Speaker: Daniela Martinez Correa, Memorial University
Time/Date: Wednesday, December 10, 2025, 2 p.m.
Room: HH-3017
Title: On the finite basis problem for varieties generated by upper triangular matrices

Abstract:
In this seminar, we talk about the Specht problem for varieties of graded algebras generated by UT_n^(-), the Lie algebra of upper triangular matrices of size n×n over an infinite field K. Specifically, we give a positive answer to the finite basis problem for the variety of graded Lie algebra generated by UT_n^(-) with the canonical grading, when the characteristic p of K is either zero or greater than n−1. Furthermore, if K is a field of positive characteristic p, we construct three varieties of Z_p+1-graded Lie algebras that do not have a finite
basis of graded identities and satisfy the same graded identities that, in the case of an infinite field, define the variety generated by UT_p+1^(-). Finally, we discuss the analogous problem for the variety generated by UT₃^(-), endowed with an elementary grading.

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Speaker: Graham Cox, Memorial University
Time/Date: Tuesday, December 2, 2025, 1 p.m.
Room: HH-3013
Title: Geometry of infinite-dimensional manifolds - Part 3

Abstract:

This is an introductory talk on differential geometry in infinite dimensions. I will try to keep prerequisites to a minimum, just assuming familiarity with basic concepts from differential geometry and functional analysis (in particular, Banach spaces and finite-dimensional smooth manifolds).

Many of the definitions and constructions are identical to those in finite dimensions, so I will instead focus on some of the subtleties and differences that arise in infinite dimensions. In a future talk I will describe some classical examples of this theory, such as manifolds of mappings and their application to incompressible fluid flow.

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Speaker: Serhii Koval, Memorial University
Time/Date: Tuesday, November 25, 2025, 1 p.m.
Room: HH-3013
Title: Algebra of symplectic reduction - Part 2

Abstract:
In classical mechanics, symplectic (or Hamiltonian) reduction allows simplifying the equations of motion by considering symmetries of the phase space and its furter foliation into symplectic leaves. In this talk, I will give an introduction to the process of symplectic reduction from an algebraic perspective in the framework of affine schemes and actions of reductive groups. I will give an example of computation of Hamiltonian reduction for the commuting scheme. Time permitting, I will discuss Hamiltonian reduction along coadjoint orbit and give the construction of Calogero-Moser space of Kazhdan, Kostant and Sternberg.

This talk is based on the lecture notes of P. Etingof on Calogero-Moser systems.

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Speaker: Yuri Bahturin, Memorial University
Time/Date: Wednesday, November 19, 2025, 1 p.m.
Room: HH-3017
Title: Identities in finite algebras

Abstract:
Using methods of the classical theory of varieties of groups, one can get new results on the (graded) identical relations of finite dimensional (Omega-)algebras over finite fields (finite algebras). In particular, one can show that any two graded simple finite Omega-algebras satisfying the same graded identities must be isomorphic as graded algebras.

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Speaker: Graham Cox, Memorial University
Time/Date:
Wednesday, November 12, 2025, 1 p.m.
Tuesday, November 18, 2025, 1 p.m.
Room: HH-3013
Title: Geometry of infinite-dimensional manifolds - Parts 1 & 2

Abstract:

This is an introductory talk on differential geometry in infinite dimensions. I will try to keep prerequisites to a minimum, just assuming familiarity with basic concepts from differential geometry and functional analysis (in particular, Banach spaces and finite-dimensional smooth manifolds).

Many of the definitions and constructions are identical to those in finite dimensions, so I will instead focus on some of the subtleties and differences that arise in infinite dimensions. In a future talk I will describe some classical examples of this theory, such as manifolds of mappings and their application to incompressible fluid flow.

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Speaker: Tom Baird, Memorial University
Time/Date: Tuesday, November 4, 2025, 1 p.m.
Room: HH-3013
Title: An introduction to Cohomological Field Theories - Part 2

Abstract:
Having introduced moduli spaces of curves and Gromov-Witten theory last week, this week I will present the abstract definition of a cohomological field theory, explore some of its properties, and describe the Givental-Teleman classification of semisimple cohomological field theories.

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Speaker: Christopher Lang, Memorial University
Time/Date: Tuesday, October 28, 2025, 1 p.m.
Room: HH-3013
Title: An introduction to topological recursion - Part 2

Abstract:

Topological recursion is a construction in algebraic geometry that recursively computes invariants of spectral curves. In this talk, I will (finally) introduce topological recursion, examine the connection between topological recursion and Airy ideals, and explore some applications of this construction.

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Speaker: Serhii Koval, Memorial University
Time/Date: Tuesday, October 21, 2025, 1 p.m.
Room: HH-3013
Title: Algebra of symplectic reduction - Part 1

Abstract:
In classical mechanics, symplectic (or Hamiltonian) reduction allows simplifying the equations of motion by considering symmetries of the phase space and its furter foliation into symplectic leaves. In this talk, I will give an introduction to the process of symplectic reduction from an algebraic perspective in the framework of affine schemes and actions of reductive groups. I will give an example of computation of Hamiltonian reduction for the commuting scheme. Time permitting, I will discuss Hamiltonian reduction along coadjoint orbit and give the construction of Calogero-Moser space of Kazhdan, Kostant and Sternberg.

This talk is based on the lecture notes of P. Etingof on Calogero-Moser systems.

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Speaker: Tom Baird, Memorial University
Time/Date: Thursday, October 16, 2025, 1 p.m.
Room: HH-3013
Title: An introduction to Cohomological Field Theories - Part 1

Abstract:
In this expository lecture, I will give an introduction to cohomological field theories in the sense of Kontsevich and Manin. Along the way, we will learn about moduli spaces of complex curves, Gromov-Witten theory, and 2D topological field theories. I hope to make my presentation accessible to anyone acquainted with manifolds and cohomology (singular or de Rham).

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Speaker: Christopher Lang, Memorial University
Time/Date: Tuesday, October 7, 2025, 2 p.m.
Room: HH-3013
Title: An introduction to topological recursion - Part 1

Abstract:
Topological recursion is a construction in algebraic geometry that recursively computes invariants of spectral curves. It has applications to enumerative geometry, string theory, knot theory, mathematical physics, and random matrix theory, among others. In this talk, I will introduce some of the components of this construction.

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Speaker: Sebastiano Argenti, Memorial University
Time/Date: Wednesday, October 1, 2025, 1 p.m.
Room: HH-3017
Title: Minimal varieties of graded algebras

Abstract:
A cornerstone result in the theory of polynomial identities is the existence of the exponent of any variety of associative algebras, proved by Giambruno and Zaicev at end of the last century. Their theorem allows to classify the varieties on an integral scale whose steps are the minimal varieties of given exponent d, namely those varieties of exponent d such that every proper subvariety has exponent strictly less than d. Some years later, Giambruno and Zaicev gave also a characterization of the minimal varieties: they are precisely those with
factorable T-ideal of identities. Moreover, they can also be characterized by being precisely those generated by the Grassmann envelope of ”minimal algebras”, that in finite dimension are equivalent to upper block triangular matrix algebras.

In this talk we give an account of the efforts made to generalize the previous results to graded algebras and graded polynomial identities. The existence of the graded exponent was proved by Aljadeff and Giambruno. On the other hand, the classification of the minimal varieties of graded algebras poses several challenges. It was found that minimal graded algebras do not produce minimal varieties. Moreover, the graded T_G-ideal of minimal varieties is not always factorable. Therefore, new techniques are needed to deal with the graded case. When the grading group G is finite abelian, both the classification problem and the factorability problem were recently solved.