Conference on Low Dimensional Topology and Quantum Geometry, Kansas City, MO

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

A scientific symposium titled Low Dimensional Topology and Quantum Geometry will take place at the National Meeting of the Society for the Advancement of Chicano and Native Americans in the Sciences (SACNAS) in Kansas City, Missouri on October 12, 2007. The two a priori disparate fields of low dimensional topology and quantum geometry are related through theoretical physics and string theory. Exciting progress has recently been made in each of these subjects independently, including a proof of the Weinstein conjecture in dimension three, and the degree-0 Donaldson-Thomas/Gromov-Witten duality. Important open conjectures motivate continued study; these include notonly the higher-degree Gromov-Witten/Donaldson-Thomas conjecture and the general Weinstein conjecture, but also such important topics as the Volume conjecture, the Crepant Resolution Conjecture. Furthermore, and central to our symposium, there are important conjectures relating these two sub jects. Most notable is Large N duality, relating Gromov-Witten theory to knot theory and low dimensional topology. The speakers at this symposium will announce accomplishments and also discuss new directions of research. Specifically, Joel Kamnitzer will give an introduction to knot theory and its relation to derived categories, Mariel Vazqeuz will discuss applications of knot theory, and Kevin Costello will discuss connections to Algebraic Geometry and Gromov-Witten theory. This symposium will enable and encourage students and other scientists to pursue research in areas related to the interaction of quantum geometry and low dimensional topology, 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 low dimensional topology and quantum geometry 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 both low dimensional topology and quantum geometry and certainly the intersection of these subjects. There are very important questions that need to be addressed in these subjects, 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. Low dimensional topology is not only of basic importance in geometry and topology, but in several areas of applied mathematics as well, as highlighted in this symposium. It is predicted that underrepresented minorities will become the majority of United States Citizens; as such, it is in the long term interest of low dimensional topology and quantum geometry to have increased participation from members of these groups. Moreover, given the importance of these sub jects 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. Further information about mathematics at SACNAS in general, and about this symposium in particular, can be found, respectively, at http://www.uprh.edu/~sacnas/ and http://math.berkeley.edu/~dkarp/sacnas/2007.html.