Teaching, 2021WT1I am not teaching this term.
Research InterestsMy 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.
Subsequently, I 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 function.
Keywords and phrases combinatorial representation
theory, graph theory, posets, symmetric functions and
their generalizations, tableaux combinatorics.
Students in algebraic 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).
MSc: Matt Morin
(2003-05), Vasu Tewari (2009-11), Caleb Cheek (2010-12),
Foster Tom (2016-18), Damara Gagnier (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
Current Conference Organisation
Email:steph (at math splotch ubc followed by another