This mini-course will focus on Representation Theory of simple complex finite dimensional and affine Lie algebras. We will start with the introduction to the theory of infinite dimensional weight representations. Though the classification of irreducible representations is still open beyond the sl(2) case in general, in some subcategories this problem can be managed successfully. In particular, we will discuss the theory of Gelfand-Tsetlin modules and their generalizations in the finite dimensional case. A comparison will be given with the representations…

Leandro Vendramin of the University of Buenos Aires will give a special minicourse from January 13-17. The course will be on the computer algebra system GAP. It will take place in the Department of Mathematics and Statistics at Dalhousie, and will also be live-streamed. It will be suitable for undergraduates, graduate students, postdocs, faculty, and everyone interested in symbolic computation. The first lecture of the minicourse will also work as a colloquium. Please see below for the precise dates and…

From May 3, 2021 to May 7, 2021, Professor O. Kharlampovich from City University of New York will teach a mini course on Groups acting on Trees. Due to the current situation caused by the corona virus disease, the mini course will take place virtually. Bass-Serre theory relates group actions on trees with decomposing groups as iterated applications of the operations of amalgamated product and HNN extension, via the notion of the fundamental group of a graph of groups. One…

Taught by Professor Eli Aljadeff, Technion University, Israel The main theme of this mini-course is gradings by finite groups on finite-dimensional algebras. Similar to the classical situation of ungraded algebras, we will be interested in finite-dimensional graded simple algebras and finite-dimensional graded division algebras. An important role is played by a generalization of central simple algebras, called Azumaya algebras. Our main tool will be polynomial identities and, in particular, graded polynomial identities. This tool will allow us to construct generic graded…

Mini-course by Professor Leonid Makar-Limanov, Wayne University,  USA Brief description of the mini course After this course you will know the proofs of several classical theorems of Affine Algebraic Geometry. The original proofs of these theorems were quite involved and a much longer course would be needed for their exposition. In the first lecture we will discuss the theorems of Heinrich Jung and Rudolf Rentschler. The first one describes all invertible transformations of the plane by polynomials and the second all…

Topological Quantum Field Theory lives at the intersection of category theory, algebraic topology, representation theory, and theoretical physics. Physically, TQFTs describe and control the symmetries of quantum systems, including quantum symmetries, anomalous symmetries, and higher-form symmetries. Mathematically, TQFTs provide a dictionary between manifold topology and structures in representation theory, and as such allow computations and results to move between these separate fields. This school, aimed at early- to mid-career graduate students, will consist of three 5-hour minicourses related to TQFTs,…

The goals of the summer school are two-fold. First, to introduce students to research level mathematics and second, to encourage more female and female-identifying students to pursue graduate school in the mathematical sciences. The research theme of the 2024 summer school will be Combinatorial Commutative Algebra, as described below. By introducing the advanced mathematics in a supportive and engaging environment, we aim to give students the tools and the support structure that will enable them to thrive in graduate school.