# Algebraic Geometry Seminar

#### Boundedness Properties for Birational Automorphisms

**Speaker:**
Constantin Shramov, Higher School of Economics, Moscow

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, April 16, 2015, 2:30 p.m.

**Synopsis:**

An old theorem due to H.Minkowski says that the orders of finite subgroups of the group GL_{N}(Q) are bounded by a constant that depends only on N. Another classical result (due to C.Jordan) is that for any finite subgroup G of GL_{N}(C) there is an abelian subgroup whose index in G is bounded by a constant that depends only on N. It is partially known and partially expected that birational automorphism groups of many varieties over Q and C, respectively, enjoy similar properties. I will survey the relevant results including low-dimensional cases, higher dimensional cases modulo standard conjectures of birational geometry, and explicit estimates for relevant constants.