Zixuan Xu

I'm currently a fourth-year Ph.D. student at MIT advised by Lisa Sauermann. Previously, I obtained my Bachelor's degree in Mathematics and Computer Science and Engineering from MIT. I was also fortunate to be mentored by Virginia Vassilevska Williams and Dor Minzer.

My main research interest lies in extremal and probabilistic combinatorics.

Email: zixuanxu at mit dot edu

Here is my CV.

Last updated: 2025.08.24

Research

Extremal Combinatorics

Nondegenerate hyperplane covers of the hypercube
with Lisa Sauermann. Submitted.
Preprint: arXiv:2507.00773
Even-degeneracy of a random graph
with Dingding Dong, Ting-Wei Chao. Submitted.
Preprint: arXiv:2506.01021
On off-diagonal F-Ramsey numbers
with Sammy Luo. Submitted.
Preprint: arXiv:2412.19042
Essential covers of the hypercube require many hyperplanes
with Lisa Sauermann. Combinatorics, Probability, and Computing, 2024.
Preprint: arXiv:2310.05775

Theoretical Computer Science

New Separations and Reductions for Directed Preservers and Hopsets
with Gary Hoppenworth, Yinzhan Xu. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2025.
Preprint: arXiv: 2411.08151
More Asymmetry Yields Faster Matrix Multiplication
with Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu, Renfei Zhou. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2025.
Preprint: arXiv:2404.16349
Additive Spanner Lower Bounds with Optimal Inner Graph Structure
with Greg Bodwin, Gary Hoppenworth, Virginia Vassilevska Williams, Nicole Wein. EATCS International Colloquium on Automata, Languages, and Programming (ICALP) 2024.
Preprint: arXiv:2404.18337
New Bounds for Matrix Multiplication: from Alpha to Omega
with Virginia Vassilevska Williams, Yinzhan Xu, Renfei Zhou. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2024.
Preprint: arXiv:2307.07970
Simpler and Higher Lower Bounds for Shortcut Sets
with Virginia Vassilevska Williams, Yinzhan Xu. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2024.
Preprint: arXiv:2310.12051
Improved Roundtrip Spanners, Emulators, and Directed Girth Approximation
with Alina Harbuzova, Ce Jin, Virginia Vassilevska Williams. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2024.
Preprint: arXiv:2310.20473
Faster Detours in Undirected Graphs
with Shyan Akmal, Virginia Vassilevska Williams, Ryan Williams. The European Symposium on Algorithms (ESA) 2023.
Preprint: arXiv:2307.01781
Better Lower Bounds for Shortcut Sets and Additive Spanners via an Improved Alternation Product
with Kevin Lu, V. Vassilevska Williams, Nicole Wein. ACM-SIAM Symposium on Discrete Algorithms (SODA) 2022.
Preprint: arXiv:2110.15809

Miscellaneous

Electrical networks and the grove algebra
with Yibo Gao, Thomas Lam. Canadian Journal of Mathematics, 2024.
Preprint: arXiv:2208.12798
On virtually Cohen–Macaulay simplicial complexes
with Nathan Kenshur, Feiyang Lin, Sean McNally, Teresa Yu. Journal of Algebra, 2023.
Preprint: arXiv:2007.09443
Dihedral sieving on cluster complexes
with Zachary Stier, Julian Wellman. Enumerative Combinatorics and Applications, 2022.
Preprint: arXiv:2011.11885

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