Yuqing Shi

Research Interests

My research interests lie in algebraic topology, with special interests in periodic and chromatic homotopy theory, Koszul duality, Goodwillie calculus and stable infinity categories.

In my PhD thesis I considered unstable periodic homotopy theory. Here, "unstable" refers to the homotopy theory of homotopy types (instead of spectra). One shall view unstable periodic homotopy theory as an extension of rational homotopy theory of homotopy types: In rational homotopy theory we study the localisatin of the infinity category of simply connected homotopy types at the set of degree p self-maps of spheres for every prime number p. Fix a prime number p. For every natural number h, the vh-periodic homomotopy theory is about the localisation of the infinity category of (simply-connected) p-local homotopy types at the set of certain "degree vh self-maps" of certain finite complexes. The set of v0 self-maps is the set of the degree p self-maps of spheres. Thus, the v0-periodic homotopy theory recovers by construction the rational homotopy theory. See the introduction of my PhD thesis for more details.

In my master's thesis, I studied the application of manifold calculus to the theory of Vassiliev knot invariants. I still find the application of homotopy theory to geometric topology intriguing and would like to explore it further.