Speaker: Nicolás Andruskiewitsch, Universidad Nacional de Córdoba/CONICET (Argentina)
Time/Date: Friday, August 22, 2025, 1 p.m.
Room: HH-3017
Title: Noetherian enveloping algebras of simple graded Lie algebras

Abstract:
We show that the universal enveloping algebra of an infinite-dimensional simple Zn-graded Lie algebra is not Noetherian, a partial answer to a well-known conjecture that is unavoidable for the classification of Noetherian Hopf algebras. This is joint work with Olivier Mathieu.

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MSc Thesis Seminar
Speaker: Zikang Lei, Memorial University of Newfoundland
Time/Date: Friday, May 30, 2025, 1 p.m.
Room: HH-3017
Title: Fine gradings on associative superalgebras with superinvolution over an algebraically closed field

Abstract:
Assuming that the ground field is algebraically closed and of characteristic not equal to 2, we classify, up to equivalence, the fine gradings on finite-dimensional associative graded-simple superalgebras. Our approach relies on Wedderburn structure theory for associative graded-simple superalgebras satisfying the descending chain condition on graded left ideals. This framework naturally leads to the study of nondegenerate sesquilinear forms associated with superinvolutions. To address the equivalence problem, we construct explicit models that are equivalent to the given graded-simple superalgebras and analyze the conditions under which such models are themselves equivalent. 

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MSc Thesis Seminar
Speaker: Ranran Zhao, Memorial University of Newfoundland
Time/Date: Thursday, March 27, 2025 at 1:00 p.m.
Room: HH-3017
Title: Eversible rings and zero divisors: insights from triangular and polynomial rings

Abstract:
Zero divisors play a crucial role in understanding the structure of noncommutative rings, and their behavior is central to many open questions in ring theory. In this talk, we introduce eversible rings, a generalization of reversible rings, and explore their algebraic significance. We begin by discussing the motivation behind eversibility and its relationship to zero divisors, providing intuitive examples to build familiarity with the concept.

Next, we focus on the eversibility of formal triangular matrix rings and upper triangular matrix rings, a topic inspired by previous work in the literature. However, several key results in this area were found to be incorrect. We highlight these inaccuracies and present our corrected theorems, offering a more precise characterization of eversible triangular matrix rings.

Finally, we extend our discussion to polynomial rings, where the interaction between eversibility and polynomial extensions remains an open question: If  R  is eversible, is  R[x]  also eversible? While partial progress has been made, a complete resolution is still unknown. We conclude by discussing the implications of this question and potential directions for future research.

This talk is structured to be accessible to graduate students with a background in abstract algebra, emphasizing intuition and conceptual clarity over technical proofs.

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Graduate Seminar
Speaker: Mikhail Kotchetov, Memorial University of Newfoundland
Time/Date: Thursday, March 20, 2025, 1:00 p.m.
Room: HH-3017
Title: An invitation to Representation Theory

Abstract:
Since the pioneering works of Ferdinand Georg Frobenius (1849 - 1917) and Issai Schur (1875 - 1941), Representation Theory has become one of the central themes of algebra and, at the same time, one of its main links to applications in other branches of mathematics and in natural sciences. In particular, starting with Hermann Weyl (1885 - 1955) and Eugene Wigner (1902 - 1995),  Lie groups and their representations have been extensively used in quantum mechanics.

In this talk, I will present some basic examples of representations of algebraic structures (namely, groups and Lie algebras), discuss some classical results and, time permitting, show an application of Representation Theory to finding spherical harmonics.

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MSc Thesis Seminar
Speaker: Thushanthani Rajendran, Memorial University of Newfoundland
Time/Date: Thursday, December 19, 2024, 11:00a.m.
Room: HH-3017
Title: An Application of Polynomial Optimization to the Study of Hookean Solids

Abstract:
A Hookean solid is described by a so-called elasticity tensor, which is a fourth-order tensor with certain index symmetries that yield, in general, 21 independent components. However, a Hookean solid can also exhibit material symmetries. For example, an isotropic solid is described by an elasticity tensor that is invariant under all rotations of the 3D space and, as a consequence, has only two independent components. Material symmetries give insight into the mechanical properties of the solid and facilitate mathematical modelling. Therefore, it is desirable to approximate a given general elasticity tensor (for example, measured experimentally) by one that belongs to a chosen symmetry class. In this talk, we compare two different formulations of the problem of finding the closest element in the symmetry class as a polynomial optimization problem. We apply the polynomial optimization technique due to Lasserre to specific elasticity tensors, utilizing the implementation of Lasserre’s method in MATLAB through the Gloptipoly 3 toolbox.

