The Applied Algebra Seminar

A
Monday afternoon research seminar

The seminar will resume Fall 2013 (2012-13 was on sabbatical)

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 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 at 2:30pm in N638 Ross Building (York University).

Date Speaker Title (click titles for abstract) 12 Nov. 2012 Josh Grochow

(U. of T.)Introduction to Geometric Complexity Theory The Geometric Complexity Theory (GCT) program was introduced by Mulmuley and Sohoni to attack fundamental lower bound problems in computational complexity theoryâ -- such as P vs NPâ -- using algebraic geometry and representation theory. In addition to presenting the basic structure of the GCT program, I will discuss some of the intuition behind the use of representation theory in complexity, as well as how GCT relates to classical questions in representationtheory such as the Littlewood-Richardson rule for the decomposition of tensor products of representations of GL_n into irreducibles.

5 Nov. 2012 Laura Escobar

(Cornell U.)A combinatorial strategy to solve the F-conjecture. The space of phylogenetic trees is a beautiful space that parametrizes rooted trees with a fixed number of leaves. This space can be subdivided into a fan in multiple ways; we will present the toric variety of one of this subdivisions. We will discuss some nice families of divisors on this toric variety which come from a strategy by Gibney and Maclagan to give a polyhedral description of the nef cone on the divisors of the moduli space $\overline{M}_{0,n}$.22 Oct. 2012 Juana Sanchez Ortega

(Fields Institute/ York)Nonassociative dialgebras This talk is based on the recent discovery of many new varieties of nonassociative structures that can be regarded as noncommutative analogues of classical structures. This development originated in the work of Bloh [1, 2] in the 1960s, but became much better known after the work of Loday [6, 7] in the early 1990s on Leibniz algebras. Associative dialgebras, also introduced by Loday, provides the natural context for the universal enveloping algebras of Leibniz algebras. Ten years later, Liu [5] introduced alternative dialgebras. Shortly after, Felipe and VelÃ¡squez [8] initiated the study of quasi-Jordan algebras (Jordan dialgebras), which are related to Jordan algebras as Leibniz algebras are to Lie algebras. Around the same time, Kolesnikov [4] developed a general method for passing from a variety of nonassociative algebras defined by polynomial identities to the corresponding variety of dialgebras. KP algorithm, the simplified form of this method stated in [3], will be presented and some examples will be given.8 Oct. 2012

NO SEMINARThanksgiving 1 Oct. 2012 Mikhail Mazin

(Stony Brook University)Generalized q,t-Catalan Numbers and Jacobi Factors We study combinatorics of cell decompositions of Jacobi factors of quasi-homogeneous plane curve singularities. The cells are enumerated by certain Young diagrams, and the dimensions of cells can be computed in a combinatorial way. The resulting combinatorial theory turns out to be related to a generalization of (q,t)-Catalan numbers. In the talk I will also discuss some symmetry properties of these polynomials.

This is a joint work with Eugene Gorsky.

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