Hi, I am a second-year PhD student in Mathematics at the University of Michigan, Ann Arbor.
I was an undergraduate student at the University of Chicago from 2020 to 2024.
Before that, I spent my high school years in the beautiful city of Maastricht, the Netherlands.
I was born and raised in Hefei, China.
Research interests
I am interested in problems that arise in number theory, homotopy theory, and representation theory.
Recently, I have been interested in mathematical biology and machine learning.
Papers
Performed Bach Trio Sonatas Reveal Topological Encoding of Polyphonic Music arxiv Short description.
Notes
- Number theory Kolyvagin systems
- Homotopy theory Cofreeness of Lubin-Tate theory
- Miscellaneous The structure theory of complete local rings
Lawrence-Venkatesh
Complex multiplication
Power operations and HKR character theory
Notes on real orientations
On realizing rational and polynomial cohomology rings
Elements of complex K-theory
Phylogenetic Treespace
Kähler manifolds and Hodge theory
Music
I am a pianist and an organist. You can access some of my recordings on Youtube and Bilibili. Here are some recent ones:
- Piano J. S. Bach: Prelude and Fugue in E Major from WTC Book II, BWV 878
- Organ J. S. Bach: Prelude and Fugue in C minor, BWV 546
Medtner: Sonata-Reminiscenza from Forgotten Melodies, Op. 38 No. 1
Gubaidulina: Chaconne
Franck: Chorale No. 3 in A minor
Tunder, Brahms, Messiaen recital
Other writings
I write in Chinese. They are mostly prose or scholarly articles that concern music, travelling, and philosophy. Here are some recent ones:
Contact
You can reach me at: yhsheng AT umich DOT edu.