Waterloo Combinatorics Seminar

This is the website for the Algebraic and Enumerative Combinatorics Seminar at the University of Waterloo. We view algebraic combinatorics broadly, explictly including algebraic enumeration and related asymptotic and bijective combinatorics as well as algebraic combinatorics as it appears in pure algebra and in applications outside mathematics.

We begin with a pre-seminar which is designed to get participants up to speed on useful and interesting background for the talk. It will be at the level for beginning grad students. Then there will be a short coffee break followed by the seminar itself.

Our audience consists principally of combinatorics faculty and grad students. Seminar talks are 50 minutes with questions following.

If you are speaking, we need your abstract at least a week in advance so it can make the deadline for the Friday math faculty seminar mailing.

Winter 2026

Usual location and time: 1:30 pre-seminar, 2:30 seminar, both in MC 5417.

• January 15: Mahrud Sayrafi Cancelled on account of snow

• January 22: No seminar on account of CAAC

• January 29: Nathan Pagliaroli

• February 5: Jonathan Boretsky

• February 12: Santiago Estupiñán

• February 19: No seminar on account of reading week

• February 26: Adrien Segovia

• March 5: Maria Gillespie

• March 12: Stephan Pfannerer

• March 19: Moriah Elkin, Open quiver loci, CSM classes, and chained generic pipe dreams
  Click here for abstract

  In the space of type A quiver representations, putting rank conditions on the maps cuts out subvarieties called "open quiver loci." These subvarieties are closed under the group action that changes bases in the vector spaces, so their closures define classes in equivariant cohomology, called "quiver polynomials." Knutson, Miller, and Shimozono found a pipe dream formula to compute these polynomials in 2006. To study the geometry of the open quiver loci themselves, we might instead compute "equivariant Chern-Schwartz-MacPherson classes," which interpolate between cohomology classes and Euler characteristic. I will introduce objects called "chained generic pipe dreams" that allow us to compute these CSM classes combinatorially, and along the way give streamlined formulas for quiver polynomials.

• March 26: Ian George

• April 2: Hadleigh Frost

• April 9: Mahrud Sayrafi, Constructing exceptional collections for toric varieties
  Click here for abstract

  Exceptional collections are a powerful tool for understanding the derived category of coherent sheaves on algebraic varieties, with applications in commutative algebra, birational geometry, and mirror symmetry. While the existence of exceptional collections is known for classical varieties such as Grassmannians and flag varieties, constructing explicit collections for toric varieties presents challenges in combinatorial algebraic geometry. In this talk I will describe a computational approach to constructing full strong exceptional collections consisting of complexes of line bundles for toric varieties.
  No background in derived categories is assumed.

• …

• April 23: Melissa Sherman-Bennett. Note date outside of term!