2014 - 2019: Ph.D. in Mathematics, UC San Diego.

2010 - 2014: B.S. in Mathematics, Zhejiang University.

Mathematics Department, Beijing Jiaotong University

Email: qiudun123 (at) 163 (dot) com

My research area is enumerative combinatorics and algebraic combinatorics.

**NSFC Grant (12001037)**:
Combinatorial Problems Derived from the Shuffle Conjecture.

**Schur function expansions and the Rational Shuffle Theorem**[with Jeff Remmel] (*Journal of Combinatorial Theory, Series A*,**175**, 2020) [pdf]**The valley version of the Extended Delta Conjecture**[with Andy Wilson] (*Journal of Combinatorial Theory, Series A*,**175**, 2020) [pdf]**$e$-positivity results and conjectures**[with Adriano Garsia, Jim Haglund and Marino Romero] (arXiv, 2019) [pdf]**Patterns in words of ordered set partitions**[with Jeff Remmel] (*Journal of Combinatorics*,**10 (3)**, 2019) [pdf]

The original version also discussed pattern avoidance in parking functions [pdf]**Classical pattern distributions in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$**[with Jeff Remmel] (*Discrete Mathematics & Theoretical Computer Science*,**21 (2)**， 2019) [pdf]**Counting Consecutive Pattern Matches in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$**[with Ran Pan and Jeff Remmel] (*Advances in Applied Mathematics*,**105**, 2018) [pdf]**Schur Function Expansions and the Rational Shuffle Conjecture**[with Jeff Remmel]

Extended abstract appear in Proceedings of FPSAC 2017, (*Seminaire Lotharingien de Combinatoire*,**78B**, 2017) [pdf]**On the Schur positivity of $Δ_{e_2} e_n[X]$**[with Jeff Remmel, Emily Sergel and Guoce Xin] (*Electronic Journal of Combinatorics*,**25 (4)**, 2018) [pdf]**Quadrant marked mesh patterns in 123-avoiding permutations**[with Jeff Remmel] (*Discrete Mathematics & Theoretical Computer Science*,**19 (2)**, 2018) [pdf]

- (2020.7)
**Bijectivity Problems in Parking Functions**, 2020 Workshop on Algebraic Combinatorics, Sichuan University, Sichuan, China - (2020.6)
**Mod $k$-alternating permutations in $\mathcal{S}_{n}(132)$**, Permutation Patterns Virtual Workshop 2020, Valparaiso University, IN, USA - (2019.5)
**Some conjectures about column LLT polynomials**, UC Davis Algebraic Geometry Seminar, UC Davis, Davis, CA, USA - (2019.1)
**Counting classical patterns in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$**, UCLA Combinatorics Seminar, UCLA, Los Angeles, CA, USA [website] [pdf] - (2018.7)
**Classical permutation distribution in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$**, Permutation Patterns 2018, Hanover, NH, USA [website] [pdf] - (2018.7)
**Combinatorial Problems in Dyck paths and Parking Functions**, Center for Combinatorics Seminar, Nankai University, Tianjin, China [website] [pdf] - (2018.3)
**Conjectures for the delta operator expression $\Delta'_{e_k}\Delta_{h_r}e_n$**, The CAGE Seminar, University of Pennsylvania, Philadelphia, PA, USA [website] [pdf] - (2018.1)
**Conjectures for $\Delta'_{e_k}\Delta_{h_r}e_n$**, LaCIM, Université du Québec à Montréal, Montréal, Canada [website] [pdf] - (2017.8)
**Special Cases in the Combinatorics of Rational Shuffle Conjecture**, Center for Combinatorics Seminar, Nankai University, Tianjin, China [website] [pdf] - (2016.6)
**Patterns in Ordered Set Partitions and Parking Functions**, Permutation Patterns 2016, Washington D.C., USA [website] [pdf] - (2016.5)
**Rational Shuffle Conjecture When $n = 3$ or $m = 3$**, UC San Diego, La Jolla, USA [website] [pdf]

- (2017.7)
**Schur Function Expansions and the Rational Shuffle Conjecture**, FPSAC 2017, London, UK [website] - (2017.6)
**Quadrant marked mesh patterns in $123$-avoiding permutations**, Permutation Patterns 2017, Reykjavik, Iceland [website]

- (2019.1) Representation Theory Connections to (q,t)-Combinatorics, Banff, Canada [website]
- (2018.7) FPSAC 2018, Hanover, NH, USA [website]

- (Fall 2017)
**Math 3C**: Precalculus, UCSD. Course website.

- (Spring 2019)
**Math 152**: Data Mining, UCSD. Course website. - (Winter 2019)
**Math 152**: Topics in Data Science, UCSD. Course website. - (Fall 2018)
**Math 109**: Mathematical Reasoning, UCSD. Course website. - (Summer II 2018)
**Math 20D**: Introduction to Differential Equations, UCSD. Course website. - (Spring 2018)
**Math 184A**: Combinatorics, UCSD. Course website. - (Winter 2018)
**Math 190**: Introduction to Topology, UCSD. Course website. - (Winter 2018)
**Math 202B**: Applied Algebra II, UCSD. Course website. - (Spring 2017)
**Math 152**: Game Theory, UCSD. Course website. - (Winter 2017)
**Math 184A**: Combinatorics, UCSD. Course website. - (Fall 2016)
**Math 184A**: Combinatorics, UCSD. Course website. - (Summer I 2016)
**Math 20B**: Calculus for Science and Engineering, UCSD. Course website. - (Summer I 2016)
**Math 20E**: Vector Calculus, UCSD. Course website. - (Spring 2016)
**Math 152**: Game Theory, UCSD. Course website. - (Winter 2016)
**Math 20F**: Linear Algebra, UCSD. Course website. - (Fall 2015)
**Math 184A**: Combinatorics, UCSD. Course website. - (Spring 2015)
**Math 10A**: Calculus, UCSD. Course website. - (Winter 2015)
**Math 20C**: Calculus and Analytic Geometry for Science and Engineering, UCSD. Course website.