fkranhold.de

Algebraic topology, music theory and more.

Current affiliation

I am a third year PhD student at the Mathematical Institute of the university of Bonn under the supervision of Carl-Friedrich Bödigheimer, in the area of algebraic topology. I am funded by the Max Planck Ins­titute for Mathematics in Bonn and am a member of the International Max Planck research school (IMPRS) on moduli spaces.

Research interests

My PhD project deals with various coloured topological operads, which allow arguments of ‘higher multiplicity’. Particular examples are clustered versions of May’s little cubes or of Tillmann’s surface operad. On the one hand, their free algebras are certain clustered configuration spaces which have been studied recently by Tran and Palmer. On the other hand, they act on moduli spaces of Riemann surfaces with multiple boundary curves. This gives rise to a system of operations on the homology of moduli spaces, helping us to understand unstable classes, and also exhibits ‘parametrised’ variants of the classical moduli spaces as infinite loop spaces in the spirit of Madsen and Weiss.

I am working together with Andrea Bianchi from the university of Copenhagen (former PhD student in Bonn) and Jens Reinhold from the university of Münster.

Teaching

In the upcoming summer term 2021, I will be tutor for the lecture Algebraic Topology 2 given by Carl-Fried­rich Bödigheimer. In the summer term 2020, I co-organised a graduate seminar on Operads in Algebra and Topology together with Andrea Bianchi. Moreover, I have been tutor for the following topology lectures:

winter 2020/21 Algebraic Topology 1 Carl-Friedrich Bödigheimer
summer 2020 Algebraic Topology 2 Christoph Winges
winter 2019/20 Algebraic Topology 1 Wolfgang Lück
summer 2019 Topology 2 Daniel Kasprowski
winter 2018/19 Topology 1 Wolfgang Lück
summer 2018 Einführung in die Geometrie und Topologie Wolfgang Lück

Preprints

Selected talks