Conferences  >  Mathematics  >  Algebra  >  Canada

University of British Columbia

The Fields Institute

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds, begun by S. Lefschetz, and well established by the late 1950's. Many of the important Artinian graded algebras appear as cohomology rings of an algebraic variety or manifold, though recent important developments have demonstrated important cases of the Lefschetz properties beyond such geometric settings (such as Coxeter groups or matroids). This renews interest in understanding the Lefschetz property, and Artinian algebras that admit them, systematically.

Geometry and Topology,    Graph Theory and Combinatorics

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

There exists a mysterious algebraic structure in 8-dimensional space that does not behave in the same way as the ordinary arithmetic that we all learn as children. Somewhat surprisingly, this strange algebra, called the octonions, shows up naturally in the study of certain higher dimensional geometric spaces, called manifolds, that are of importance in physics and in the study of the equations introduced by Einstein in general relativity. Geometers have been studying such spaces for a number of years, mostly using tools from calculus and differential equations. The proposed workshops intends to introduce these researchers to experts in the special octonion algebra, as well as in related special algebraic structures called spinors, to facilitate a cross-pollination of ideas, methods, and techniques. Some of these groups have never before been brought together in this way.

Queen's University, Kingston, Ontario

Structure of finite dimensional algebras Structure of module categories Auslander--Reiten components Homological methods in representation theory Homological conjectures Algebras of finite global dimension Self-injective algebras Tame algebras Combinatorial aspects of representation theory Geometry of algebras and modules Homological invariants of algebras and modules Triangulated categories and tilting theory Relations of the above topics with Lie theory, Singularity theory, Cohen--Macaulay modules, quantum groups and other algebraic structures.

Banff International Research Station (BIRS) / UBCO

How primes and L-functions are linked is at the core of analytic number theory, with the Gener- alized Riemann Hypothesis (GRH) being its star conjecture. The field of explicit number theory focuses on simple yet notoriously difficult questions such as the Goldbach conjecture (Can every even number be written as the sum of two primes?) and Legendre’s conjecture (Is there a prime number between every two consecutive squares?). It is likely one of the most exacting flavors of number theory: in addition to scientific creativity, it requires precision and endurance to produce meaningful results. Working in teams with complementary expertise would allow to tackle some problems in the field more efficiently.

Centre de recherches mathématiques (CRM)

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

This workshop focuses on addressing general theoretical problems that underpin cutting-edge applications of linear algebra, including low-rank approximation and tensor decomposition, optimization, machine learning, nonlocal network dynamics, and uncertainty quantification. By bringing together experts from these different communities at a BIRS workshop, new insights in applied linear algebra will be brought to these challenging problems, which we expect to generate significant advances to state-of-the-art computational algorithms in the next decade.

Neural Networks and Artificial Intelligence, Machine Learning,    Complex Networks

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

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

The workshop is conceived in response to recent breakthroughs in physics and mathematics. One is the real quantization of Hitchin moduli spaces due to Gaiotto and Witten, and the other is a deformation quantization theory of Kontsevich and Soibelman that has achieved a vast mathematical foundation and generalization of topological recursion of Eynard and Orantin in random matrix theory. The vision of the organizers is that these two theories should be related through mirror symmetry. The workshop is organized to test this vision, and to explore its mathematical consequences.

ICMS - International Centre for Mathematical Sciences

This event will be a twinned transatlantic conference on “C*-algebras and tensor categories”, promoting new connections between C*-algebra theory and tensor categories/subfactors - an interface with tremendous, yet barely explored, potential. The two locations of the conference will be the Fields Institute in Canada and ICMS in Edinburgh.

Many major breakthroughs in the classification of C*-algebras of finite topological dimension have been underpinned by the large-scale transfer of von Neumann techniques on multiple levels. The overarching objective of this conference is to bring together researchers at the interface of the rapidly developing areas of the structure and classification of C*-algebras and subfactor theory/tensor categories.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

Centre de recherches mathématiques (CRM)

Centre de recherches mathématiques (CRM)

Centre de recherches mathématiques (CRM)