# Fan Wei's homepage

Photo credit: Andrea Kane/Institute for Advanced Study

### Welcome to my website!

I am actively seeking motivated students to join my reading group or research group.

## Research Interests:

Extremal combinatorics, probabilistic combinatorics, applications of combinatorics to computer science.

I am especially interested in using tools from probability, analysis and algebra to analyze large networks or other combinatorial objects.

## Short Bio:

I am currently an assistant professor of Mathematics and assistant professor of Computer Science at Duke University. I completed my PhD in mathematics in 2019 from Stanford University, where I was fortunate to be advised by Jacob Fox. Then I spent one year as a post-doctoral member at the Institute for Advanced Study where I was part of Avi Wigderson's CSDM (computer science and discrete math) program.

Prior to that, I received my bachelors degree in Mathematics from MIT, and a Master of Advanced Study with Distinction from Cambridge University, UK. My previous internships include conducting research at Microsoft Research New England and Microsoft Research Redmond Theory group.

## Funding:

I am grateful to be /have been funded by the following sources:

NSF Award DMS-2401414 (2023-2028),

NSF Award DMS-1953958, DMS-2404167 (2020-2023).

Simons Foundation, Algorithms & Geometry Unit (for the academic year 2020).

Founders’ Circle Member, Cynthia and Robert Hillas (for the academic year 2019 while I was at IAS).

## Publications:

Also available at Google Scholar.

Local graph removal lemma, Jacob Fox, F. Wei. coming out soon!

Extremal number of cliques of given orders in graphs with a forbidden clique minor, Ruilin Shi, F. Wei, (arXiv)

The binomial random graph is a bad inducer, Vishesh Jain, Marcus Michelen, F. Wei, (arXiv).

The limit points of the top and bottom eigenvalues of regular graphs, Noga Alon, F. Wei, Israel Journal of Mathematics (arXiv)

Near Ramanujan graph with many localized eigenvectors, Noga Alon, F. Wei, (preprint)

Undecidability of polynomial inequalities in weighted graph homomorphism densities, Grigoriy Blekherman, Annie Raymond, F. Wei. Forum of Math, Sigma (arXiv)

Common graphs with arbitrary chromatic number, Dan Kral', Jan Volec, F. Wei. Compositio Mathematica (arXiv)

On the asymptotic confirmation of the Faudree-Lehel Conjecture for general graphs, Jakub Przybyło, F. Wei, Combinatorica. (arXiv)

Short proof on the asymptotic confirmation of the Faudree-Lehel conjecture, Jakub Przybyło, F. Wei, submitted. (arXiv) (a companion paper of the one above. This short note focuses on regular graphs.)

Irregular subgraphs, Noga Alon, F. Wei, submitted. (arXiv)

Threshold Ramsey multiplicity for paths and even cycles, David Conlon, Jacob Fox, Benny Sudakov, F. Wei, submitted. (arXiv)

Threshold Ramsey multiplicity for odd cycles, David Conlon, Jacob Fox, Benny Sudakov, F. Wei, submitted. (arXiv)

Non-bipartite k-common graphs, Daniel Král', Jonathan A. Noel, Sergey Norin, Jan Volec, F. Wei, Combinatorica. 2021 (arXiv)

Finding Cliques in Social Networks: A New Distribution-Free Model, Jacob Fox, Tim Roughgarden, C. Seshadhri, F. Wei, Nicole Wein. SIAM Journal on Computing (SICOMP). 2020 (arXiv), (a quick overview and motivation can be found in Tim Roughgarden's homepage, under section "Beyond the Worst-Case Analysis of Algorithms".）

Phase transition of degeneracy in minor-closed families, Chun-Hung Liu, F. Wei, Advances in Applied Mathematics. (arXiv)

On the inducibility problem for random Cayley graphs of abelian groups with a few deleted vertices, Jacob Fox, Lisa Sauermann, F. Wei. Random Structures & Algorithms. 2021 (arXiv)

Local max-cut in smoothed polynomial time, Omer Angel, Sébastien Bubeck, Yuval Peres, F. Wei, STOC 2017. (arXiv), (A very nice blog written by Sébastien Bubeck about this project.) ( Slides )

Strongly testing hereditary permutatiorn properties with polynomial query complexity, Jacob Fox, F. Wei, in preparation.

Fast permutation property testing and metrics of permutations, Jacob Fox, F. Wei, Combinatorics, Probability and Computing, 2018.(arXiv).

Permutation property testing under different metrics with low query complexity , Jacob Fox, F. Wei, SODA, 2017.

On the number of cliques in graphs with a forbidden minor, Jacob Fox, F. Wei, Journal of Combinatorial Theory, Series B, 2017. (arXiv)

On the number of cliques in graphs with a forbidden subdivision or immersion , Jacob Fox, F. Wei, SIAM Journal on Discrete Mathematics. 2020 (arXiv) (Python code)

An asymptotically sharp bound on the maximum number of independent transversals, Jake Ruotolo, Kevin Wang, F. Wei, Electronic Journal of Combinatorics. (arXiv)

Graphs with the local Sidorenko property, Jacob Fox, F. Wei, (conference shortened version). Paper version in preparation.

Product decompositions of the symmetric group induced by separable permutations, F. Wei, European Journal of Combinatorics, 2012. (arXiv)

Dvoretzky--Kiefer--Wolfowitz inequalities for the two-sample case, F. Wei, Richard Dudley, Statistics & Probability Letters, 2011. (Journal Version, arXiv)

Arithmetic Properties of Generalized Rikuna Polynomials, J. Cullinan, H. Hausman, A. Pacelli, S. Pegado, F. Wei, Publications Mathématiques de Besançon, Algèbre et Théorie des Nombres, 2014. (Journal Version)

Involutions on standard Young tableaux and divisors on metric graphs, R. Agrawal, M. Gregg, V. Sotirov, F. Wei, Electronic Journal of Combinatorics, 2013. (Journal Version)

Two-Person Fair Division of Indivisible Items: Bentham vs. Rawls on Envy, S. Brams, D. Kilgour, C. Klamler, F. Wei, The Journal of Philosophy, 2023.

## Teaching / Mentoring Experience

I was a mentor of NYC Discrete Math REU organized by Prof. Adam Sheffer in summer 2021, where I mentored three undergraduate students. The papers are in preparation.

I am currently instructor at Princeton University teaching Calculus (MAT100).

Previously, I have been teaching assistants for the following courses:

Calculus several times (led problem sessions and lectures)

Math undergraduate research course (guided groups of undergraduate students to work on math research projects)

Discrete math series (led problem sessions; topics included basic real analysis and topology, graph theory and combinatorics)

I have also been course assistants for many other courses, where the duties included hosting office hours, grading exams and homework.

## Miscellaneous

Contact Me:

fan.wei [at] duke [dot] edu

Physics 215