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


Title How homotopy theory helps to classify vector bundles
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.

TitleHilbert 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.