I mentored Josh Swanson, an SEW postdoc UCSD in 2018-21. Josh does work in algebraic and asymptotic combinatorics and is currently a postdoc at USC.
I mentored Marino Romero, a University of California Presidential Postdoctoral Fellow, in 2020-21. Marino is currently a postdoc at UVienna.
I mentored Sean Griffin, an instructor at UCSD in Fall 2020. Sean is currently a postdoc at UC-Davis.
Sutanay Bhattacharya is a current PhD student. He is studying differential coinvariant rings.
Moxuan (Jasper) Liu is a current PhD student. He is studying notions of locality and degree for statistics on complex reflection groups, and in so doing uncovered an algebraic notion of `longest increasing subsequences' in colored permutations.
Nathaniel (Tanny) Libman is a current PhD student. He is studying Schur positive expansions arising from the theory of `Chern plethysm' (developed by Lou Billera, Sara Billey, Vasu Tewari, and myself). He found a homological model of a special case of Chern plethysm. Tanny advanced to candidacy in November 2023.
Tianyi Yu is a current PhD student. One thread of his research is on a K-theoretic extension of Demazure characters called `Lascoux polynomials'. In joint work with Mark Shimozono, he proved a conjecture of Reiner-Yong giving a positive Grothendieck-to-Lascoux expansion. In further work with Jianping Pan, he proved a conjecture of Ross-Yong on a Kohnert-style expansion of the Lascoux polynomials. He developed an analogue of the Fomin-Stanley algebra in the context of bumpless pipe dreams. He has also done work on harmonic spaces and Groebner theory tied to generalized coinvariant algebras. Tianyi advanced to candidacy in February 2022. He will be a CRM-ICM postdoc at UQAM starting in Fall 2024.
Jesse Kim is a current PhD student. He is studying various skein relations which resolve crossings in set partitions. He tied the combinatorics of these relations to `block operators' on exterior algebras. He used related skein relations to give a combinatorial model for the fermionic diagonal coinvariant ring, and is interested in representation-theoretic web bases in general. He has also developed a version of chip firing for simplicial complexes and solved a tiling problem of Jim Propp. Jesse advanced to candidacy in February 2022.
Dr. Daniël Kroes is a former PhD student. He is studying a generalization of the coinvariant quotient of the Stanley-Reisner ring of the Boolean algebra whose properties are connected with the combinatorics of ordered set partitions. Daniël successfully defended his thesis in May 2021 and is currently working at Rubrik in Palo Alto.
Dr. Kyle Meyer is a former PhD student. He studied an extension of the Adin-Brenti-Roichman descent representation theory to a new family of generalized coinvariant algebras introduced by Haglund-Rhoades-Shimozono related to the Delta Conjecture of Haglund-Remmel-Wilson. Kyle proved a generalization of Adin-Brenti-Roichman's results. Kyle successfully defended his thesis in June 2020 and is currently a lecturer at UCSD.
Dr. Dun Qiu is a former PhD student, formerly advised by Jeff Remmel. Dun does work involving Schur expansions of symmetric functions arising in Macdonald theory (notably the Extended Rational Shuffle Conjecture and the Delta Conjecture). Dun successfully defended his thesis in May 2019. He is currently an associate professor at the Center for Combinatorics at Nankai University.
Dr. Michelle Bodnar is a former PhD student. She studied rational Catalan combinatorics and cyclic sieving. She proved a cyclic sieving conjecture of Armstrong-Rhoades-Williams and expanded an extension of theirs to the `a > b' rational Catalan regime. Michelle successfully defended her thesis in April 2018. She is currently working at Google.
In 2023-24 I am mentoring Chen-an (Jack) Chou in a Math 199H Honors Thesis project at UCSD. Along with my PhD student Tianyi Yu, Jack is studying the Grothendieck polynomials of combinatorial K-theory.
In Summer 2019 I performed research with Tianyi Yu and Zehong Zhao (two UCSD undergraduates) related to the combinatorics of harmonic spaces attached to generalized coinvariant rings. Based in part on this research, Tianyi was one of three students in the Division of Physical Sciences to receive the Selma and Robert Silagi Award for Undergraduate Excellence. This work produced a paper which Tianyi presented at FPSAC 2020 and appeared in the Electronic Journal of Combinatorics.
In Summer 2016 I did research with Jonathan Chan (a UCSD undergradute) related to the combinatorics of generalized coinvariant algebras. Jonathan won a 2016-2017 Physical Sciences Dean's Undergraduate Award for Excellence. Our research produced a joint paper. Jonathan started a masters programme in math at the University of Bonn in Fall 2017.
In Summer 2015 I co-organized the Collaborative Undergraduate Research Experience (CURE) with Todd Kemp; I was in charge of curriculum development. Michelle Bodnar served as the graduate student mentor. There were three undergraduate students participating in the program; one from UCSD and two from UMinnesota. We did research related to hyperplane arrangements and Shi/Ish duality. Their final report is here. Among these students, Christian Gaetz got a PhD in math from MIT and is currently a postdoc at Cornell and Björn Wehlin is a software engineer at Silvaco Inc. in the Bay Area.
In Summer 2014 I co-organized the Collaborative Undergraduate Research Experience (CURE) program with Todd Kemp here at UCSD. I was in charge of curriculum development. There were five UCSD undergraduates participating in the program. We did research in rational Catalan theory and cyclic sieving. The students produced a website for the CURE program with (among other things) freely available code used in their research. Among these students, Patrick De Jesus completed a graduate program at SDSU in statistics and is a data scientist at Playstation, Chenzhi Li won a 2014-2015 Physical Sciences Dean's Undergraduate Award for Excellence and completed a MA in statistics at Berkeley (she is currently a data scientist at Google), and Fengpei Li got a PhD in operations research at Columbia and is working at Morgan Stanley.
In Summer 2014 I did research with Jonathan Haapala (a UCSD undergraduate) related to the combinatorics of hyperplane arrangements. Jon's final report is here. Based on his work, Jon won a 2014-2015 Physical Sciences Dean's Undergraduate Award for Excellence.