Speaker: Samuel Bauer, University of Hamburg
Time/Date: Friday, November 6, 2026, 1 p.m.
Room: HH3017
Title: Grothendieck-Verdier Categories and Frobenius Structures

Abstract:
We relate Frobenius Monoidal Functors to Frobenius algebras, allowing the use of algebraic tools to understand functorial structure. Given two K-linear monoidal categories, C and D, the functor category Funct(C,D) can be given the structure of a monoidal category using the Day convolution. With this structure, algebras with respect to the Day convolution are in bijection with lax monoidal functors from C to D. If we want to generalize this connection between algebraic structure on the one hand, and functor structures on the other, we need additional structure on the monoidal categories involved. In the case of Frobenius algebras and Frobenius Monoidal functors, the appropriate generalization is that of the Grothendieck-Verdier category. We prove that, given two K-linear Grothendieck-Verdier categories, C and D, the functor category Funct(C,D) can be given the structure of a Grothendieck-Verdier category in part using the Day convolution; then, Frobenius Monoidal functors between Grothendieck-Verdier categories are in bijection with Grothendieck-Verdier Frobenius algebras with respect to the Grothendieck-Verdier structure on Funct(C,D). This generalizes the results from Day in a fruitful direction.

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Speaker: Tom Baird, Memorial University of Newfoundland
Time/Date: Thursday, November 5, 2026, 12 p.m.
Room: HH3017
Title: The Cohomology of Sheaves, part 4

Abstract:
I will explain how a short exact sequence of sheaves gives rise to a long exact sequence in cohomology, and use this to prove that cohomology can calculated with acyclic resolutions. This lecture will include a multimedia segment.

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Speaker: Tom Baird, Memorial University of Newfoundland
Time/Date: Thursday, October 29, 2026, 12 p.m.
Room: HH3017
Title: The Cohomology of Sheaves, part 3

Abstract:
We will finish proving that injective resolutions of sheaves exist and are unique up to homotopy, so that sheaf cohomology is well-defined. Next we show that a short exact sequence of sheaves determines a long exact sequence in cohomology, which is essential for calculations.

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Speaker: Sebastiano Argenti, Memorial University of Newfoundland
Time/Date: Wednesday, October 28, 2026, 1 p.m.
Room: HH3017
Title: Distance-biregular graphs and coherent algebras

Abstract:
Distance-biregular graphs (DBRGs) capture the properties of many remarkable incidence structures, such as affine and projective spaces, generalized polygons, designs and partial geometries. In a recent work with A. Siciliano we obtained existence conditions for a family of DBRGs of diameter d and girth 2d-2. The proof relies on the representation theory of non-commutative algebras and on the factorization of integer polynomials, thus providing an example of how algebra can be applied to graph theory.

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Speaker: Tom Baird, Memorial University of Newfoundland
Time/Date: Thursday, October 22nd, 2026, 12 p.m.
Room: HH3017
Title: The Cohomology of Sheaves, part 2

Abstract:
Having defined the category of sheaves in lecture 1, in this lecture I will introduce stalks, the global sections functor, and sheaf cohomology.

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Speaker: Yuri A. Bakhturin, Memorial University of Newfoundland
Time/Date: Wednesday, October 21st, 2026, 1 p.m.
Room: HH3017
Title: Spectral sequences in locally finite varieties of algebras

Abstract:
I will talk about numerical characteristics of the sets of identical relations of algebras over finite fields.

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Speaker: Tom Baird, Memorial University of Newfoundland
Time/Date: Thursday, October 15th, 2026, 12 p.m.
Room: HH3017
Title: The Cohomology of Sheaves

Abstract:
Sheaves and their cohomology play a fundamental role in algebra, geometry, and topology. In this series of lectures, I will introduce these concepts, develop their theory, and explore applications.
In this first lecture, I will explain what a sheaf is and why is interesting, and then define the cohomology of a sheaf.

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Speaker: Serhii Koval, Memorial University/Saint Mary's University
Time/Date: Wednesday, October 14th, 2026, 1 p.m.
Room: HH3017
Title: Generic graded contractions of Lie algebras

Abstract:
Contractions and degenerations of Lie algebras have been extensively studied since the 1950s. The idea is to pass from one Lie algebra to another by some kind of limit process. Another type of contractions was introduced by de Montigny and Patera (1991) in the context of Lie algebras over a field F equipped with a grading by an abelian group G. In this framework, the Lie bracket of two homogeneous elements is modified by a scalar factor that depends on the degrees of the elements. The resulting scaling function must satisfy specific conditions to ensure that the new bracket remains antisymmetric and satisfies Jacobi identity.
We are interested in generic graded contractions, i.e., those that produce a new Lie bracket for any G-graded Lie algebra. They can be viewed as lax monoidal structures on the identity endofunctor of the category of G-graded vector spaces. We show that generic graded contractions with a fixed support S are classified by a certain abelian group H²_S(F^x), which we explicitly describe. We also analyze which generic graded contractions define graded degenerations of a given G-graded Lie algebra.
This talk is based on a joint work with M. Kochetov.
Kochetov M. and Koval S., Generic graded contractions of Lie algebras,  J. Algebra 696 (2026), 245-277. arXiv:2506.00610.

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Speaker: Daniel Offin, Queen's University
Time/Date: Thursday, October 8th, 2026, 12 p.m.
Room: HH 3017
Title: Dynamics and symmetry: minimizing brake orbits

Abstract:
After Newton proposed his universal laws of motion, there was a lively debate in the 18th c concerning the principle of least action championed by Maupertuis and later Euler and Lagrange. This approach was based on Maupertuis's principle of minimum action. Maupertuis’s principle of least action states that in all natural phenomena a quantity called ’action’ tends to be minimised. We shall give a short history of this principle and its modern formulations culminating in the study of the spectrum of minimizers, bringing together symplectic geometry, dynamcial systems and symmetry groups.