About me

EDIT (01/04/2023): I am no longer a senior at Harvard, and indeed my Harvard email below has since been deactivated. I am now a math G2 at Columbia, still doing representation theory, under Prof. Mikhail Khovanov. My new email is fz2326 (at sign) columbia dot edu, and my new website is math.columbia.edu/~fanzhou .

I am a senior at Harvard majoring in mathematics. My primary interests are in geometric and combinatorial representation theory. I am also interested in combinatorial species. 

Email: fanzhou (at sign) college dot harvard dot edu

My Resume.

Notes and Works

Selected Undergraduate Files:

Research paper (conducted at Duluth in Summer 2020) in what might be best categorized as additive combinatorics, "On Eventually Periodic Sets as Minimal Additive Complements", submitted to Electronic Journal of Combinatorics: Duluth pdf, arXiv.

Expository paper (Summer 2020) on the classical proof of the Bernstein-Gelfand-Gelfand (BGG) resolution and its application to the Weyl character formula: BGG. 

Writeup of progress (Summer, Winter 2019) on categorifying the Jacobi-Trudi determinant formula via a BGG-esque combinatorial resolution; calculated for the 3-part partition case the generating series of the coefficients describing the differential maps of the complex: Combo BGG Jacobi-Trudi

 

Some Other Undergraduate Files:

Expository note (Spring 2019) on analytic combinatorial species and a proof of the composition law for species: Analytic Species and Composition.

Expository note (Spring 2020) on spectral sequences and a proof of the symmetry of the Tor functor: Spectral Sequences and Tor.

Expository note (Fall 2019) on modular forms, the valence formula, and a dimension formula: Modular Forms.

Expository note (Spring 2020) on quantum Schubert polynomials and quantum cohomology: Quantum Schubert.

 

High school:

Writeup of a solution (Summer 2017) to the problème des ménages using the theory of combinatorial species: Ménages Species. (This was done and written in the summer after my 12th grade year, and I posted this work to my personal blog on the ArtofProblemSolving.com website that same summer. Being only a high schooler, my writing was rather unpolished; however I have printed above a pdf version of the blog post faithful to the rough edges of that high schooler I once was.)