Speaker: Ian Payne (University of Waterloo)
Time/Date: August 13, 2012, 1 p.m.
Room: HH-3017
Title: A Short Introduction to Universal Algebra

Abstract:
I will begin by defining universal algebras, and describing how they generalize familiar things like groups and rings. I will then explain how the notions of homomorphisms, subalgebras, and powers all can be defined in a natural way so that they agree with the corresponding notions for groups and rings. Finally, I will define and discuss varieties of algebras, which are a central object of study in universal algebra. 

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Speaker: Leandro Vendramin (University of Buenos Aires, Argentina) 
Time/Date: July 31, 2012, 1 p.m.
Room: HH-3017
Title: Nichols algebras with many quadratic relations

Abstract:
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the homogeneous component of degree two of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a nice factorization assumption on the Hilbert series. The talk is based on a joint work with M. Graña and I. Heckenberger.

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Speaker: Nicolas Andruskiewitsch (University of Cordoba, Argentina)
Time/Date: July 27, 2012, 1 p.m.
Room: HH-3017
Title: From Hopf algebras to tensor categories

Abstract:
Tensor categories are the natural setting for the understanding of many applications of Hopf algebras. In this talk I will introduce them and then I will discuss how to obtain tensor categories from spherical Hopf algebras and how we hope to discover new examples in this way.

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Speaker: Csaba Schneider (CAUL, Universidade de Lisboa, Portugal) 
Time/Date: July 19, 2012, 1 p.m.
Room: HH-3017
Title: Constructive membership testing in classical groups

Abstract:
Computational matrix group theory has been the fastest growing area of computational group theory during the last 20 years. Efficient computations in finite matrix groups require that we are able to solve some basic tasks in groups generated by a finite set of matrices over a finite field. One of these tasks, known as the "Constructive Membership Problem", requires that we write an arbitrary element of a quasisimple matrix group as a product of its generators. I will present several approaches to solve this problem in different contexts. The implementations of the existing algorithms are written in Magma and I will also show how these implementations perform in practice.

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Speaker: Alexey Gordienko (Memorial University of Newfoundland)
Time/Date: June 13, 2012, 1 p.m.
Room: HH-3017
Title: Amitsur's conjecture for polynomial H-identities of H-module Lie algebras

Abstract:
In the 1980's (or even earlier), a conjecture about the asymptotic behaviour of codimensions of ordinary polynomial identities was made by S.A. Amitsur. Amitsur's conjecture was proved in 1999 by A. Giambruno and M.V. Zaicev for associative algebras, in 2002 by M.V. Zaicev for finite dimensional Lie algebras.

Alongside with ordinary polynomial identities of algebras, graded polynomial identities, G- and H-identities are important too. Usually, to find such identities is easier than to find the ordinary ones. Furthermore, the graded polynomial identities, G- and H-identities completely determine the ordinary polynomial identities. Therefore the question arises whether the conjecture holds for graded codimensions, G- and H-codimensions.

We consider a finite dimensional H-module Lie algebra L over a field of characteristic 0 where H is a finite dimensional semisimple Hopf algebra, and prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of polynomial H-identities of L. As a consequence, we obtain the analog of Amitsur's conjecture for graded codimensions of any finite dimensional Lie algebra graded by a finite group not necessarily Abelian.

This result is a generalization of the result of the author where he proved the analog of Amitsur's conjecture for G-codimensions for a finite group G and graded codimensions for a finite Abelian group.

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Speaker: Alexey Gordienko (Memorial University of Newfoundland)
Time/Date: May 2, 2012, 1 p.m.
Room: HH-3017
Title: Structure of H-(co)module Lie algebras

Abstract:
The applications of Lie and associative algebras with an additional structure, e.g. graded, H-(co)module, or G-algebras, gave rise to the studies of the objects and decompositions that have nice properties with respect to these structures. I will discuss the H-(co)invariant analog of the Levi theorem that is one of the main results of the structure Lie theory. Also I am going to talk about the stability of the radicals and about further decompositions of the solvable radical and a maximal semisimple subalgebra. In the end of the talk I will discuss the applications of the results obtained to graded Lie algebras and Lie algebras with a rational action of a reductive affine algebraic group by automorphisms.

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Speaker: Alexey Gordienko (Memorial University of Newfoundland)
Time/Date: March 6, 2012, 1 p.m.
Room: SN-1019
Title: Graded polynomial identities, group actions, Hopf module algebras, and exponential growth

Abstract:
We prove the analog of Amitsur's conjecture on asymptotic behavior for codimensions of different generalizations of polynomial identities, e.g. graded polynomial identities and G-identities for any finite not necessarily Abelian group G, and H-identities for finite dimensional associative algebras with an action of a finite dimensional semisimple Hopf algebra H.

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Speaker: Mikhail Kotchetov (Memorial University of Newfoundland)
Time/Date: anuary 18, 2012, 1 p.m.
Room: HH-3017
Title: Weyl groups of fine gradings

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Speaker: Edgar Goodaire (Memorial University of Newfoundland)
Time/Date: February 15, 2012, 1 p.m.
Room: HH-3017
Title: Jordan loops and loop rings: a mix of combinatorics and algebra

Abstract:
Think of a loop as a group which is not necessarily associative. So the multiplication table of a loop is nothing but a standard Latin square. In this talk, we study loops that are Jordan in the sense that they are commutative and satisfy the Jordan identity:(x^2y)x=x^2(yx). We also discuss a subclass of Jordan loops we call RJ for ''ring Jordan,'' these being loops whose ''loop rings'' are also Jordan. We describe ways to construct finite Jordan loops and finite RJ loops. Our method involves finding Latin squares whose entries satisfy certain functional equations on an abelian group. We find some solutions, but wish we had more. There are a number of open combinatorial problems associated with this work.

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Speaker: Alexey Gordienko (Memorial University of Newfoundland)
Time/Date: November 30 & December 7, 2011, 1 p.m.
Room: HH-3017
Title: Graded polynomial identities, group actions and exponential growth of Lie algebras

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Speaker: Jonny Lomond (Memorial University of Newfoundland)
Time/Date: November 23, 2011, 3 p.m.
Room: HH-2010
Title: Growth functions of G-sets II

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Speaker: Toma Albu (Simion Stoilow Institute of Mathematics of Romanian Academy, Romania)
Time/Date: September 28, 2011, 1 p.m.
Room: HH-3017
Title: The Hopkins-Levitzki Theorem: old and new II

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Speaker: Alexey Gordienko (Memorial University of Newfoundland)
Time/Date: September 21, 2011, 1 p.m.
Room: HH-3017
Title: Codimensions of polynomial identities of representations of Lie algebras