Mirror Symmetry in the Midwest 2012

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

This proposal is for a conference entitled Mirror Symmetry in the Midwest II to be held at University of Wisconsin from November 8-11, 2012, which is a continuation of the one held in Kansas State University in November 2011. Mirror symmetry is a relatively new subject that has attracted a great deal of attention over the past two decades. Mirror symmetry has its roots in string theory and is the study of a duality between the complex and symplectic geometry of certain objects. The number of ways to approach the subject has grown vast over the years and today many researchers can be said to be studying a subject inspired in some way by mirror symmetry. The rapidly expanding field of mirror symmetry has inspired a great deal of the research in complex, algebraic and symplectic geometry over the past twenty years. These ideas--the algebraic and geometric theories inspired by mirror symmetry--form the scientific focus of the conference. Important innovations include Gromov-Witten invariants, Fukaya categories and tropical geometry. In addition, mirror symmetry has cast renewed attention on and greatly expanded the scope of existing disciplines--Floer theory, derived categories, and special Lagrangian geometry are a few examples. An explanation of mirror symmetry would not only provide a link between complex and symplectic geometry, but it would also have a deep impact on a wide range of current subjects. The goal of the proposed conference is to bring together researchers studying a wide range of aspects of mirror symmetry. The conference will lead to increased collaboration among researchers in the Midwest and special attention will be paid to recruiting participants from the Midwest to further this aim. An important additional point of the conference is to bring in experts from outside the region. The conference will attract a wide range of participants with a diversity of backgrounds. An essential feature of the conference will be education. A portion of the talks will constitute a ``mini-course'', aimed at graduate students and non-experts and intended to give an introduction to some aspect of the field. The goals of the mini-course are two fold: One, to open and facilitate lines of communication between researchers with different areas of expertise; and two, to get graduate students involved, excited and actively participating in the scientific activities of the conference. In addition to the impacts highlighted above--increasing collaboration among researchers in the Midwest and teaching graduate students and young researchers about the subject--it is hoped that the conference will lead to the founding of an annual Midwest mirror symmetry conference. Another intent of the the conference is to expand the regional ties between University of Wisconsin group of mathematicians working on the areas related to mirror symmetry and the M-Center (Mirror Symmetry Center) at Kansas State University. Mirror symmetry has its roots in high-energy physics and string theory and the mathematics involved has an impact on these sciences. To take advantage of these ties, the conference will feature physicists and mathematicians. More information can be found on the conference website http://www.math.wisc.edu/~oh/uw-ksu-index.html