steph

Stephanie van Willigenburg

Faculty

Steph van Willigenburg obtained a PhD in Mathematics from the University of St Andrews and was a Postdoctoral Fellow at York University and then Cornell University. She is currently a full professor at UBC Mathematics. More details can be found on her website.

Selected Honours

2023 MAA Robbins Prize
2023 Fellow of the AMS
2019 A plenary speaker at the JMM
2018 A Simons CRM Professor
2017 The Krieger-Nelson Prize
2008 - 2009 An Alexander von Humboldt Fellow
2007 - 2008 A Killam Teaching Award
2002 - 2007 NSERC University Faculty Award

She is also the co-founder of the Algebraic Combinatorics Research Community to facilitate both research and mentorship for women in algebraic combinatorics. Her passion for mentorship also extends to her teaching, helping the next generation of mathematicians reach their full potential.

Selected Publications

  • Resolving Stanley's e-positivity of claw-contractible-free graphs (with Samantha Dahlberg and Angele Foley), J. Eur. Math. Soc. (JEMS) 22:2673-2696 (2020).
  • Modules of the 0-Hecke algebra and quasisymmetric Schur functions (with Vasu Tewari), Adv. Math. 285:1025-1065 (2015).
  • Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions (with Louis Billera and Hugh Thomas),   Adv.  Math. 204:204-240 (2006).

Research Interests:

Her area of expertise is algebraic combinatorics. Her research interests include combinatorial representation theory, graph theory, posets, symmetric functions and their generalizations, and tableaux combinatorics.

Initially she 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, she 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, she has 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. She has also become interested in a generalization of the chromatic polynomial, known as the chromatic symmetric function.

Awards

Students and Postdocs

Ethan Shelburne
Maria Esipova
no-phd
Farid Aliniaeifard
no-ugrad