# University of Toronto's Symplectic Geometry Seminar

January 15, 2007, 12:10pm

BA 6183

## Nicholas Proudfoot

### Columbia University

## Toric and hypertoric combinatorics

**Abstract: **
I will discuss three classes examples in which the geometry of
an algebraic variety illuminates a certain combinatorial object. The
first example will involve the classical relationship between toric
varieties and polytopes. The next two examples will deal with a
relatively new class of spaces called hypertoric varieties. These may be
thought of as quaternionifications of toric varieties, and they interact
richly with the combinatorics of matroids, or of finite collections of
hyperplanes in a vector space.