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
- "Math-life balance" is back, hurrah! New videos appear on Fridays at 6 pm
CET.
-
New paper: we compute slices of the motivic spectrum of twisted algebraic K-theory.
"Let's twist again!"
- It's bragging time: someone was awarded SwissMAP Innovator Prize 2021, for her joint work on Hilb(A∞)!
- On March 24th I will give a talk at Geometry Graduate Colloquium at ETH.
Abstract: Classically, topological vector bundles are classified by homotopy classes of maps into infinite Grassmannians. This allows us to study topological vector bundles using obstruction theory: we can detect whether a vector bundle has a trivial subbundle by means of cohomological invariants. In the context of algebraic geometry, one can ask whether algebraic vector bundles over smooth affine varieties can be classified in a similar way. Recent advances in motivic homotopy theory give a positive answer, at least over an algebraically closed base field. Moreover, the behaviour of vector bundles over general base fields has surprising connections with the theory of quadratic forms.
- On March 31st I will give a talk at the Arithmetic seminar in Lyon.
Title: Hilbert schemes of affine spaces
Abstract: Hilbert schemes of smooth surfaces are well-studied objects, however not much is known about Hilbert schemes of higher dimensional varieties. In this talk, we will speak about topological properties of Hilbert schemes of affine spaces. In particular, we will compute the homotopy type of the Hilbert scheme of infinite affine space. Time permitting, we will discuss a generalization of this computation for certain Quot schemes. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.
Events
- In May I will discuss Algebraic K-theory with my
colleagues and the cows of Schwarzwald.
- In June I will be part of "K-theory, algebraic cycles and motivic homotopy
theory" at the Newton Institute.
- ICM 2022 will no longer take place in St. Petersburg because Russian government is leading a horrible war in Ukraine.