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
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.
Title: Higher Chow-Witt groups
Abstract: Algebraic K-theory of smooth schemes is built out of blocks given by motivic cohomology, via a spectral sequence. Motivic
cohomology groups, defined as hypercohomology groups of a motivic analogue of the singular chain complex, have a beautiful geometric presentation in terms of algebraic cycles, by higher Chow
groups. For hermitian K-theory there is a similar spectral sequence, however in this case the spectral sequence has additional terms, given by the Milnor-Witt motivic cohomology of Calmès-Fasel.
In this talk, we provide a geometric presentation of MW-motivic cohomology in the flavour of higher Chow groups. The main ingredient is our computation of Levine’s homotopy coniveau tower for
“discrete” motivic spectra. This is joint work with Tom Bachmann.