
Teaching, 2016WT1
I am not teaching this term.
Research Interests
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.
Subsequently, I worked on Pieri operators on
posets that link the diverse areas of Schubert calculus,
combinatorics
of polytopes, and Ppartitions, amongst others. One particular
discovery was the duality between peak functions and the cdindex. 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
LittlewoodRichardson rule, and their role in the representation theory
of the 0Hecke algebra.
Keywords and phrases Coxeter
group, representation
theory, graded poset, quasisymmetric and noncommutative symmetric
function, skew Schur
function, quasisymmetric Schur function, Macdonald polynomial.
Students in algebraic combinatorics
Those mentored in other subjects are not listed here.
Undergrad research: Kristin
Shaw
(2003, 2004, 2005), Chris Ryan (2005), Josh Fiddler (2006), Andrew
Brown (2007), Farzin Barekat (2008), Jesseca Eng (2015), Ian Mak
(2015), Foster Tom (2016).
MSc: Matt Morin
(20035), Vasu Tewari (200911), Caleb Cheek (201012), Foster Tom
(2016 ).
PhD: Matt Morin
(20052010), Vasu Tewari (20112015), Brian Chan (2016 ).
Postdoc (joint):
Kevin Purbhoo (20067), Eric Fusy (20089), Kurt Luoto
(200911), Mahdad Khatirinejad (201011), Ed Richmond (201114),
Julian Courtiel (20156), Samantha Dahlberg (2016 ).
Current Conference Organisation
In the past I have also coorganized FPSAC 2004 and a CRM special
semester, BIRS 2 and 5Day Workshops plus FRGs and RITs, plus
CMS and AMS special sessions. I have organized both Algebraic
Combinatorixx and Algebraic Combinatorixx 2 at BIRS to faciliate both
research and mentorship for women in algebraic combinatorics. At a
departmental level I am currently
the Associate Head for Research.
Contact Information
Email:steph (at math splotch ubc followed by another
splotch
ca)
Phone:+1 604 8222630
Fax:+1 604 8226074
Paper mail:
Department of Mathematics, University of British Columbia,
1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada.
Other
My husband is the medieval historian Niall Christie.
Stephanie van Willigenburg September 2016
