Welcome to my home page!

I'm a 4th 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

- We have posted a sequel to our work on motivic infinite loop spaces. Enjoy :)

- A preliminary, full-detailed version of (a part of) my PhD-thesis is now available here. Comments welcome!

- On 29th November I will give a talk in the Oberseminar at the University of Munich.

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, the analogous spectrum MGL was constructed by Voevodsky, and over a base field of
characteristic 0, its corresponding homotopy groups can be expressed via algebraic “cobordism groups” of varieties, as defined by Levine-Morel. In this talk we will discuss a model for the
underlying space of MGL as an algebro-geometric incarnation of the cobordism space. As an application, we will present a geometric description of this space as a (homotopy type of) some Hilbert
scheme. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.

- On 23rd October I will give a talk in the Topology seminar at the University of Osnabrück.

Title: How to encode 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.

- On 4th October I gave a talk in the Geometry seminar at the University of Oslo.

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 5th September I gave a talk during the summer school "Motives in St Petersburg".

Title: Framed transfers in motivic homotopy
theory

Abstract: In motivic settings, generalized cohomology theories acquire additional structure called “framed
transfers”. We will discuss this structure from different perspectives. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.

- On 3-14 September I enjoyed Motives in St.
Petersburg.

- On 15-16 November I will congratulate Max Karoubi with his
Birthday.

- ICM 2022 will happen in St. Petersburg, with visa-free entry for all participants!