The Applied Algebra Seminar

A
Monday afternoon research seminar

The seminar is currently organized by Laura Colmenarejo and Nantel Bergeron.

During 2017-18, the seminar takes place from 15:00-16:00 in Ross Building room N638. If you come by bus, the route 196A, 196B takes you to campus from Downsview subway station. If you come by car, you can find the available parking lots here.

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 Laura Colmenarejo 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 15:00-16:00 in N638 Ross Building (York University).

Date Speaker Title (click titles for abstract) 30 Oct. 2017 23 Oct. 2017

Laura Colmenarejo

(York U.)Factorization formulas for singular Macdonald polynomials We prove some factorization formulas for singular Macdonald polynomials indexed by particular partitions called quasistaircases. We also show some applications of these factorizations and some conjectures we are working on. This is joint work with Charles F. Dunkl and Jean-Gabriel Luque.16 Oct. 2017 Hugh Thomas

(UQAM)Robinson-Schensted-Knuth via quiver representations The Robinson-Schensted-Knuth correspondence is a many-faceted jewel of algebraic combinatorics. In one variation, it provides a bijection between permutations of n and pairs of standard Young tableaux with the same shape, which is a partition of n. In another (more general) version, it provides a bijection between fillings of a partition lambda by arbitrary non-negative integers and fillings of the same shape lambda by non-negative integers which weakly increase along rows and down columns. I will discuss an interpretation of RSK in terms of the representation theory of type A quivers (i.e., directed graphs obtained by orienting a path graph). This allows us to generalize RSK to other Dynkin types (plus a choice of minuscule weight), and is related to periodicity results for piecewise-linear toggling. I will not assume familiarity with either RSK or with quiver representations. This is joint work with Al Garver and Becky Patrias.13 Oct. 2017

Friday, York U.Jerzy Wejman

(U. of Connecticut)Finite free resolutions and root systems. In this talk I will discuss the structure of free resolutions of length 3 over Noetherian rings. Associate to a triple of ranks (r_3, r_2, r_1) in our free complex a triple (p,q,r)=(r_3+1, r_2-1, r_1+1). Associate to (p,q,r) the graph T_{p,q,r} (three arms of lengths p-1, q-1, r-1 attached to the central vertex). The main result is the explicit construction of a generic ring R_{gen} for resolutions of the format with the differentials of ranks r_1, r_2, r_3. This ring carries an action of a Kac-Moody Lie algebra associated to the graph T_{p,q,r}. In particular the ring R_{ten} is Noetherian if and only if T_{p.q.r} is a Dynkin graph. I will discuss the structure of the ring R_{gen} and possible consequences for the structure of perfect ideals of codimension 3.09 Oct. 2017 Thanksgiving Day! 02 Oct. 2017

At 4pm!Chi-Kwong Li

(College of William and Mary)Preserver Problems and Quantum Information Science Preserver problems concern the study of transformations on matrices or operators with special properties. In this talk, we will describe the history and recent advance of the topic. In particular, we will mention some results and problems related to quantum information science. No quantum mechanics background is needed. Undergraduates who have taken an linear algebra course are welcomed to attend.25 Sep. 2017 Rafael S. González D'León

(York U.)A family of symmetric functions associated with Stirling permutations We present exponential generating function analogues to two classical identities involving the ordinary generating function of the complete homogeneous symmetric function. After a suitable specialization the new identities reduce to identities involving the first and second order Eulerian polynomials. These results led us to consider a family of symmetric functions associated with the Stirling permutations introduced by Gessel and Stanley.18 Sep. 2017 Shu Xiao Li

(York U.)Structure of R-Polytopes on Relations We introduce a class of {0,1} polytopes, assiciated to relations on a finite set, called R-polytopes. The R-polytopes generalize a number of classic polytopes including non-attacking rook placement polytopes and Stanley's chain polytopes. We have a general theorem that describes their 1-skeleton. The R-polytopes also appear in graph theory, finding their facets is central in vertex packing problem. We will discuss and give description of some of the facets. This is joint work with Aliniaeifard, Benedetti, Bergeron & Saliola.

Below you will find links to the seminar webpages for previous years.