Duality Workshop: A MathPhysics Collaboration
Coordinators: Ron Y. Donagi, Albrecht Klemm, Burt Ovrut, Eric Zaslow
The Duality Workshop: A Math/Physics Collaboration, is a four week program to be held at the Institute for Theoretical Physics of the University of California, Santa Barbara from June 18July 13, 2001. The program will focus on the interplay between physics and mathematics in string and Mtheory, aiming to create an atmosphere mutually beneficial to members of the two communities. There will be a series of short courses on specific topics, interspersed with specialized seminars. The short course lecturers, and the titles of their minicourses, are
Week 1, Tuesday 6/19  Friday 6/22:

Ashoke Sen: DBranes as Solitons
Dan Freed: The Geometry and Topology of pForm Gauge Fields
Week 2, Monday 6/25  Thursday 6/28:

Paul Aspinwall: DBranes on CalabiYau Varieties
Greg Moore: DBranes, RRFields and KTheory
Week 3, Monday 7/2  Friday 7/6:

Discussion groups and informal seminars
Week 4, Monday 7/9  Thurday 7/12:

Mark Gross: Geometrical Approaches to Mirror Symmetry
Hiraku Nakajima: Equivariant Ktheory of Moduli of Sheaves on ALE Spaces
WORKSHOP TOPICS:
The emphasis of the workshop will be on combining the resources of mathematicians and physicists to better interpret and explore geometric concepts and the dualites originating in string theory, M and Ftheory and quantum field theory. These developments offer new insights into the structure of string theory at strong coupling, which may ultimately lead to a better nonperturbative formulation and improved phenomenology. Mathematically, they have spawned new invariant quantities in differential and symplectic/algebraic geometries; novel techniques for computation; and new categories. The joint effort at the workshop should help to sharpen the definitions of these subjects and to explore more of their physical and mathematical consequences.
Most notably, the following dualities stand at the fore: mirror symmetry; heterotictype II and field theory dualities; heteroticMtheory and heteroticFtheory dualities; and the AdSCFT correspondence. These represent not only new views of physical theories and their phenomenologies, but new connections between the mathematical objects they employ. Scanning these dualities, one easily arrives at a list of relevant mathematical topics: GromovWitten theory at higher genus and/or with boundaries; derived categories and symplectic(Fukaya) categories; specialLagrangian submanifolds and fibrations; new integrable systems; spectral curves and Gbundles over fibrations; SeibergWitten invariants. In addition, there are a number of geometric concepts that are directly relevant to important physical issues. These include supergravity solutions and superconformal algebras; Ktheory of nonBPS solitons; construction of holomorphic bundles subject to topological constraints. Some physics counterparts are: nonperturbative mirror symmetry; Yukawa couplings and effective actions; Dbrane and boundary state couplings, and moduli spaces; BPS state counting in M(atrix) theory and Ftheory; string vacua and supergravity compactifications; construction of realistic particle physics vacua.
THE PROGRAM:
During the first two weeks of the workshop, corresponding to the overlap period with the Mtheory program, and also during the last week, there will be two minicourses per week, each 46 hours in length. These courses will cover the most uptodate topics in Math/Physics, such as Ktheory, mirror symmetry and bundle theory, each taught by an expert in the field. These courses will be interspersed with specialized seminars covering an unrestricted range of topics. In the holiday shortened third week, we will be less formal, holding discussion groups and informal seminars on particularly interesting, new and "hot" topics. Throughout the workshop we will try to initiate new Math/Physics collaborative research efforts through such discussions.
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