Welcome to my home page!

I'm a 3rd year math PhD student in Marc Levine's group

at the University of Duisburg-Essen, in Germany.

The focus of our research group is motivic homotopy theory,

which applies powerful methods of algebraic topology

to shed light on mysteries of algebraic geometry.

"The more I learned, the more conscious did I become of the fact that I was ridiculous. So that for me my years of hard work at the university seem in the end to have existed for the sole purpose of demonstrating and proving to me, the more deeply engrossed I became in my studies, that I was an utterly absurd person."

Fyodor Dostoevsky, The Dream of a Ridiculous Man

- On 28th June Tom Bachmann will report on our joint work in progress on the conference "Motivic Homotopy Groups of Spheres III".

Title: Generalized cycle complexes

Abstract: Given a strictly homotopy invariant sheaf M and smooth scheme X, we define for q≥0 a complex of abelian groups

C*(X, M, q) which combines a Bloch-Levine style cycle complex with coefficients in M with part of the Rost-Schmid complex of M. Using moving lemmas for the Rost-Schmid complex, we show that C*(X,
M, q) is quasi-isomorphic to M^{(q)}(X), the q-th layer of the homotopy coniveau tower for M. This allows us to produce a cycle-style complex computing the generalized motivic cohomology
groups of X in the sense of Calmès-Fasel, among other applications.

- On 6th July I will give a talk in the SFB-Seminar at Regensburg University.

**Title**: Motivic stable homotopy groups via framed correspondences**
Abstract**: A modern approach to the motivic stable homotopy category allows
one to express its mapping spaces in terms of geometric data called "framed correspondences". We will explain this approach and illustrate it by
computing Gm-homotopy groups of the special linear algebraic cobordism spectrum MSL.

- On 25-29 June I will be participating in Homotopy Theory Summer in Berlin.

- On 9-13 July I will learn about Homotopy
theory and Arithmetic geometry in London.

- On 13-17 August I will attend Equivariant and motivic homotopy
theory in Cambridge.

- On 3-14 September I will be enjoying Motives in St. Petersburg!