Maria Yakerson
Welcome to my home page!
I'm a 3rd year math PhD student in Marc Levine's group
at the University of Duisburg-Essen, in Germany.
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.
"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
-
ICM 2022 will happen in St. Petersburg, with visa-free entry for all
participants!
- Tom Bachmann will report on our joint work in progress during the conference "Motives in St Petersburg".
Title: From strictly homotopy invariant sheaves to
effective homotopy modules
Abstract: Let SHS1(k) and SH(k) denote the motivic S1- and
P1-stable homotopy categories, respectively. They are related by the
Gm-stabilization adjunction SHS1(k) <-> SH(k). Following Levine-Voevodsky, this adjunction can be factored further as
SHS1(k) <-> SHS1(k)(1) <-> ... <-> SH(k).
Each of the above categories has a t-structure, and all of the adjunctions are compatible with the t-structures
(i.e. the left adjoints are right-t-exact). In studying the effect of Gm-stabilization on the hearts, we are lead to the following
Conjecture: the functor SH(k)♥ -> SHS1(k)(n)♥ is an equivalence for n > 0.
Using the theory of framed transfers and the homotopy coniveau tower, we provide two pieces of evidence for this conjecture:
(1) the functor is fully faithful, and (2) if M is a strictly homotopy invariant sheaf, then M-2 is an effective homotopy module.
- On 6th July I gave a talk in the SFB-Seminar at Regensburg University.
Title: Motivic stable homotopy groups via framed correspondences
Abstract: A modern approach to the motivic stable
homotopy category allows one to express its
mapping spaces in terms of geometric data called "framed correspondences". We will explain this approach and illustrate it by computing Gm-homotopy
groups of the special linear algebraic cobordism spectrum MSL.
Events
- On 25-29 June I will be participating in Homotopy Theory Summer in Berlin.
- On 13-17 August I will attend Equivariant and motivic homotopy
theory in Cambridge.
- On 3-14 September I will be enjoying Motives in St. Petersburg!