Mura Yakerson
Welcome to my home page!
I'm a Hermann-Weyl-Instructor at ETH Zürich,
at the Institute for Mathematical Research (FIM).
My mentor is Rahul Pandharipande.
The focus of my research is motivic homotopy theory,
which applies powerful methods of algebraic topology
to shed light on mysteries of algebraic geometry.
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
- New title, new author, many new results: "The Hilbert scheme of infinite affine space and algebraic K-theory"
- Our online seminar on algebraic K-theory eAKTS will run on Tuesdays at 6 pm CEST in the fall!
-
Motives and What Not: videos of our four mini-conferences are available here.
- On 11th September I will give a talk at the online conference "Motivic Geometry", CAS, Oslo.
Abstract: Among various features of algebraic K-theory, there is known to be covariance with respect to finite flat morphisms of schemes. In this talk we will discuss, in which sense K-theory is universal as a cohomology theory with such covariance. As one of the applications, we will obtain Hilbert scheme models for the K-theory space and for higher spaces of the very effective K-theory spectrum kgl. Based on joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro, and on the work of Tom Bachmann.
- On 21st July I gave a talk on the MIT Topology seminar.
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.
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!