The Applied Algebra Seminar
A Monday afternoon research seminar

About the seminar (click here to see more)


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.


Schedule

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)
23 Mar. 2015
Karola Meszaros
(Cornell U.)
16 Mar. 2015
9 Mar. 2015
2 Mar. 2015
23 Feb. 2015
16 Feb. 2015
NO SEMINAR
Family Day (Univeristy is closed)
9 Feb. 2015
Ryan Kaliszewski
(Drexel U.)
2 Feb. 2015
26 Jan. 2015
Greg Warrington
(U. of Vermont)
19 Jan. 2015
Emily Redelmeier
1 Dec. 2014
Diana Ojeda
(U. of Toronto)
Finite forms of Gowers' Theorem on the oscillation stability of c_0
I will present an example of the interaction between Ramsey Theory and Geometry of Banach Spaces. Hindman's Theorem states that given any 2-coloring of FIN, the collection of finite sets of natural numbers, there exists an infinite sequence of elements of FIN all of whose finite unions get the same color. Gowers formulated and proved a generalization of Hindman's Theorem to obtain the oscillation stability of c_0, the space of real sequences converging to 0 endowed with the supremum norm. Namely, he proved that any Lipschitz function defined on the unit sphere of c_0 is almost constant on the unit sphere of some infinite dimensional subspace.
In this talk I will first translate the oscillation stability of c_0 into the language of Ramsey Theory. Then, I will present a combinatorial proof of a finite version of the resulting Ramsey type theorem. It is worth pointing out that Gowers' argument uses ultrafilter dynamics, and up to now there is no combinatorial proof of the original (infinite) version of this theorem.
24 Nov. 2014
Rafael S. Gonzalez
(U. of Kentucky)
On the free Lie algebra with multiple brackets
We explore a beautiful interaction between algebra and combinatorics in the heart of the free Lie algebra on n generators: The multilinear component of the free Lie algebra Lie(n) is isomorphic as a representation of the symmetric group to the top cohomology of the poset of partitions of an n-set tensored with the sign representation. Hence, we can understand the algebraic object Lie(n) by applying poset theoretic techniques to the poset of partitions whose description is purely combinatorial. We will show how this relation generalizes further in order to study free Lie algebras with multiple compatible brackets. In particular we obtain combinatorial bases and compute the dimensions of these modules answering a question posed by F. Liu.
17 Nov. 2014
Yannic Vargas
(LaCIM, UQAM)
NCQsym revisited: a packed words approach
The hopf algebra NCQSym (aka WQSym) is a natural generalization of the Hopf algebra of permutations FQSym, introduced by N. Bergeron & M. Zabrocki (2006) / F. Hivert (1999) / F. Chapoton (1999)/ A. Jöllenbeck (1997)(independently, from different points of view). A basis of NCQSym is given by sets compositions, who are also equivalent to packed words. When studying this hopf algebra from the packed words point of view, it is not difficult to generalize some properties from FQSym to NCQSym. We discuss this approach, introduce analogous of the monomial basis to NCQSym and give an application to the study of the Drinfeld double of FQSym and NCQSym.
10 Nov. 2014
NO SEMINAR
(due to travel)
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 SEMINAR
Thanksgiving
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 Mbius 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.

Archives

Below you will find links to the seminar webpages for previous years.
Year 2013-14 Year 2012-13 Year 2011-12 Year 2010-11
Year 2009-10 Fall 2008 & Winter 2009 Fall 2007 Winter 2006
Fall 2005 Winter 2005 Fall 2004 Winter 2004
Fall 2003 Winter 2003 Fall 2002 Winter 2002
Fall 2001 Winter 2001 Fall 2000 Winter 2000
Fall 1999 Winter 1999 Fall 1998 Winter 1998
Fall 1997