Abstracts for The Unterseminar

Algebraic K-theory is a rich invariant of rings with connections throughout mathematics. I will motivate and define the 0-th K-group with example computations. Next, we will take a detour through homotopy theory, which will allow us to construct the higher K-groups in a conceptually clear way. These higher groups are notoriously difficult to compute, a challenge I will illustrate through applications to number theory, arithmetic geometry, and/or topology, depending on time constraints and popular demand.

You might think that non-noncommutative geometry is just geometry. But what kind, really? In other words, what is the geometry that is generalised in noncommutative geometry (NCG)? I will try to answer this by giving a (slightly fake) history of NCG as originating from a combination of C*-algebra theory, spectral geometry (hearing the shape of a drum), and some K-theory. Depending on the time, I might then sketch some cool theorems in NCG and applications in mathematics and physics.

I will explain some ideas about sheaves, categorification and geometric representation theory following an n-category café post 'geometric function theory' written by David Ben-Zvi.