# Fan Wei's homepage

Photo credit: Andrea Kane/Institute for Advanced Study

### Welcome to my website!

### I am currently an instructor at the Department of Mathematics, Princeton University.

## 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 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-1953958 (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!**Undecidability of polynomial inequalities in weighted graph homomorphism densities**, Grigoriy Blekherman, Annie Raymond, F. Wei. (arXiv)**Common graphs with arbitrary chromatic number**, Dan Kral', Jan Volec, F. Wei. (arXiv)**On the asymptotic confirmation of the Faudree-Lehel Conjecture for general graphs**, Jakub Przybyło, F. Wei, submitted. (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.*SI**AM Journal on Computing (SICOMP)**.*2020**Phase transition of degeneracy in minor-closed families**, Chun-Hung Liu, F. Wei, submitted. (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)**Graphs with the local****S****idorenko property**, Jacob Fox, F. Wei, (conference shortened version).**Random permutation patterns and online algorithm**, Jacob Fox, László Miklós Lovász, F. Wei,*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 Math**é**matiques de Besan**ç**on, Alg**è**bre et Th**é**orie 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)

## 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.