Yuqing Shi

Research Interests

I'm a PhD student in algebraic topology, with a special interest in chromatic homotopy theory. Currently I'm studying unstable vn-periodic homotopy theory, with a focus on the structural properties of the Bousfield–Kuhn functors.

In my master's thesis, I studied the application of manifold calculus to the theory of Vassiliev knot invariants. Joint with Danica Kosanović and Peter Teichner, we are working on a geometric interpretation of the manifold calculus tower associated to the embedding space of knots, using the theory of capped gropes.

The theory of Goodwillie calculus plays important roles in the above two projects. I find this theory very elegant and would like to discover more of its applications!

A key notion in Goodwillie calculus are excisive functors. Together with Hana Jia Kong, Ang Li and Mingcong Zeng, we are working towards a model of N-spectra using excisive functors where the N-algebra structure does not necessarily come from a G-universe.

Preprint

Thesis