I am a second-year PhD student 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.
Before that, I lived a happy life in Hefei, China.

You can reach me at: yhsheng at umich dot edu.

Writings

Number theory
The S-unit equation using Lawrence-Venkatesh
Kolyvagin systems
Complex multiplication

Homotopy theory
Notes on real orientations
Cofreeness of Lubin-Tate theory
Power operations and HKR character theory
On realizing rational and polynomial cohomology rings
Complex K-theory

Miscellaneous
The structure theory of complete local rings
Phylogenetic Treespace
Kähler manifolds and Hodge theory

Music

I play piano, organ, and carillon. You can access some of my recordings on Youtube or Bilibilibi. Here are some recent ones:

Piano
J. S. Bach: Prelude and Fugue in E Major from WTC Book II
Gubaidulina: Chaconne
Medtner: Sonata-Reminiscenza from Forgotten Melodies, Op. 38 No. 1

Organ
Franck: Chorale No. 3 in A minor
Organ recital (Tunder, Brahms, Messiaen, 04/10/25)
Organ recital (Bach, Brahms, Messiaen, 05/26/24)

I am broadly interested in philosophy (Aristotle, Hegel, and Kierkegaard etc.). I often find connections between music and philosophy, so I write them down when I get a chance. They are mostly in Chinese, although I do plan to write in English in the future. Here are some of them:

精神的归程——贝多芬降A大调第三十一号奏鸣曲Op. 110的演奏与哲学解读
A Hegelian phenomenological interpretation of Beethoven’s piano sonata Op. 110.
追寻钟声的脚步
A Documentation of my trip to Europe where I played on different caillons.
幻想曲式：北德管风琴学派与巴赫
On the topic of Stylus Phantasticus as represented by the north German organ school.
一篇德语翻译练习
A Chinese translation of a paper in German on Bach’s Pièce d’Orgue BWV 572.