Mura Yakerson
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".
I did my PhD under supervision of Marc Levine
at the
Duisburg-Essen University.
And here is a story how my PhD program started: Jail-dreaming
"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
My News
- Motives and What Not: next edition of our Zoom mini-conference happens on May 20!
- A bank robbery helps to compute the Motive of the Hilbert
scheme of infinite affine space!
- On 27 April I will give a talk on the Algebra/Topology seminar in Copenhagen.
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.
- On 13th May I will give a talk in the Algebraic Geometry and Moduli Zoominar in ETH.
Title: The Hilbert scheme of infinite affine
space
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.
Events
- During 16 March - 10 April I would take part in the program "K-theory,
algebraic cycles and motivic homotopy theory" at INI.
- During 10 February - 6 March I was a research member of the program "Higher Categories
and Categorification" at MSRI.
- ICM 2022 will happen in St. Petersburg, with visa-free entry for all participants!