# Thomas Nikolaus: Algebraic L-Theory

**Time: **
Tue 2022-02-22 14.15 - 16.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Thomas Nikolaus (University of Münster)

**Abstract:** In this talk we will give an introduction into algebraic L-Theory. This is an invariant of rings with involution \((R,\sigma)\). One has an L-theory spectrum \(L(R,\sigma)\) and the homotopy groups are called the L-groups, which can also be indepently described and are related to classical Witt-groups. There is a close relation between L-theory and K-theory that has been exploited in recent work in arithmetic situation. We will explain how the relation generally works. Specifically in the case of \(C^*\)-algebras one also comparisons between *topological* K-theory and algebraic L-theory which I will explain. The latter is based on joint work with M. Land and M. Schlichting.