The Simons Center for Geometry and Physics, Stony Brook, USA is hosting a String-Math 2013 conference in June 17-21, 2013. (http://scgp.stonybrook.edu/events/event-pages/string-math-2013) This is a third annual meeting of String-Math series of conferences. The main goal of the conference is to bring together mathematicians and physicists who work on ideas related to string theory. String theory, as well as quantum field theory, has contributed a series of profound ideas which gave rise to entirely new mathematical fields and revitalized older ones. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to advances in symplectic topology, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to the use of modular forms and other arithmetic techniques. The depth, power and novelty of the results obtained in both fields thanks to their interaction is truly mind boggling. String-Math is the annual conference that was founded to reflect the most significant progress at the interface of string theory and mathematics.

String theory is the attempt to build a mathematical model which describes all four fundamental forces and all forms of matter. It assumes that the fundamental objects of the theory are one-dimensional objects - "strings" with elementary particles (i.e., electrons and quarks) being oscillations of fundamental strings. In particular, string theory aims to reconcile gravity, i.e., general relativity, with quantum mechanics which is the formalism in which the other three forces are described. String theory is very mathematical in nature and its development was based on advances in modern mathematics and inspired many recent developments in mathematics. The main goal of the String-Math conference is to bring together mathematicians and physicists who work on ideas related to string theory. By now there is a large and rapidly growing number of both mathematicians and physicists working at the string-theoretic interface between the two academic fields. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. Following the success of first two meetings of String-Math series the conference String-Math 2013 is expected to have a major impact on the field and to serve as a record of the state of the art in string-related mathematics.

Project Report

The goal of this project was to hold the third meeting of String-Math series of conferences in June 2013 at the Simons Center for Geometry and Physics. The main goal of the conference is to bring together mathematicians and physicists who work on ideas related to string theory. String theory, as well as quantum field theory, has contributed a series of profound ideas which gave rise to entirely new mathematical fields and revitalized older ones. By now there is a large and rapidly growing number of both mathematicians and physicists working at the string-theoretic interface between the two academic fields. The influence flows in both directions, with math- ematical techniques and ideas contributing crucially to major advances in string theory. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten the- ory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key par- tial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to the use of modular forms and other arithmetic techniques. The depth, power and novelty of the results obtained in both fields thanks to their interaction is truly mind boggling. The String Math Conference was held at the Simons Center for Geometry and Physics from June 17-21, 2013. The local organizing committee was comprised of: Aexander Abanov, Michael Douglas, Ljudmila Kamenova, Claude LeBrun, John Morgan, Nikita Nekrasov, Leonardo Rastelli, and Martin Rocek. The organizers were guided by a steering committee comprised of: Ron Donagi, Dan Freed, Nigel Hitchin, Sheldon Katz, Maxim Kontsevich, David Morrison, Edward Witten, Shing-Tung Yau as well as an International Advisory Committee comprised of: Mina Aganagic, Michael Atiyah, Niklas Beisert, Jean-Pierre Bourguignon, Kevin Costello, Robbert Dijkgraff, Jacques Distler, Simon Donaldson, Edward Frenkel, Matthias Gaberdiel, Jerome Gauntlett, Rajesh Gopakumar, Antonella Grassi, Mark Gross, Chris Hull, Ludmil Katzarkov, Albrecht Klemm, Juan Maldacena, Marcos Marino, Greg Moore, , Hirosi Ooguri, Tony Pantev, Nicholas Read, Volker Schomerus, Ashoke Sen, Samson Shatashvili, Cumrun Vafa, Johannes Walcher, Katrin Wendland, Paul Wiegmann, Maxim Zabzine, and Eric Zaslow. The objectives of this conference were to bring together mathematicians and physicists who work on ideas related to string theory. String theory, as well as quantum field theory, has contributed a series of profound ideas which gave rise to entirely new mathematical fields and revitalized older ones. By now there is a large and rapidly growing number of both mathematicians and physicists working at the string-theoretic interface between the two academic fields. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geome- try, to work on the Jones polynomial in knot theory, to advances in symplectic topology, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to the use of modular forms and other arithmetic techniques. The depth, power and novelty of the results obtained in both fields thanks to their interaction is truly mind boggling. String-Math is the annual conference that was founded to reflect the most significant progress at the interface of string theory and mathematics. Topics Included: New and exotic supersymmetric field theories Localization and gauge theory Gauge theory and Khovanov homology Perturbative amplitudes Topological phases of matter Gauge theory angle at integrability Homological mirror symmetry Categorical constructions of topological field theories Mathematical string phenomenology Non-perturbative dualities, F-theory Wall-crossing formulas Hitchin systems Geometric Langlands Arithmetic of strings Gromov-Witten theory and enumerative geometry A-twisted Landau-Ginzburg models String topology Elliptic cohomology Heterotic mirror symmetry Topological T duality Superstring scattering amplitudes Chiral de Rham complexes Noncommutative geometry

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1305697
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
2013-05-15
Budget End
2014-07-31
Support Year
Fiscal Year
2013
Total Cost
$59,722
Indirect Cost
Name
State University New York Stony Brook
Department
Type
DUNS #
City
Stony Brook
State
NY
Country
United States
Zip Code
11794