Mulase Motohico - Counting the lattice points on the moduli space of curves

In these lectures, Gromov-Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be explained. Some

We will give an introduction to Donaldson-Thomas theory and some basic tools and computations. In the last lecture, we hope to explain some aspects of the proof of the GW/DT correspondence for toric

In these lectures, Gromov-Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be explained. Some

Out of the quantum product of a projective smooth variety, we can construct a vector bundle with a at connection and a pairing, these data are called quantum D-modules. In a recent paper of

The counting function associated to the moduli space of stable pairs on a 3-fold X is conjectured to give the Laurent expansion of a rational function. For toric X , this conjecture can be

The Satake isomorphism identi es the irreducible representations of a semisimple algebraic group with the intersection cohomologies of the Schubert varieties in the a ne Grassmannian of

In these lectures, Gromov{Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be

Quantum K-theory is as quantum cohomology a generalisation of the classical coho- mology algebra of a variety X . In this talk I will explain the connection between the geometry of the moduli

In these lectures, Gromov{Witten theory will be introduced, assuming only basic moduli theory covered in the rst week of the School. Then the Crepant Transformation Conjecture will be

The topic concerns relations among the kappa classes in the tautological ring of the moduli space of genus g curves. After a discussion of classical constructions in Wick form, we derive an

We will give an introduction to Donaldson-Thomas theory and some basic tools and computations. In the last lecture, we hope to explain some aspects of the proof of the GW/DT

Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going