Yibo Gao

If you are an undergraduate student interested in learning more about algebraic combinatorics, please don't hesitate to reach out to me via email or in person.

Here is a list of programs in which I participated during my time at MIT.

PRIMES

Program for Research in Mathematics, Engineering and Science for High School Students at MIT.

• 2021, with Anthony Wang, on Consecutive Patterns in Coxeter groups.
• 2020, with Joshua Guo, Karthik Seetharaman and Ilaria Seidel, on The Rank-Generating Functions of Upho Posets. Here are their slides during the PRIMES conference. Their poster is selected as MAA Undergraduate Outstanding Poster during JMM 2021.
• 2019, with Rupert Li, on Compatible Recurrent Identities of the Sandpile Group and Maximal Stable Configurations and Pulses of Flow-firing Processes. Here are his slides during the PRIMES conference. Rupert won the 4th place (with prize money $100K) in the 2020 Regeneron STS.

DRP

Directed Reading Program at MIT.

• Jan 2022, with M. C. and T. S., on Symmetric Functions, Schubert Polynomials, and Degeneracy Loci by Manivel.
• Jan 2021, with M. H. and C. S., on The Symmetric Group by Sagan.
• Jan 2020, with Z. X., on Combinatorics and Commutative Algebra by Stanley.
• Jan 2019, with J. P. and Z. X., on Introduction to Lie Algebras and Representation Theory by Humphreys.
• Jan 2018, with J. G., on Enumerative Combinatorics Vol. II by Stanley.
• Jan 2015, as a student, mentored by Jonathan Weed, on Enumerative Combinatorics Vol. I by Stanley.

SPUR

Summer Program in Undergraduate Research at MIT.

• June 2021 -- Aug 2021, with Enrico Colón, on Multiplicity-free flagged Schur polynomials.
• June 2019 -- Aug 2019, with Andrew Gu, on Arithmetic of weighted Catalan numbers.
• June 2019 -- Aug 2019, with Kaarel Hänni, on Wilf-equivalence in Weyl Groups and Signed Permutations.
• June 2018 -- Aug 2018, with Junyao Peng, on Counting shellings of complete bipartite graphs and trees.
• June 2014 -- Aug 2014, as a student, with Yuzhou Gu, mentored by Adrian Vladu and Richard Peng, on Fast algorithms for solving SDPs on graphs.

UROP

Undergraduate Research Opportunities Program at MIT.

• Jun 2022 -- Aug 2022, with Elaine Liu, on Tree enumeration polynomials of separable permutations.
• Feb 2020 -- May 2020, with Kaarel Hänni, on Boolean elements in the Bruhat order.
• Sep 2019 -- Dec 2019, with Kaarel Hänni, on Generating trees and permutation pattern avoidance in signed permutations.
• Sep 2015 -- May 2016 (superUROP), as a student, mentored by Henry Cohn, on The largest pure partial planes of order 6 have size 25. I also made a preliminary poster.
• May 2015 -- Aug 2015, as a student, with YiYu Zhang, mentored by Richard Stanley, on Diagonal Form of the Varchenko Matrices.

RSI

Research Science Institute at MIT.

• June 2018 -- Aug 2018, with Roshan Warman, on Generalization of Bridge Length to other Cartan-Killing Types.

PROMYS

Program in Mathematics for Young Scientists at Boston University.

• June 2017 -- Aug 2017, as a counselor.