Principal Investigator: Alan D. Weinstein
A scientific symposium titled "Geometry and Theoretical Physics" will take place at the National Meeting of the Society for the Advancement 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 of the intersection of contemporary geometry and theoretical physics. Great strides have recently been made in our understanding of these subjects, including a complete determination of the Gromov-Witten theory (and Donaldson-Thomas theory) of local curves, and of toric Calabi-Yau threefolds, and new proofs of Witten's conjecture; announced results include the computation of the quantum cohomology of certain Hilbert schemes of basic importance, and a construction of the Equivariant Vertex, determining the Gromov-Witten theory of all toric threefolds. A number of important conjectures drive the field, including Chern-Simons/Gromov-Witten duality, the Donaldson-Thomas/Gromov-Witten correspondence, and the Crepant Resolution Conjecture. The speakers at this symposium will announce accomplishments and also discuss new directions of research. Specifically, Jim Bryan will discuss Topological Quantum Field Theories, Robin Wilson will discuss knots and three-manifolds, and Vincent Bouchard will discuss the Standard Model of particle physics, and its relation to geometry.
This symposium will enable and encourage students and other scientists to pursue research in areas related to the interaction of theoretical physics and mathematics, provide the opportunity for scientists to interact and foster collaboration and new research, and disseminate knowledge to a wide and extraordinarily diverse audience. While the reasons for organizing a scientific symposium on geometry and theoretical physics are many, there is additionally an acute need to do so for an audience of underrepresented minorities. There is at this time significant underrepresentation of minorities in the mathematical sciences; this underrepresentation is evidently severe in Gromov-Witten theory and other fields relating to the interactions of geometry and physics. There are very important questions that need to be addressed in Gromov-Witten theory, and it is necessary to attract a broad and diverse audience to work on these problems. Gromov-Witten theory and related fields have been extremely successful in solving outstanding problems, some over 100 years old, in several branches of mathematics and physics. It is predicted that underrepresented minorities will become the majority of United States Citizens; as such, it is in the long term interest of geometry and physics to have increased participation from members of these groups. Moreover, given the importance of geometry and theoretical physics to mathematics and science in general, it is in our National interest to work against the underrepresentation of minorities conducting research in these fields. This symposium has been approved and scheduled by SACNAS. In addition, funding has been secured from SACNAS to cover the speakers' and organizers' travel, lodging and conference registration fees. The funding requested in this proposal will be used for student support.
Further information about mathematics at SACNAS in general, and about this symposium in particular, can be found, respectively, at www.uprh.edu/~sacnas/ and http://math.berkeley.edu/~dkarp/sacnas.
