The PM-seminar takes place on Wednesday at 2pm in McCrea 219.

Here is a campus plan.

September 26:

Abstract: The graph of isogenies of supersingular elliptic curves has many

applications in computational number theory and public key

cryptography. I will present some of these applications and I will also

discuss some open problems.

October 3:

Abstract: We will introduce the concepts mentioned in the title, explain why they

are interesting and show a connection between them. Thereby we will see examples

of simple locally compact groups without lattices; finitely generated, simple amenable

groups and the famous Higman-Thompson groups.

October 10:

Abstract: There are (at least) 3 competing notions of "dimension" for discrete groups:

cohomological dimension, geometric dimension (the smallest dimension of a classifying

space), and Lusternik-Schnirelmann category (of a classifying space). Theorems of

Eilenberg-Ganea and Stallings and Swan from the 1950’s and 60's imply that these all

coincide, except for the possible existence of a group with cat=cd=2 and gd=3.

I will discuss equivariant generalisations of these theorems to the setting of groups with

operators. The statements involve Bredon cohomological dimension with respect to families

of subgroups, which I'll define during the talk.

October 17:

Abstract: Ashot Minasyan and I construct groups that establish the result in the title,

resolving a question that has been around for almost 30 years. I will start by explaining

the phrases `CAT(0)' and `biautomatic'. After that I will talk about our groups and why

they have the properties that we claim.

October 18:

(!!note change of day, time and venue!!)

October 31:

November 7:

Abstract: We will consider some questions in classical knot theory, and see how surfaces

play a part. In particular, we will look at how knot theory compares with the physical

world, and how hard it is to untangle a knot.

November 14:

November 21:

November 28:

December 5:

December 12: