The American Mathematical Society (AMS) invites mathematicians just beginning their research careers—those who are close to finishing their doctorates or have recently finished— to become part of Mathematics Research Communities, a unique and successful program that builds social and collaborative networks to inspire and sustain each other in their work. Women and underrepresented minorities are especially encouraged to participate. The structured program engages and guides all participants as they start their careers.
"It was empowering and created a more lasting learning experience because participants created their own knowledge based on the well-organized background, building blocks, and current research ideas presented by the conference organizers. Great conference!" --- MRC 2011 participant
The program includes:
Those accepted into this program will receive support (full room and board at Snowbird and up to US$630 in air transportation) for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2013. The summer conferences of the MRC are held in the breathtaking mountain setting of the Snowbird Resort, Utah, where participants can enjoy the natural beauty and a collegial atmosphere. This program is supported by a grant from the National Science Foundation.
June 10 - 16, 2012 - Discrete and Computational Geometry
Satyan Devadoss, Williams College
Vida Dujmovic, Carleton University
Joseph O'Rourke, Smith College
Yusu Wang, The Ohio State University
Discrete geometry is a relatively new focus within pure mathematics, while computational geometry is an emerging area in applications-driven computer science. The field has expanded greatly from its origins, and the new connections to areas of mathematics (such as computational topology) and new application areas (such as mathematical biology) seems only to be accelerating. The fundamentals cover polygons, convex hulls, triangulations, Voronoi diagrams, curves, and polyhedra. And even within this traditional core, many unresolved questions remain. This material is accessible to graduate students at nearly all levels since one needs little background to reach some of the most beautiful and intriguing questions in the field. Moreover, a strong intuition of this subject can be obtained and developed through visualization.
The organization of this MRC is based on three goals:
1. Introduce young mathematicians to the research world of discrete and computational geometry.
2. Introduce some key techniques in this area.
3. Most importantly, use the research talents and knowledge of the participants to attack open problems.
Due to the relative youth of the field, there are many accessible unsolved problems, and it is not too much to expect that we will make significant progress on several. This will be the heart of this MRC. We will close the workshop by sketching out possible papers, assigning lead writing, and mapping out potential conference and journal venues, along with plans for continuing our work together at future meetings.
June 17 – 23, 2012 - Partial Differential Equations, Harmonic Analysis, Complex Analysis, and Geometric Measure Theory
Dorina Mitrea, University of Missouri at Columbia
Irina Mitrea, Temple University
Katharine Ott, University of Kentucky
This workshop focuses on research problems at the interface between Complex Analysis, Harmonic Analysis, PDE, and Geometric Measure Theory. This choice is motivated by the fact that combinations of techniques originating in these fields have proved to be extremely potent when dealing with a host of difficult and important problems in analysis. Topics to be analyzed at the workshop include boundary value problems for single equations and systems of equations, the Poisson kernel for elliptic systems, and the boundary point principle for the Laplacian.
During the workshop, participants will have the opportunity to both review classical results and techniques related to these topics, and to research and work on various remaining open problems. The attendees of this research community will benefit by strengthening their background in these areas and by becoming aware of possible new avenues of research and collaboration.
June 17 – 23, 2012 - Geometry and Representation Theory Related to Geometric Complexity and Other Variants of P v. NP.
Shrawan Kumar, University of North Carolina, Chapel Hill
J. M. Landsberg, Texas A&M University
Jerzy Weyman, Northeastern University
The Geometric Complexity Theory program initiated by K. Mulmuley and M. Sohoni proposes to approach the P versus NP problem via algebraic geometry and representation theory. This program has already given rise to new problems in geometry and representation theory of interest in their own right.
Participants in this workshop will work on these open questions in groups while learning background material. The mathematics is centered on the geometry and representation theory associated to orbit closures. This includes determining the boundary, the extension problem, algebraic properties, and differential-geometric
This is a new and exciting area—using tools from geometry to work on problems in theoretical computer science.
June 24 – 30, 2012 - Arithmetic Statistics
Brian Conrey, American Institute of Mathematics
Chantal David, Concordia University
Wei Ho, Columbia University
Michael Rubinstein, University of Waterloo
Nina Snaith, University of Bristol
William Stein, University of Washington
L-functions, attached to modular forms and/or to algebraic varieties and algebraic number fields, are prominent in quite a wide range of number theoretic issues. Our recent growth of understanding of the analytic properties of L-functions has already led to profound applications regarding, among other things, the statistics related to arithmetic problems. Much of this exciting development involves a coming-together of arithmetic algebraic geometry, of automorphic forms and representation theory, of analytic number theory and of statistics, such as the statistical heuristics obtained from the contemporary work regarding random matrices.
This MRC conference will emphasize statistical aspects of L-functions, modular forms, and associated arithmetic and algebraic objects from several different perspectives--theoretical, algorithmic, and experimental. It will bring together graduate students and postdocs interested in modular forms, analytic number theory, arithmetic and algebraic geometry, mathematical physics, and computational number theory to investigate several problems in number theory from the point of view of understanding their limiting behavior. This MRC will offer an occasion for young mathematicians to learn about and contribute to research in this fast-moving subject.
Situated in a beautiful, breathtaking mountain setting, Snowbird Resort provides an extraordinary environment for the MRC. The atmosphere is comparable to the collegial gatherings at Oberwolfach and other conferences that combine peaceful natural ambience with stimulating meetings. MRC participants have access to a range of activities such as a tram ride to the top of the mountain, guided hikes, swimming, mountain bike tours, rock climbing, plus heated outdoor pools. More than a dozen walking and hiking trails head deep in the surrounding mountains. Participants also enjoy the simpler pleasures of convening on the patios at the resort to read, work, and socialize. In the evenings colleagues enjoy informal gatherings to network and continue discussion of the day's sessions over refreshments. Within a half hour of the University of Utah, Snowbird is easily accessible from the Salt Lake City International Airport. For more information about Snowbird Resort, see www.snowbird.com. InformationFor further information, please contact Ellen J. Maycock at firstname.lastname@example.org.