About the RTG

• EMSW21 postdocs. Three-year postdoctoral positions funded jointly by NSF and the university, with a reduced teaching load of one course per semester, support for summer research in each of the first two years, and additional funds for travel and other research-related expenses. We currently have three EMSW21 postdocs, David Hill, Dagan Karp, and Joshua Sussan, and one more, Michael Rose, who will join us in Fall 2008. Future postdoc openings will depend on the possibility of renewing our current grant, which expires in 2009.
  
• Graduate student fellowships. Fellowship support is avaliable during the period 2004-2009 for a core group of 8 to 10 graduate students whose research interests belong to the areas covered by the RTG. RTG students normally receive six semesters of research fellowship support, and are expected to teach two semesters. Eligibility is limited to US citizens or permanent residents.
  
• Seminars. The RTG runs a joint research seminar, meeting weekly for two hours, featuring research talks by students, faculty and outside visitors. The usual format involves an overview talk in the first hour, followed by a short break and more technical discussion in the second hour. In addition, we run instructional seminars on topics not readily available in the standard courses. Instructional seminars typically feature talks primarily by students, concentrating on a single topic over the course of anywhere from several weeks to a whole semester.
  
• Summer workshops. Each summer from 2005 through 2009, the RTG expects to run a week-long workshop featuring series of lectures by distinguished invited speakers and local faculty members, intended for a graduate student and postdoctoral level audience. Participation is open to attendees from other institutions as well as from Berkeley. Funding is available to support travel by participants attending the workshops.

Faculty members associated with the RTG

The faculty members affiliated with the group are listed below with brief descriptions of their research interests.

Richard Borcherds: I used to work on vertex algebras, infinite dimensional Lie algebras, and automorphic forms. I am currently trying to figure out what a quantum field theory really is.

Edward Frenkel's research centers on representation theory of infinite-dimensional Lie algebras and quantum groups, integrable systems such as the KdV hierarchy, and the geometric Langlands correspondence.

Alexander Givental works in Gromov-Witten theory and its relationships with other subjects such as symplectic topology, singularity theory, mirror symmetry, integrable hierarchies, representations or combinatorics.

Mark Haiman works on combinatorial problems connected with symmetric functions, representations, and algebraic geometry. Some of his topics of current interest are Macdonald polynomials, LLT polynomials, Hecke algebra characters, and quantum groups.

Allen Knutson was a member of our original group, but has since moved to UC San Diego.

Martin Olsson works on problems in algebraic and arithmetic geometry. Much of his current work is on stacks and their applications to the study of moduli spaces, group actions, and arithmetic.

Nicolai Reshetikhin: In recent years many questions in representation theory, combinatorics and geometry appeared as problems at the interface of these subjects with mathematical physics. Some of them are: representation theory of infinite dimensional Lie algebras and quantum groups, combinatorics of weight multiplicities, invariants of knots and 3-manifolds, geometry of moduli spaces of flat G-bundles over surfaces, etc. This is roughly the direction of my research.

Vera Serganova: I work in representation theory. Right now I am mostly interested in geometric methods such as D-modules, localization and associated varieties. Also working on Lie superalgebras and quantum groups.

Bernd Sturmfels works on polyhedral combinatorics and algebraic geometry. He is particularly interested in computational aspects and applications (e.g. to statistics, optimization and biology).

Constantin Teleman works on problems in topology and algebraic geometry inspired by topological quantum field theories and 2D conformal field theory. Most of his work has centered around loop groups and bundles on Riemann surfaces. More recently, he has been interested in bundles on complex surfaces and Gromov-Witten theory.

Joseph Wolf works in Geometry, Group Theory and Complex Analysis. In recent years his research has been concentrated on the interplay between the theory of representations of semisimple Lie groups and the geometry of complex flag manifolds. He also works on unitary representations of certain types of infinite dimensional Lie groups.

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