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.

Objectives: The mathematical institutes in Canada have joined forces to offer annual summer schools geared toward women and underrepresented groups in mathematics and related sciences. The first school will be at Dalhousie University in Summer 2024. 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,…

Vertex operator algebras have been a topic of interest in mathematical physics for several decades, as they constitute one possible approach to formalize physical concepts from conformal field theory. They have relations to several other areas of mathematics, most notably to the theory of finite simple groups. This specific relation lead in fact to the award of the Fields Medal to Professor Richard Borcherds at the International Congress of Mathematicians in Berlin in 1998. Professor Gannon is the author of…

Topological Quantum Field Theory (TQFT) emerged in the 1980s in an effort to interpret quantum field theory through cobordism categories. Today, TQFTs play a central role in both mathematics and theoretical physics, especially in understanding global symmetries and the low-energy behaviour of gapped systems. This week-long school, aimed primarily at early-career graduate students, will feature three lecture series plus TA-led problem sessions, introducing students to cutting-edge topics brought together by TQFTs. Lecture topics will include fusion categories and condensed matter,…

Increasing Diversity in Mathematical & Related Sciences 2026 May 17 - 22, 2026, UBC Okanagan   This is a 5-day Summer School that will bring together a diverse group of undergraduate students who identify as women or other underrepresented gender identities studying math at a Canadian university. Overview: This will be an inspiring week of learning new math from influential women and gender-diverse mathematicians, and collaborating with peers from across the country!  You will connect professionally and socially, build networks…