Teaching, 2018WI am on sabbatical.
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 a natural
quasisymmetric refinement of Schur functions that reflect
many of the properties displayed by Schur functions, such
as Pieri rules, a Littlewood-Richardson rule, and their
role in the representation theory of the 0-Hecke algebra.
I have also become interested in a generalization of the
chromatic polynomial, known as the chromatic symmetric
Keywords and phrases chromatic symmetric function,
Coxeter group, representation theory, graded poset,
quasisymmetric and noncommutative symmetric function, skew
Schur function, quasisymmetric Schur function, Macdonald
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
MSc: Matt Morin
(2003-05), Vasu Tewari (2009-11), Caleb Cheek (2010-12),
Foster Tom (2016-18).
PhD: Matt Morin
(2005-2010), Vasu Tewari (2011-2015), Brian Chan (2016- ).
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-).
Current Conference Organisation
Email:steph (at math splotch ubc followed by another