American Institute of Mathematics, Palo Alto, California
Jarod Alper, Maksym Fedorchuk, Brendan Hassett, and David Smyth
A fundamental problem in algebraic geometry is the problem of constructing a moduli space for a nice class of varieties (e.g. smooth curves, smooth polarized K3 surfaces) and of finding a geometrically meaningful compactification for this moduli space. Once a compactification is constructed, one applies the methods of deformation theory and projective geometry to study, respectively, the local and the global geometry of the moduli space. Compactifications of moduli spaces of smooth objects can be constructed using different methods, including stack-theoretic methods, Geometric Invariant Theory (GIT), and the MMP. The principal focus of the workshop will be to use the minimal model program as a framework for understanding the relationships between these different compactifications.
More specifically, the main topics for the workshop are:
An important goal of the workshop will be to consolidate and disseminate the variety of different techniques, heuristics, and approaches that has been applied to these problems in recent years.
The workshop schedule.
A report on the workshop activities.