Meetings/Workshops on Algebra in Canada

University of Manitoba

The theory of Banach algebras has had a strong presence in Canada's mathematical community for several decades; this is partly because almost everyone who does research in abstract harmonic analysis is also somewhat involved with Banach algebra theory and, additionally, because the theory of Banch algebras has many connections with the theory of operator algebras and operator theory. The Banach algebras series of conferences have provided a forum for researchers in these areas. It also provides a forum for junior researchers to get exposure to the community, and the 2019 instalment of the conference will continue this legacy. We will bring together researchers and graduate students who are working in Banach algebras theory and related areas such as abstract harmonic analysis, operator algebras, operator spaces and quantum groups.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The Fields Institute

The conference intends to focus on the following topics in representation theory: Lie algebras and Lie superalgebras, extended affine Lie algebras and toroidal Lie algebras, quantum affine algebras. In particular, crystal bases and canonical bases, Yangian algebras, quantum toroidal algebras, cluster algebras, Khovanov-Lauda-Rouquier algebras or quiver Hecke algebras and categorification are to be covered. The conference hopes to provide an introduction to graduate students and young researchers as well as offering a platform for experts to survey and discuss recent developments on these subjects.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Probability and Statistics, Game Theory,    Quantum Mechanics and Quantum Information Theory

The Fields Institute

Applied model theory is currently experiencing a golden age. The past decade has seen fundamental contributions to a broad range of topics in algebra, geometry, number theory, combinatorics, and analysis.

Number Theory, Arithmetic,    Graph Theory and Combinatorics

The Fields Institute

University of Ottawa

The event focuses on operads and other higher structures. Although it will be oriented on Algebraic Topology and Category Theory, all communities are welcome.

The Fields Institute

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The Fields Institute

The beautiful utility of any duality is that it allows for the surprisingly meaningful flow of ideas between two disparate areas. Indeed, through Homological Mirror Symmetry, symplectic considerations have yielded concrete results in the theory of derived categories of coherent sheaves on algebraic varieties. These results are unexpected: the apparent flexibility of symplectic topology contrasts with the rigidity found in solutions of polynomial equations. That difference has been resolved by the surprising abundance found in the group of autoequivalences of the derived category. One particularly successful example was the paper of Seidel and Thomas on spherical twists, which inspired many successors and enjoyed further expansions.

The Fields Institute

The mathematical scope of the program is within noncommutative geometry, quantum groups, graph C*- algebras, KK-theory, index pairing, C*-dynamical systems and crossed products, Dirac operators, spectral triples, curvature, and quantum Gromov-Hausdorff distance. There are a number unifying principles which establish connections among the proposed topics of the meeting. For example, dynamical systems link together graph C*-algebras and noncommutative metric geometry. We aim to construct quantum metric geometries of crossed products and graph algebras relating the Lipschitz norm and Dirac-operator approaches. This links the metric and spectral features of noncommutative geometry. A key research focus of the proposed activities is to make precise the impact of metric and spectral noncommutative geometry on noncommutative topology. Graph C*-algebras are an abundant source of examples which test the bridges between the topics of the proposed conference.

Geometry and Topology,    Group Theory

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The Fields Institute

Kontsevich's original conjecture dealt solely with Calabi-Yau varieties. Later, it was realized that to incorporate Fano varieties into the statement one needed something a bit more general than varieties: the objects called Landau--Ginzburg models in physics. At its roughest a Landau--Ginzburg model is a (complex) variety X equipped with a regular function w:X→C. Landau--Ginzburg models provide theories where the interesting behavior localizes to the singular locus of w. As such, they are well-known in a number of mathematical fields. This workshop is meant to gather experts in a broad range of areas around the theme of Landau-Ginzburg models -- all of which are touched by HMS. Specific problems of interest are are the study of Fan--Jarvis--Ruan--Witten Theory and Homological Projective Duality through matrix factorizations in Algebraic Geometry and their dual realization in Fukaya Categories.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The Fields Institute

The purpose of the workshop is to accelerate the development of this emerging subject and to extend its applications to other areas, in particular to group theory, geometry and combinatorics.

Banff International Research Station for Mathematical Innovation and Discovery

The modern approaches to computing algebraic K-groups step through equivariant commutative ring spectra via the natural S1-action on topological Hochschild homology. Ongoing and transformative work by Bhatt--Morrow-Scholze in p-adic Hodge theory uses cyclotomic spectra and therefore subtle equivariant information. This workshop, at the vanguard of work in this area, seeks to bring together experts in algebraic topology, (derived) algebraic geometry, and number theory to explore these exciting new connections.

The Fields Institute

The eighth edition of ARTA will present recent research developments in tilting and \tau-tilting theory, torsion theory, combinatorial methods in representation theory, geometric representation theory, module categories and self-injective algebras, homological methods in representation theory, triangulated categories, derived categories and relationship with cluster algebras. We will also explore the deep links with other closely related areas such as Lie theory and geometry, as well as possibly new research directions that would appear between now and the conference.

Banff International Research Station for Mathematical Innovation and Discovery

An equation is called Diophantine if whole number or fractional solutions are sought. Diophantine equations are named after Diophantus of Alexandria, a 3rd century mathematician and were popularized by Pierre de Fermat, a 17th century lawyer and amateur mathematician. Unlike most branches of mathematics, many Diophantine questions and theorems can be understood and appreciated by the general public, and the subject is a favourite with popularizers of mathematics. The methods for tackling Diophantine equations are however deep and varied, and the subject has recently experienced an explosion of new directions and results. This workshop will bring together experts and young scholars to explore these new directions and stimulate further research into Diophantine problems.