Mar 16 2016

### Weyl groups, and their generalizations, in enumerative geometry II

Speaker: Andrei Okounkov

4:00pm
These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In particular, we will meet the...

Mar 15 2016

### Weyl groups, and their generalizations, in enumerative geometry I

Speaker: Andrei Okounkov

4:00pm | S-101
These lectures will be about enumerative K-theory of curves (and more general 1-dimensional sheaves) in algebraic threefolds. In the first lecture, we will set up the enumerative problem and survey what we know and what we conjecture about it. In particular, we will meet the...

Nov 06 2014

### Ramanujan graphs of every degree

Speaker: Daniel Spielman

2:00pm | S-101
We explain what Ramanujan graphs are, and prove that there exist infinite families of bipartite Ramanujan graphs of every degree. Our proof follows a plan suggested by Bilu and Linial, and exploits a proof of a conjecture of theirs about lifts of graphs. Our proof of their...

Nov 05 2014

### The solution of the Kadison-Singer problem

Speaker: Daniel Spielman

2:00pm | S-101
We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function arguments to bound the roots of...

Nov 03 2014

### Sparsification of graphs and matrices

Speaker: Daniel Spielman

2:00pm | S-101
Random graphs and expander graphs can be viewed as sparse approximations of complete graphs, with Ramanujan expanders providing the best possible approximations. We formalize this notion of approximation and ask how well an arbitrary graph can be approximated by a sparse...

Nov 04 2011

### Chow Rings, Decomposition of the Diagonal and the Topology of Families

Speaker: Claire Voisin

3:30pm | S-101
Nov 03 2011

### Chow Rings, Decomposition of the Diagonal and the Topology of Families

Speaker: Claire Voisin

11:00am | S-101
Nov 02 2011

### Chow Rings, Decomposition of the Diagonal and the Topology of Families

Speaker: Claire Voisin

11:00am | S-101
Nov 01 2011

### Chow Rings, Decomposition of the Diagonal and the Topology of Families

Speaker: Claire Voisin

2:00pm | S-101
Summary: These lectures are devoted to the interplay between cohomology and Chow groups of a complex algebraic variety, and also to the consequences, on the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general fiber. A...