Welcome to my home page!
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
Title: The Gm-stabilization conservativity conjecture
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.
Title: Encoding transfers in motivic homotopy theory
Abstract: Voevodsky’s approach to constructing the (derived) category of motives starts with introducing so called presheaves with transfers. Later Calmès and Fasel added extra data of quadratic forms to this construction, by considering presheaves with Milnor-Witt transfers. We will show that these transfers are examples of a more general construction of E-transfers, defined for any motivic ring spectrum E. We will also discuss relation of E-transfers with framed transfers, and some consequences for understanding the category of E-modules. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.