The seminar has been running since 1997. The topics of talks have typically been any mixture of algebra with any other field: combinatorics, geometry, topology, physics, etc. Further down this page you will find links to the seminar webpages for previous years. The audience usually consists of 6–12 people, including several graduate students and post-docs. For this reason, speakers are encouraged to devote a portion of their talk to the suggestion of open problems and the directions for research in their area. If you are interested in speaking at the seminar, contact Cesar Ceballos or Nantel Bergeron.
You may also be interested in the Algebraic Combinatorics Seminar at the Fields Institute.
Dates are listed in reverse-chronological order. Unless otherwise indicated, all talks will take place on Monday from 14:00-15:00 in N638 Ross Building (York University).
Date Speaker Title (click titles for abstract) 31 Mar. 2014 24 Mar. 2014 17 Mar. 2014 10 Mar. 2014 3 Mar. 2014 24 Feb. 2014 17 Feb. 2014
Family Day (University is closed) 10 Feb. 2014 25 Nov. 2013 Drew Armstrong
(U. of Miami)
Rational Catalan Numbers and Rational AssociahedraFor each rational number x outisde the interval [-1,0] I will define a positive integer Cat(x) called the "rational Catalan number". The classical Catalan number corresponds to x=n and the Fuss-Catalan number corresponds to x=n/((k-1)n+1). These numbers satisfy the symmetry Cat(x)=Cat(-x-1), which implies that Cat(1/(x-1))=Cat(x/(1-x)). I will call this common value the "derived Catalan number" Cat'(x):=Cat(1/(x-1))=Cat(x/(1-x)), and it follows that Cat'(x)=Cat'(1/x). Rational Catalan numbers are categorified by various generalizations of traditional Catalan structures. In particular, I will describe joint work with B. Rhoades and N. Williams in which we define a "rational associahedron". This is a pure simplicial complex with Cat(x) many maximal faces. It is not a polytope but it is homotopy equivalent to a wedge of Cat'(x) many spheres. We conjectured that the equality Cat'(x)=Cat'(1/x) is represented by Alexander duality of rational associahedra. This conjecture was recently proved by B. Rhoades. 18 Nov. 2013 Nathan Williams
CatalandI will talk about two combinatorial miracles relating purely poset-theoretic objects with purely Coxeter-theoretic objects. The first miracle is that there are the same number of linear extensions of the root poset as reduced words of the longest element (occasionally), while the second is that there are the same number of order ideals in the root poset as certain group elements (usually). I will conjecturally place these miracles on remarkably similar footing and examine the generality at which we should expect such statements to be true. 11 Nov. 2013 Laura Colmenarejo
(U. de Sevilla)
Trying to prove stabilityWe define the plethysm of two Schur symmetric functions as a new operation, which is more complicated and interesting than the Kronecker product. We will discuss this and other technics (like FI-modules and Vertex operators) which can be used to study stability problems that appear in different contexts. 4 Nov. 2013 Christopher Hanusa
Applications of abacus diagrams: Simultaneous core partitions, alcoves, and a major statisticA t-core partition is a partition whose Young diagram has no hooks of length t. Partitions that are both s-core and t-core for integers s and t are called simultaneous core partitions. We will discuss the applications of simultaneous core partitions--we visit with lattice paths, alcoves in a hyperplane arrangement, and a "major index" statistic that recovers a q-analog for Catalan numbers. This is joint work with Brant Jones and Drew Armstrong. 28 Oct. 2013 Laura Escobar
Bott-Samelson varieties, subword complexes and brick polytopesThe Bott-Samelson varieties are a resolution of singularities for Schubert varieties. Intuitively, Bott-Samelson varieties factor G/B into a product of ℂℙ1's via a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational, however in this talk we will study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we will translate this problem into a purely combinatorial one in terms of subword complexes. These simplicial complexes, defined by Knutson and Miller, encode a lot of information about reduced words in a Coxeter system. Pilaud and Stump realized certain subword complexes as the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is generalized associahedron. These stories connect in a nice way: for certain words a fiber of the Bott-Samelson map is the toric variety of the Brick polytope. 21 Oct. 2013 Farid Aliniaeifard
The Zero-Divisor Graphs of Semigroups, Rings, and Group RingsWe associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. The Zero-divisor graph of a semigroup S is a graph with non-zero zero-divisors of S as vertex set and distinct vertices x and y are adjacent if xy = 0 or yx = 0. We investigate diameter, girth, and Isomorphism Problem for zero-divisor graphs of rings. Also, we show that the set of ideals of R is a semigroup. So we can define a zero-divisor graph for the set of ideals of R. At the end we investigate the genus of these graphs. 14 Oct. 2013
Below you will find links to the seminar webpages for previous years.