Welcome to my home page!
This academic year I'm a postdoc at Regensburg University,
in the research group of Marc Hoyois.
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.
We are partly supported by SFB 1085 "Higher invariants".
"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
Title: Modules over algebraic cobordism
Abstract: When k is a field with resolution of singularities, it is known that Voevodsky’s category of motives DM(k) is equivalent to the category of modules over the motivic cohomology spectrum HZ. This means that a structure of an HZ-module on a motivic spectrum is equivalent to a structure of transfers in the sense of Voevodsky. In this talk, we will discuss an analogous result for modules over the algebraic cobordism spectrum MGL. Concretely, a structure of an MGL-module is equivalent to a structure of coherent transfers along finite syntomic maps, over arbitrary base scheme. Time permitting, we will see a generalization of this result to modules over other motivic Thom spectra, such as the algebraic special linear cobordism spectrum MSL. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.
Title: The Gm-stabilization conservativity
Abstract: Classically, the functor from pointed spaces to the derived ∞-category of abelian groups, sending a space to its singular chain complex, is conservative on simply connected spaces. This fact is an important tool in the unstable homotopy theory, since it reduces homotopy-theoretic questions to questions in homological algebra, which are in general more accessible. In this talk, we discuss an analogous conjecture in motivic settings and our partial progress towards proving it. This is joint work with Tom Bachmann.