiple Dirichlet series. It has gradually emerged that the local structure of these multiple Dirichlet series shows a rich connection to combinatorial representation theory.

This program will explore this interface between automorphic forms and combinatorial representation theory, and will develop computational tools for facilitating investigations. On the automorphic side, Whittaker functions on p-adic groups and their covers are the fundamental objects. Whittaker functions and their relatives are expressible in terms of combinatorial structures on the associated L-group, its flag... (more)