Department of Mathematics, University of Hawaii

2565 McCarthy Mall, Keller 401A

Honolulu HI 96822

The seminar is organized by Clément Dell'Aiera, Erik Guentner , and Rufus Willett ; please get in touch with one of us if you would like more information.

In Fall 2017, we (usually) meet 2:30-3:30 on Wednesday in Keller 403.

The Furstenburg boundary and injectivity

Abstract: Four weeks ago Matt introduced the notion of a G-boundary. Today I’ll prove that there is a maximal such G-boundary called the ‘Furstenburg boundary’, and that C*-algebra of continuous functions on the Fursternburg boundary is an injective C*-algebra in the sense of last week’s talk.

October 3: Rufus Willett

The Furstenburg boundary and injectivity

Abstract: Two weeks ago Matt introduced the notion of a G-boundary. Today I’ll prove that there is a maximal such G-boundary called the ‘Furstenburg boundary’, and that C*-algebra of continuous functions on the Fursternburg boundary is an injective C*-algebra in the sense of last week’s talk.

September 26: Rufus Willett

Injective C*-algebras

Abstract: Injective C*-algebras are analogues of injective modules from pure algebra. Although not immediately obvious why, they turn out to be very important in various aspects of the theory (particularly von Neumann algebras). I’ll aim to introduce injective C*-algebras and some of the underlying theory, and deduce some consequences.

September 19: Matthew Lorentz

G-C*-algebras

Abstract: I’m going to talk about groups acting on compact Hausdorff spaces X by homeomorphism and C*-algebras by automorphism. This will lead to showing that P(X) is weak* closed and G-invariant. Then an introduction to a G-boundary.

September 12: Clement Dell'Aiera

C*-simplicty continued.

Abstract: We give two proofs that if a group has a non trivial amenable normal subgroup, then it is not C*-simple. One uses induction for unitary representations, the other is direct but restricts to the discrete countable case.

September 5: Rufus Willett

C*-simplicty of discrete groups.

Abstract: A discrete group is called C*-simple if its reduced group C*-algebra C*_r(G) is simple. This roughly says (in stark contrast to the case e.g. of finite groups) that all subrepresentations of the regular representation of G on l^2(G) are equivalent to the regular representation itself. The inputs for proving that a particular group has this property come, however, not from representation theory but from geometric group theory and dynamics.

I’ll discuss some background to this, and the (non-)connection with amenability, and a little on the classic (‘Powers’) technique for proving it. In the next few weeks, we’ll discuss the recent work of Kennedy et al that completely solves the problem of characterizing C*-simple groups.

August 29: Benedikt Hunger (Ausburg University), Almost flat bundle

Bott periodicity

April 19: Samantha, Reading class on K-theory

April 12: Samantha, Reading class on K-theory

April 3: Matthiew, Reading class on K-theory

March 20: Matthew, Reading class on K-theory

Algebraic K-theory

March 16: Clément Dell'Aiera, Classification and the UCT

March 13: Kenny, Reading class on K-theory

Algebraic K-theory March 6: Kenny, Reading class on K-theory

Second K-theory group

February 27: Samantha, Reading class on K-theory

Clutching theorems

February 20: Samantha, Reading class on K-theory

Clutching theorems

February 13: Matthew, Reading class on K-theory

Definition of the first K-theory group

February 6: Matthew, Reading class on K-theory

Definition of the first K-theory group

January 30: Rufus Willett, Reading class on K-theory

Algebra continued

January 23: Rufus Willett, Reading class on K-theory

(Algebra) Review of projective modules, first definition of K(R) for a ring R.

What are the finitely genereated projective modules over C(X)? (X a Hausdorff compact space)

Definition of complex vector bundles. Example: the tangent budle of the 2-dimensional sphere.