The Talbot workshop program is a series of yearly workshop retreats bringing together graduate students, recent PhDs, and faculty mentors for an intense exploration of a topic of active mathematical research. Past workshops have been devoted to Topological Modular Forms (mentored by Michael Hopkins), Automorphisms of Manifolds (mentored by Michael Weiss), Geometric Langlands (mentored by David Ben-Zvi), and Geometric Models of Elliptic Cohomology (mentored by Stephan Stolz). Dennis Gaitsgory will mentor the 2008 Talbot workshop, Affine Lie Algebras and Chiral Structures, which will focus on geometric approaches to the representation theory of affine Lie algebras and quantum groups using Beilinson and Drinfeld's theory of chiral algebras. Chiral algebras are certain structured D-modules on curves that encode the data of the operator product expansion of a conformal field theory; they provide a flexible geometric analogue of the theory of vertex algebras for describing the symmetries of conformal field theories. In recent work of Gaitsgory and Jacob Lurie, the theory of chiral algebras has been combined with ideas of homotopy theory and higher category theory to produce important new results in geometric representation theory. A particular focus of the workshop will be some of this work, in particular Gaitsgory-Lurie's derived version of the geometric Satake equivalence and a formulation of geometric Langlands duality for quantum groups.
The Talbot workshops seek to introduce aspiring mathematicians to active areas of mathematical research, foster community and collaboration across subdisciplinary and institutional lines, and form pedagogical and research ties between established mathematicians and young researchers. The topic for Talbot 2008 concerns the mathematical study of the symmetries that exist in fundamental physical theories. Understanding the structure of these symmetries lead to understanding the conservation principles, such as the conservation of energy, that define physical theories. The study of symmetries from recent quantum physics have led to new algebraic structures defining these symmetries. The 2008 workshop will introduce participants to recent work on these algebraic structures. The workshop will bring together graduate students and junior faculty with different specialties and from many universities to spend a week focused on this important subject. The participants and their mentor, Dennis Gaitsgory, will share a residence as well as lectures, discussions, and meals. This informal atmosphere, mixing fellowship and intellectual interest, will promote a concentrated study of the material and lay the foundation for future collaboration and research.
