I am an NSF Postdoc at the Department of Mathematics at Columbia University. Previously, I was a visitor at the IAS (’20-21) and before that, I did my PhD at MIT, advised by Jacob Lurie, and my undergraduate work at Harvard. My research is supported by NSF Grant DMS-2002029.
My work draws broadly from higher category theory, chromatic and equivariant homotopy theory, and algebraic K-theory to solve problems in algebraic topology and seek out connections to other fields of math.
- Examples of chromatic redshift in algebraic K-theory (2021).
- Chromatic convergence for the algebraic K-theory of the sphere spectrum with Andrew Blumberg and Mike Mandell (2021). Submitted.
- Higher semiadditive Grothendieck-Witt theory and the K(1)-local sphere with Shachar Carmeli (2021). Submitted.
- A version of Waldhausen’s chromatic convergence for TC with Andrew Blumberg and Mike Mandell (2021). Submitted.
- Wilson Spaces, Snaith Constructions, and Elliptic Orientations with Jeremy Hahn and Hood Chatham (2019). Submitted.
- Integral Models for Spaces via the Higher Frobenius (2019). To appear in Journal of the American Mathematical Society. There are some wonderful notes on this work thanks to the participants of a seminar organized by Marc Hoyois and Maria Yakerson: http://www.mathematik.ur.de/hoyois/SS20/iht/index.html.
- Exotic Multiplications on Periodic Complex Bordism with Jeremy Hahn. Journal of Topology 13 (2020).
- Multiplicative Structure in the Stable Splitting of ΩSLn(C) with Jeremy Hahn. Advances in Mathematics 348 (2019).
Department of Mathematics
New York, NY 10027
yuan (at) math (dot) columbia (dot) edu