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 space of algebraic cobordism
Abstract: Classically, the universal oriented cohomology theory is represented by the complex cobordism spectrum MU, which has a description in terms of cobordism spaces of compact smooth manifolds with an extra structure. In motivic settings, there is an analogous spectrum MGL, constructed by Voevodsky. In this talk we will discuss a model for the infinite loop space of MGL as an algebro-geometric incarnation of the cobordism space. Time permitting, we will discuss some applications, in particular a recognition principle for
MGL-modules. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.
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.