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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