This thorough and detailed exposition is the result of an intensive month-long course on
mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry …

Let R n be the ring of coinvariants for the diagonal action of the symmetric group S n. It is
known that the character of R n as a doubly graded S n-module can be expressed using the …

The local Gromov-Witten theory of curves is solved by localization and degeneration
methods. Localization is used for the exact evaluation of basic integrals in the local Gromov …

We address the nonperturbative structure of topological strings and c= 1 matrix models,
focusing on understanding the nature of instanton effects alongside with exploring their …

We demonstrate the equivalence of all loop closed topological string amplitudes on toric
local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons …

Gromov-Witten theory, Hurwitz numbers, and matrix models Page 341 Proceedings of Symposia
in Pure Mathematics Proceedings of Symposia in Pure Mathematics Volume 80.1 , 2009 …

In the past 20 years, compactifications of the families of curves in algebraic varieties X have
been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable …

In this paper, we propose a mathematical definition of a new “numerical invariants” of Calabi–
Yau 3-folds from stable sheaves of dimension one, which is motivated by the Gopakumar …

The main goal of the paper is to present a new approach via Hurwitz numbers to
Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of …

Elliptic and genus one fibered Calabi-Yau spaces play a prominent role in string theory and
mathematics. In this article we discuss a class of genus one fibered Calabi-Yau threefolds …