Eric Zaslow

Mirror symmetry is T duality

Abstract It is argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to T -duality on the 3-cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed.

BPS STATES, STRING DUALITY, AND NODAL CURVES ON K3

We describe the counting of BPS states of Type II on K3 by relating the supersymmetric cycles of genus g to the number of rational curves with g double points on K3. The generating function for the number of such curves is the left-moving partition function of the bosonic string.

Constructible sheaves and the Fukaya category

Let

Topological orbifold models and quantum cohomology rings

X

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories

be a compact real analytic manifold, and let

Solitons and helices: The search for a math-physics bridge

T^*X

Coisotropic branes, noncommutativity, and the mirror correspondence

be its cotangent bundle. Let

Legendrian knots and constructible sheaves

Sh(X)

A categorification of Morelli's theorem

be the triangulated dg category of bounded, constructible complexes of sheaves on

Dynkin diagrams of CP1 orbifolds

X