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Speaker: Serhii Koval, Memorial University of Newfoundland
Time/Date: Wednesday, December 4, 2024, 1 p.m.
Room: HH-3017
Title: Point and generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation - Part II

Abstract:
In the first part of the talk, we discussed the basic theory of point symmetries of differential equations together with some aspects of the classical group analysis of the remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation. The second part of the talk is devoted to generalized symmetries of differential equations and, in particular, to the comprehensive description of the algebra of generalized symmetries of the remarkable Fokker-Planck equation. It turns out that the essential part of this algebra is generated by the recursion operators associated with the nilradical of the essential Lie invariance algebra, and is thus related to the index-two Weyl algebra.

Speaker: Serhii Koval, Memorial University of Newfoundland
Time/Date: Wednesday, November 20, 2024, 1 p.m.
Room: HH-3017
Title: Point and generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation

Abstract:
We begin by briefly discussing the basic theory of generalized symmetries of differential equations and their state of the art descriptions for specific differential equations. Next, we discuss some aspects of the classical group analysis of the remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation. This equation is also called the Kolmogorov equation and it is singled out within the entire class of ultraparabolic linear second-order partial differential equations with three independent variables by its wonderful symmetry properties. We comprehensively describe the algebra of generalized symmetries of this equation. It turns out that the essential part of this algebra is generated by the recursion operators associated with the nilradical of the essential Lie invariance algebra of the Kolmogorov equation and is thus related to the index-two Weyl algebra.

Speaker: Eduardo Martinez-Pedroza, Memorial University of Newfoundland
Time/Date: Wednesday, November 13, 2024, 1 p.m.
Room: HH-3017
Title: The coset intersection complex

Abstract:
The coset intersection complex highlights the geometric nature of certain algebraic properties of discrete groups and their subgroups. This object also  generalizes other spaces that have been previously considered in the study of discrete groups via geometric actions. The talk will introduce the coset intersection complex and some recent results obtained in joint work with Carolyn Abbott.

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Speaker: Alfie Davies, Memorial University of Newfoundland
Time/Date: Wednesday, November 6, 2024, 1 p.m.
Room: HH-3017
Title: Playing with misère monoids

Abstract:
Most people try to win games, but trying to lose is surprisingly difficult. The study of losing is known as misère theory, and it fits within the broader field of Combinatorial Game Theory. We will give an introduction to the field, and then discuss some of its connections with algebra; most misère research is focused on understanding the structure of various commutative (po)monoids, but the area is currently severely under-explored.

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Speaker: Stefan Gille, University of Alberta
Time/Date: Wednesday, October 23, 2024, 1 p.m.
Room: HH-3017
Title: Chow motives and applications

Abstract:
In the first half of the talk I will give a short overview of the construction of Grothendieck's Chow motives. Roughly speaking Chow motives are a linearization of the category of smooth projective varieties, however the construction itself can be applied (or generalized) to other geometric objects, as for instance manifolds.

In the second part of my talk I will discuss some applications of Chow motives.

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Speaker: Yorck Sommerhäuser, Memorial University of Newfoundland
Time/Date:
Wednesday, October 9, 2024, 1 p.m.
Wednesday, October 16, 2024, 1 p.m.
Room: HH-3017
Title: Constructing mapping class group representations from Hopf algebras - Parts I & II

Abstract:
The general principles of topological field theory lead to representations of mapping class groups of surfaces on the spaces of conformal blocks, briefly called the block spaces, which in the context of this talk are spaces of homomorphisms between modules of certain Hopf algebras. There exist a variety of frameworks for this construction, and the first part of the talk will be devoted to an introduction to one of these frameworks, namely the one put forward by V. Lyubashenko. In the second part of the talk, we explain how this construction can be extended from the block spaces mentioned above to the so-called derived block spaces, which are the cohomology groups of a certain cochain complex. The talk is based on joint work with S. Lentner, S. N. Mierach, and C. Schweigert.