Conference on Geometry and Theoretical Physics

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AbstractAward: DMS-0640282Principal Investigator: Alan D. WeinsteinA scientific symposium titled "Geometry and Theoretical Physics"will take place at the National Meeting of the Society for theAdvancement of Chicano and Native Americans in the Sciences(SACNAS) in Tampa, Florida on October 27, 2006. Mirror Symmetry,Quantum Cohomology and Gromov-Witten theory lie at the heart ofthe intersection of contemporary geometry and theoreticalphysics. Great strides have recently been made in ourunderstanding of these subjects, including a completedetermination of the Gromov-Witten theory (and Donaldson-Thomastheory) of local curves, and of toric Calabi-Yau threefolds, andnew proofs of Witten's conjecture; announced results include thecomputation of the quantum cohomology of certain Hilbert schemesof basic importance, and a construction of the EquivariantVertex, determining the Gromov-Witten theory of all toricthreefolds. A number of important conjectures drive the field,including Chern-Simons/Gromov-Witten duality, theDonaldson-Thomas/Gromov-Witten correspondence, and the CrepantResolution Conjecture. The speakers at this symposium willannounce accomplishments and also discuss new directions ofresearch. Specifically, Jim Bryan will discuss TopologicalQuantum Field Theories, Robin Wilson will discuss knots andthree-manifolds, and Vincent Bouchard will discuss the StandardModel of particle physics, and its relation to geometry.This symposium will enable and encourage students and otherscientists to pursue research in areas related to the interactionof theoretical physics and mathematics, provide the opportunityfor scientists to interact and foster collaboration and newresearch, and disseminate knowledge to a wide and extraordinarilydiverse audience. While the reasons for organizing a scientificsymposium on geometry and theoretical physics are many, there isadditionally an acute need to do so for an audience ofunderrepresented minorities. There is at this time significantunderrepresentation of minorities in the mathematical sciences;this underrepresentation is evidently severe in Gromov-Wittentheory and other fields relating to the interactions of geometryand physics. There are very important questions that need to beaddressed in Gromov-Witten theory, and it is necessary to attracta broad and diverse audience to work on theseproblems. Gromov-Witten theory and related fields have beenextremely successful in solving outstanding problems, some over100 years old, in several branches of mathematics and physics. Itis predicted that underrepresented minorities will become themajority of United States Citizens; as such, it is in the longterm interest of geometry and physics to have increasedparticipation from members of these groups. Moreover, given theimportance of geometry and theoretical physics to mathematics andscience in general, it is in our National interest to workagainst the underrepresentation of minorities conducting researchin these fields. This symposium has been approved and scheduledby SACNAS. In addition, funding has been secured from SACNAS tocover the speakers' and organizers' travel, lodging andconference registration fees. The funding requested in thisproposal will be used for student support.Further information about mathematics at SACNAS in general, andabout this symposium in particular, can be found, respectively,at http://www.uprh.edu/~sacnas/ andhttp://math.berkeley.edu/~dkarp/sacnas.