The Applied Algebra Seminar

A
Monday afternoon research seminar

The seminar is currently organized by Cesar Ceballos and Nantel Bergeron.

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

Date Speaker Title (click titles for abstract) 6 Apr. 2015 Jim Haglund

(U. of Pennsylvania)30 Mar. 2015 Hugh Thomas

(U. of New Brunswick)9 Feb. 2015 Ryan Kaliszewski

(Drexel U.)26 Jan. 2015 Greg Warrington

(U. of Vermont)1 Dec. 2014 Diana Ojeda

(U. of Toronto)24 Nov. 2014 Rafael S. Gonzalez

(U. of Kentucky)17 Nov. 2014 Yannic Vargas

(LaCIM, UQAM)10 Nov. 2014

3 Nov. 2014 Vincent Genest

(U. de Montréal)The Bannai-Ito algebra, its q-extension and some applications In this talk, I will present the Bannai-Ito algebra together with some applications. Its relation with the Bannai-Ito polynomials, the Racah problem for the paraboson algebra and a quantum superintegrable system with reflections will be surveyed. Its q-extension, and the relation it has with osp_q(1|2), will also be discussed.27 Oct. 2014 Kevin Dilks

(U. of Minnesota)q-gamma nonnegativity A polynomial of degree n with symmetric coefficient sequence has a unique expansion in terms of the polynomials t^i(1+t)^(n-2i). Gal has conjectured that for the h polynomial of generalized homology spheres (which includes simplicial polytopes), this expansion has nonnegative coefficients. In this talk, we will describe a multivariate formulation of this property, and give examples of proven and conjectured results for well-known combinatorial objects like the associahedron and the Coxeter complex.20 Oct. 2014 Salvatore Stella

(North Carolina State U.)d-vector fans for cluster algebras of finite and affine type Thanks to the Laurent phenomenon a family of integer vectors (the d-vectors) can be naturally associated to each cluster algebra. This family encodes many of the combinatorial properties of the algebra itself making it an interesting object to study.

In this talk, after reviewing the basic definitions, we will construct the d-vectors associated to any finite or affine type cluster algebra with an acyclic initial seed. The construction will leverage some interesting features of the action of a particular product of reflections on the associated root system.13 Oct. 2014

NO SEMINARThanksgiving 6 Oct. 2014 Suho Oh

(Texas State U.)Wires and separation Wiring diagrams are widely used combinatorial objects that are mainly used to describe reduced words of a permutation. In this talk, I will mention an interesting property about those diagrams, and then introduce other results and problems related to this property.3 Oct. 2014* Christophe Hohlweg

(LaCIM, UQAM)Weak order and imaginary cone in infinite Coxeter groups The weak order is a nice combinatorial tool intimately related to the study of reduced words in Coxeter groups. In this talk, we will discuss a conjecture of Matthew Dyer that proposes a generalization of the framework weak order/reduced words to infinite Coxeter groups. On the way, we will talk of the relationships between limits of roots and tilings of their convex hull, imaginary cones, biclosed sets and inversion sets of reduced infinite words (partially based on joint works with M. Dyer, J.P. Labbé and V. Ripoll).29 Sep. 2014 Brendan Pawlowski

(U. of Minnesota)Permutation patterns and Stanley symmetric functions Given a permutation w, Stanley defined a symmetric function F_w which encodes information about the reduced words of w, and showed that F_w is a single Schur function exactly when w avoids the pattern 2143. We generalize this statement, showing that the Schur expansion of F_w respects pattern containment in a certain sense, and that the number of Schur function terms is determined by pattern avoidance conditions on w. Along the way, we compute the cohomology of certain subvarieties of Grassmannians, resolving some cases of a conjecture of Liu. Our proofs use the diagram Specht modules introduced by James and Peel, which in this case are closely related to the Schubert modules of Kra?kiewicz and Pragacz. This is joint work with Sara Billey.15 Sep. 2014 Joshua Hallam

(Michigan State U.)Factorization of the Characteristic Polynomial of a Poset The characteristic polynomial of a poset is the generating function for the Mšbius function of the poset. For some families of posets, the polynomial factors with nonnegative integer roots. We will present a new method which gives a combinatorial explanation for these factorizations. Additionally, we will see how this method can be used to explain a relationship between the generating function for the increasing forests of a graph and its chromatic polynomial. This is joint work with Bruce Sagan.8 Sep. 2013

Bruce Sagan

(Michigan State U.)Of antipodes and involutions, of cabbages and kings ... If H is a connected, graded Hopf algebra, then Takeuchi's formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellation-free formulas. We apply this idea to the Hopf algebras of polynomials, graphs, and noncommutative symmetric functions. This is joint work with Carolina Benedetti.

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