Preface
The conference ‘String-Math 2011’ was held June 6-11, 2011 at the University
of Pennsylvania, as the first in a new annual series of large meetings exploring the
interface of mathematics and string theory. This volume presents the proceedings
of that conference.
The nature of interactions between mathematicians and physicists has been
thoroughly transformed in recent years. String theory and quantum field theory
have contributed a series of profound ideas which gave rise to entirely new math-
ematical fields and revitalized older ones. The influence flows in both directions,
with mathematical techniques and ideas contributing crucially to major advances
in string theory. By now there is a large and rapidly growing number of both math-
ematicians and physicists working at the string-theoretic interface between the two
academic fields.
For mathematics, string theory has been a source of many significant inspira-
tions, ranging from Seiberg-Witten theory in four-manifolds, to enumerative ge-
ometry and Gromov-Witten theory 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.
Despite these profound and wide-ranging interactions, there was no major con-
ference bringing together the leading mathematicians and mathematically-minded
physicists working in this interface. We initiated the String-Math series of con-
ferences and organized String-Math 2011 to fill this gap. Our intention was that
this conference would be a vehicle for promoting such interactions, giving attendees
greater opportunities to cross cultural boundaries, learn aspects of other fields rel-
evant for their research, and advertise important developments to audiences that
might not otherwise hear of them or appreciate their importance.
The conference covered a wide array of topics at the interface of mathematics
and high energy physics, including, in no particular order,
Homological mirror symmetry
Categorical constructions of topological field theories
Mathematical string phenomenology
F-theory
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