Speaker: Felipe Yukihide Yasumura, State University of Campinas (Brazil) and Memorial University of Newfoundland
Time/Date: Wednesday, April 11, 2018 at 1pm
Room: HH-3017
Title: Do polynomial identities distinguish simple algebras? Part 2

Abstract:
In this seminar, we prove Razmyslov's Theorem: two finite-dimensional simple algebras over an algebraically closed field, both with the same arbitrary signature, satisfying the same polynomial identities are isormophic.

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Speaker: Alexander Bihlo, Memorial University of Newfoundland
Date/Time: Thursday, April 5, 2018 at 1pm
Room: HH-3017
Title: Exactly conservative discretization schemes for dynamical systems

Abstract:
In this talk I will introduce a method for finding exactly conservative discretization schemes for systems of ordinary differential equations. The method is constructive and applicable to any system of ordinary differential equations that has at least one first integral. I will illustrate the method with examples from various fields of the mathematical sciences, including a Lotka-Volterra system, the conservative Lorenz-1963 model, and the solar system. This is joint work with Andy Wan and JeanChristophe Nave at McGill University.

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Speaker: Felipe Yukihide Yasumura, State University of Campinas (Brazil) and Memorial University of Newfoundland
Time/Date: Wednesday, April 4, 2018 at 2pm
Room: HH-3017
Title: Do polynomial identities distinguish simple algebras?

Abstract:
An interesting question is if polynomial identities can uniquely determine an algebra. Some works were dedicated to studying this, and it turns out that the best-known theorem is due to Razmyslov. In parallel, the graded version of the problem also attracted the attention of some researchers. In this seminar, we discuss the question and present the main results obtained until now. We show that the graded version is a particular case of Razmyslov’s theory. This is a joint work with Professor Yuri Bahturin (Memorial University of Newfoundland).

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Speaker: Alexander Bihlo, Memorial University of Newfoundland
Date/Time: Wednesday, March 28, 2018 at 1pm
Room: HH-3017
Title: Invariant discretization beyond finite differences

Abstract:
In this talk I will introduce a method for constructing discretization schemes that preserve the invariance group of a system of differential equations. Traditionally, such methods were applied within the framework of finite difference methods only. I will discuss possible ways of constructing invariant discretization schemes also for other discretization methodologies, including finite elements and meshless methods.

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Speaker: Yiqiang Zhou, Memorial University of Newfoundland
Date/Time: Wednesday, March 14, 2018 at 2pm
Room: HH-3017
Title: An embedding theorem on triangular matrix rings

Abstract:
Every matrix in the triangular matrix $T_n(R)$ ring  over a bleached local ring R is similar to a ‘simple form’, which is, in most cases, contained in a subring $\Omega$ of $T_n(R)$ with $\Omega$ isomorphic to a direct product of two triangular matrix rings over $R$ of smaller size. This result, called the embedding theorem, suggests a new approach for handling triangular matrix rings. It is applied to proving several results on the strong cleanness and strong 2-sum property of triangular matrix rings.

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Speaker: Caio De Naday Hornhardt, Memorial University of Newfoundland
Date/Time: Wednesday, Feb 28, 2018, 1:00p.m.
Room: HH-3017
Title: Group gradings on the simple Lie superalgebras A(n, n)

Abstract:
In a recent paper, we have classified abelian group gradings on the matrix superalgebras M(m, n). These restrict to the so called Type I gradings on the special linear Lie superalgebra sl(m|n)  (or its quotient by the center in the case m=n). In this talk, we will discuss a strategy to find the remaining gradings on special linear Lie superalgebras, that is, Type II gradings. We will focus on the case m=n, which admits what we call odd Type II gradings.

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Speaker: Mikhail Kotchetov, Memorial University of Newfoundland
Date/Time: Wednesday, Feb 14, 2018. 1:00p.m.
Room: HH-3017
Title: Lie algebras of type D4 and triality (conclusion)

Abstract:
Last time we discussed the "trialitarian" models for the spin group of the space of octonions and the tangent Lie algebra of this group (which has type D4): namely, the related triples of isometries and the related triples of skew-symmetric operators on the space of octonions. The main feature of these models is that they reveal the outer action of the permutation group S3 on these objects. We will continue to explore the implications of this, including related triples of automorphisms of the algebra of matrices of order 8 (equipped with the involution determined by the octonionic norm), related triples of gradings on the said algebra, and related triples of central simple algebras of degree 8 (equipped with orthogonal involutions).

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Speaker: Mikhail Kotchetov, Memorial University of Newfoundland
Date/Time: Wednesday, January 31, 2018 at 1pm
Room: HH-3017
Title: Lie algebras of type D4 and triality (continued)

Abstract:
We will continue the discussion of "trialitarian" models of simple Lie algebras and groups of type D4, their relation to Clifford algebras and half-spin modules, and applications to the classification of gradings.

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Speaker: Mikhail Kotchetov, Memorial University of Newfoundland
Date/Time: Wednesday, January 24, 1pm
Room: HH-3017
Title: Lie algebras of type D4 and triality

Abstract:
The simple Lie algebras (or groups) of type D4 differ from all other members of the D series by the existence of a three-fold rotational symmetry of their Dynkin diagram. This so-called "triality" is not apparent in the standard matrix models of D4, but is revealed through the algebra of octonions. We will review the "trialitarian" models of D4 and, time permitting, their applications to the classification of gradings.

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Speaker: Eugene Chibrikov, Memorial University of Newfoundland
Date/Time: 1pm, Wednesday December 13, 2017
Room: HH-3017
Title: The algorithm for identifying and representing treatment exposure patterns

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Speaker: Yorck Sommerhäuser, Memorial University of Newfoundland
Date/Time: Wednesday, November 1, 2017
Room: HH-3017
Title: Extensions of Yetter-Drinfel'd Hopf algebras

Abstract:
Due to the work of N. Andruskiewitsch, J. Devoto, M. Feth, I. Hofstetter, S. Majid, W. M. Singer, and others, the extension theory for Hopf algebras is by now well-established. This theory carries over to Hopf algebras in monoidal categories, and therefore in particular to Yetter-Drinfel'd Hopf algebras, without substantial modification. 

However, this direct generalization does not cover important examples, such as those that arise in the classification of commutative semisimple Yetter-Drinfel'd Hopf algebras over groups of prime order. The reason is that in these examples the so-called cleaving map is not a morphism in the category. In the talk, we describe a framework that is able to incorporate also these examples. The talk is based on joint work with Y. Kashina.