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
- On my YouTube channel "Math-life balance" I post my interviews with colleagues about their experience in math.
New interviews appear on Fridays at 6 pm CEST!
-
New paper: hermitian K-theory obtains a new geometric model (which works even
in characteristic 2).
- Our seminar on algebraic K-theory eAKTS has restarted! We meet biweekly on Tuesdays at 6 pm CEST, videos appear here.
- On 27th April I will give a talk at the Topology seminar in Cornell University.
Abstract: Algebraic K-theory space, as a motivic space, has a known geometric model given by (Z copies of) the infinite Grassmannian. In the new geometric model that we offer, the infinite Grassmannian is replaced by the Hilbert scheme of the infinite affine space, stabilized with respect to degree. Although the geometry of the Hilbert scheme is much more complicated, this model leads to new insights on K-theory. For example, we obtain an analogous model for the hermitian K-theory space, given by the Hilbert scheme of finite Gorenstein subschemes that are equipped with an orientation. Turns out, this model works also in charactersitic 2, while the previously known model, given by the infinite orthogonal Grassmannian, represents hermitian K-theory only over a base where 2 is invertible. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.
- On 20th April I will give a talk at the Zurich Graduate Colloquim.
Title: What is... an infinity-category?
Abstract: In different areas of mathematics it is convenient to work with categories, i.e., with sets of objects (possibly united by some
property) and morphisms between them. However, when it comes to objects of topological nature, we often would like to consider the higher structure of morphisms between morphisms. For examples,
higher structures are relevant when we work with topological spaces, continuous maps and homotopies, or with smooth manifolds, their cobordisms and diffeomorphisms between them. A generalization
of a category that allows to encode the data of (infinitely many) higher morphisms is the notion of an infinity-category. In this talk, I will give a definition of an infinity-category and
explain some of the main ideas behind this concept, as well as provide various examples.
Events
- ICM 2022 will happen in St. Petersburg, with visa-free entry for all participants!