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. My CV can be found here.
- The sphere of semiadditive height 1 (2022). Submitted.
- The Chromatic Nullstellensatz with Robert Burklund and Tomer Schlank (2022).
- Examples of chromatic redshift in algebraic K-theory (2021). Submitted.
- 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). To appear in Bulletin of the LMS.
- Wilson Spaces, Snaith Constructions, and Elliptic Orientations with Jeremy Hahn and Hood Chatham (2019). Submitted.
- Integral Models for Spaces via the Higher Frobenius. Journal of the American Mathematical Society (2022). 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