My area of expertise is algebraic combinatorics. Initially I concentrated on descent algebras of Coxeter groups with a particular focus on their multiplicative structure, and the establishment of their basic algebraic structure and representation theory over fields of finite characteristic.
worked on Pieri operators on posets that link the
diverse areas of Schubert calculus, combinatorics of
polytopes, and P-partitions, amongst others. One
particular discovery was the duality between peak
functions and the cd-index. This led to studying ribbon
Schur function equality, generalising this study to skew
Schur function equality and applying the knowledge
gleaned to the study of Schur positivity.
Most recently, I
have been studying generalizations of Schur functions
that reflect many of the properties displayed by
classical Schur functions, such as Littlewood-Richardson
rules, and their role in representation theory. I have
also become interested in a generalization of the
chromatic polynomial, known as the chromatic symmetric
phrases combinatorial representation theory, graph
theory, posets, symmetric functions and their
generalizations, tableaux combinatorics.
Those mentored in
other subjects are not listed here.
Undergrad research: Kristin
2004, 2005), Chris Ryan (2005), Josh Fiddler (2006),
Andrew Brown (2007), Farzin Barekat (2008), Jesseca Eng
(2015), Ian Mak (2015), Foster Tom (2016), Adrian She
(2017, 2018), Victor Wang (2020, 2021, 2022).
MSc: Matt Morin
(2003-05), Vasu Tewari (2009-11), Caleb Cheek (2010-12),
Foster Tom (2016-18), Ethan Shelburne (2021- ).
PhD: Matt Morin
(2005-2010), Vasu Tewari (2011-2015), Brian Chan
Kevin Purbhoo (2006-07), Eric Fusy
(2008-09), Kurt Luoto (2009-11), Mahdad
Khatirinejad (2010-11), Ed Richmond (2011-14), Julian
Courtiel (2015-16), Samantha Dahlberg (2016-18), Orit
Raz (2017-19), Farid Aliniaeifard (2019-).
Current Conference Organisation