
Teaching, 2016WT2
Math
442: Optimization in Graphs and Networks
Math
444: Mathematical Research and Writing
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.
I have also become interested in a generalization of the
chromatic polynomial, known as the chromatic symmetric
function.
Keywords and phrases chromatic symmetric function,
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), Adrian She
(2017).
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 December 2016
