Mura Yakerson
Welcome to my home page!
This semester I'm a postdoc at the Osnabrück University,
in the research group of Oliver
Röndigs and Markus Spitzweck.
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.
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 13th March I turned 25 and graduated! Here is my thesis.
- I organized a seminar in Osnabrück on "Norms in motivic homotopy theory" (after Tom Bachmann and Marc Hoyois).
- On 19th June I will give a talk in the Algebra and Topology Seminar of Strasbourg University.
Title: The space of algebraic cobordism
Abstract: Classically, the universal oriented cohomology theory is represented by the complex cobordism spectrum MU, which has a description
in terms of cobordism spaces of compact smooth manifolds with an extra structure. In motivic settings, there is an analogous spectrum MGL, constructed by Voevodsky. In this talk we will discuss a
model for the infinite loop space of MGL as an algebro-geometric incarnation of the cobordism space. Time permitting, we will discuss some applications, in particular a recognition principle
for
MGL-modules. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.
- On 27th June I will give a talk in the "Algebraic K-theory" workshop at Oberwolfach Institute.
Title: Higher Chow-Witt groups
Abstract: Algebraic K-theory of smooth schemes is built out of blocks given by motivic cohomology, via a spectral sequence. Motivic
cohomology groups, defined as hypercohomology groups of a motivic analogue of the singular chain complex, have a beautiful geometric presentation in terms of algebraic cycles, by
higher Chow groups. For hermitian K-theory there is a similar spectral sequence, however in this case the spectral sequence has additional terms, given by the Milnor-Witt motivic
cohomology of Calmès-Fasel. In this talk, we provide a geometric presentation of MW-motivic cohomology in the flavour of higher Chow groups. The main ingredient is our computation of
Levine’s homotopy coniveau tower for “discrete” motivic spectra. This is joint work with Tom Bachmann.
Events
- 9-12 July I will spend in the Institute of Math in Warsaw, visiting Joachim Jelisiejew.
- During July 18-31 Elden, Marc, Adeel and I will be staying at IAS as Summer collaborators.
- On 9-13 September I will be an invited speaker at the conference "Emerging research in algebraic groups, motives and K-theory"
in Euler Institute, St. Petersburg.
- ICM 2022 will happen in St. Petersburg, with visa-free entry for all participants!