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
Title: From strictly homotopy invariant sheaves to
effective homotopy modules
Abstract: Let SH^{S1}(k) and SH(k) denote the motivic S^{1}- and
P^{1}-stable homotopy categories, respectively. They are related by the
Gm-stabilization adjunction SH^{S1}(k) <-> SH(k). Following Levine-Voevodsky, this adjunction can be factored further as
SH^{S1}(k) <-> SH^{S1}(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)^{♥ }-> SH^{S1}(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.
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.