Meetings/Workshops on Algebra in Canada

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.