Abstract:
 The method of toric varieties provides a powerful tool for the construction of many interesting algebraic varieties. Difficult equations are reduced to easy combinatorics. Many interesting examples are constructed by this method. It is also very useful for explicitly calculating difficult invariants such as GromovWitten invariants. Toroidal varieties appear everywhere. I will explain how the derived categories of toric varieties behave nicely under birational transformations in the minimal model program. As an application, I will explain McKay correspondence for finite abelian groups.
