Shengtong Zhang's Website

My name is Shengtong Zhang(张盛桐 in Chinese). I am currently pursuing a Ph. D. in Mathematics at Stanford University. I received a B.S. from MIT with a double major in Mathematics and Computer Science and a minor in economics. You can find my papers below, or view them on arxiv and google scholar . 







Combinatorics Papers (* indicates preprints)

Equiangular lines with a fixed angle.  Annals of Mathematics (2021).

MIT News Coverage

Spherical two-distance sets and eigenvalues of signed graphs. Combinatorica (2023).

Graphs with high second eigenvalue multiplicity.  Bulletin of the London Mathematical Society (2022). 

No extremal square-free words over large alphabets.  Combinatorial Theory (2022).

Note on the Turan number of the 3-linear hypergraph C_{13}.  Electronic Journal of Combinatorics (2022).

Domination polynomial is unimodal for large graphs with a universal vertex. 

     A note on the zero-free region of hypergraph independence polynomials. Combinatorics, Probability and Computing (2025).

A short proof to Defant and Kravitz's theorem on the length of Hitomezashi loops. Annals of Combinatorics (2024).

     Toroidal Hitomezashi Patterns. Discrete Mathematics (2025).

On the first two eigenvalues of regular graphs. Linear Algebra and its Applications (2024).

Triangle Ramsey number of complete graphs

    More on Nosal's Spectral Theorem: Books and 4-cycles 

    Extremal Values for the square energies of graphs

    Conic Programming to understand sums of squares of eigenvalues of graphs

The Frankl-Pach upper bound is not tight for any uniformity


Number Theory Papers (* indicates preprints)

A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors. Journal of Number Theory (2021).

Towards Heim and Neuhauser’s unimodality conjecture on the Nekrasov–Okounkov polynomials.  Research in Number Theory (2021).

Proof of the Ballantine-Merca conjecture and theta function identities modulo 2.  Proceedings of the AMS (2025).

Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang.  Proceedings of the AMS (2022).

    Euler-Kronecker constants for cyclotomic fields. Bulletin of the Australian Mathematical Society (2023).

    Initial log-concavity in power of infinite series close to (1 - z)^{-1}. Research in Number Theory (2022).


Secure Messaging

Formal Security Definition of Metadata-Private Messaging.