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: New models for motivic K-theory spectra
Abstract: Algebraic and hermitian K-theories of smooth schemes are generalized cohomology theories, represented in the motivic stable homotopy category. In this talk, we explain how to obtain new geometric models for the corresponding motivic spectra, based on the specific kinds of transfer maps that these cohomology theories acquire. As a surprising side-effect, we compute the motivic homotopy type of the Hilbert scheme of infinite affine space. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin and Burt Totaro.
Title: The Hilbert scheme of infinite affine
Abstract: Various invariants have been computed for Hilbert schemes of surfaces, however our knowledge about Hilbert schemes (of points) of higher dimensional schemes is quite limited. For example, Hilbert schemes of n-dimensional affine spaces have very complicated geometry for high n. In this talk we will present the surprising observation, that the Hilbert scheme of infinite dimensional affine space has homotopy type of a Grassmannian, and so its invariants of homotopical nature have a simple description. We will explain then how this observation allows us to obtain new properties of algebraic and hermitian K-theories as generalized cohomology theories. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.