Foster Tom

I am a postdoctoral instructor at MIT. I received my PhD in Mathematics at UC Berkeley in May 2022, advised by Mark Haiman. I received my Master's at the University of British Columbia, advised by Stephanie van Willigenburg.

I study algebraic combinatorics, specifically chromatic symmetric functions, LLT polynomials, and Schur-positivity. Here is my CV.

My main hobbies are bridge and ballroom dancing. I also play chess, go, and scrabble.

Contact

Email: ftom at mit dot edu
Office: 2-246a

Research

A signed e-expansion of the chromatic symmetric function and some new e-positive graphs

I gave a virtual talk on this work.

A horizontal-strip LLT polynomial is determined by its weighted graph
Combinatorial Theory, Vol. 3 No. 3 (2023)

A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
Combinatorial Theory, Vol. 1 No. 14 (2021)

Classifying the near-equality of ribbon Schur functions
European Journal of Combinatorics, Vol. 90, 103197 (2020)

The number of rational points of hyperelliptic curves over subsets of finite fields with Kristina Nelson, Jozsef Solymosi, and Ching Wong
Involve, a Journal of Mathematics, Vol. 12 No. 5, 755--765 (2019)

Necessary conditions for Schur-maximality with Stephanie van Willigenburg
Electronic Journal of Combinatorics, Vol. 25, P2.30 (2018)