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http://math.colorado.edu/seminars/ics/topo.ics
as the source.
Thunderbird
This is the departmental seminar on algebraic topology and related topics.
We usually have a semester theme, for which speakers from the department are invited to contribute talks, and external guest speakers who will give talks on current research in topology. The semester themes for Fall 2022 are "sheaves and logic" and "applied topology". The seminar website is here.
Hours and Venue: Tuesdays, 3:30pm - 4:30pm in MATH 350
A topological space is stratified when it is equipped with a nice decomposition into nice subsets. In the classical case, the nice subsets are manifolds. When the decomposition is nice enough, one can equip the stratified space with a stratified tangent bundle.
"Is there a category of stratified spaces whose fiber bundles include these stratified tangent bundles?" Motivated by this question, we will investigate categories of stratified spaces. In particular, we will consider cases where the underlying stratification can vary and cases where there is a fixed base stratification and find interesting topologies and group objects along the way.
Categories of Stratified Spaces
Tue, Sep. 30 1:30pm (MATH 3…
Jackson Morris (University of Washington)
X
The stable homotopy groups of spheres are an important and complicated invariant. However, there is a filtration which sorts the p-components of this group into vn-periodic layers, known as chromatic heights, which are themselves more computable. The height one piece is the only layer which we fully understand, and an invaluable tool to accessing v1-periodic stable homotopy is the BP<1>-based Adams spectral sequence.
In this talk, I will discuss joint work with Petersen and Tatum which focuses on the analogue of this problem in motivic homotopy theory. The key idea is that there are similar periodic layers in the stable homotopy of the motivic sphere. We compute the E1-page of the analogous BPGL<1>-based motivic Adams spectral sequence at all primes p and over a myriad of base schemes. Time permitting, I will discuss future directions in chromatic motivic homotopy theory.
Splittings of truncated motivic Brown-Peterson cooperations algebras
Categories of Stratified Spaces