Recent progress on moduli spaces and special varieties

Classifying and parametrizing manifolds and algebraic varieties is a natural and important problem in mathematics. For example, the moduli space of Riemann surfaces (equivalently algebraic curves, or hyperbolic surfaces) has been intensively studied since Riemann introduced the notion of moduli and counted its dimension. A closely related space is the moduli spaces of stable maps. The study of these moduli spaces involves many different subjects such as complex analysis, algebraic geometry, differential geometry, low dimensional topology, algebraic topology, mathematical physics, in particular string theory, and Lie algebras and generalizations.They also have lead to many spectacular applications, such as the Gromov-Witten theory.

Though algebraic varieties are special among topological spaces, some are more special than others. For example, K3 surfaces, Calabi-Yau manifolds, manifolds with special holonomy groups, locally symmetric varieties are jewels of algebraic varieties and manifolds. Of course, moduli spaces of these special varieties are also special varieties. Searching for their hidden properties and relations has played an important role in development of mathematics in the past decades.

This conference is one of the first workshops at the Tsinghua Sanya International Mathematics Forum. Its purpose is to bring experts on various aspects on moduli spaces in algebraic geometry and special varieties together in order to discuss recent progress and discover unexpected connections and applications. We hope and expect that interaction among participants in such a stimulating environment will promote cooperation between researchers from different areas, and that this conference will have a definite impact on further work on with these important spaces, making at the same time a younger generation of mathematicians acquainted with them.

Organizers

NameUniversity
Lizhen JiUniversity of Michigan, Ann Arbor
Eduard LooijengaUniversiteit Utrecht
Yat-Sun PoonUniversity of California, Riverside
Shing-Tung YauHarvard University