Conférences - Géométrie et topologie - Canada

Banff International Research Station

The Banff International Research Station will host the "Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4" workshop in Banff from June 7 to June 12, 2020. This workshop will highlight new results in low-dimensional topology coming from a wide range of geometric methods. Low-dimensional topology studies the global properties of geometric spaces in dimensions 3 and 4, such as 3-dimensional space and 4-dimensional space-time.

Originally introduced by Martin Bartels in the early nineteenth century, and then extensively developed by Élie Cartan in the first half of the twentieth century, the method of moving frames is a powerful tool for studying the geometry of curves, surfaces, and, more generally, submanifolds under the action of a group of transformations. In 1999, a new and more general formulation of moving frame was introduced by Fels and Olver which led to a dramatic resurgence of interest in the method accompanied by a striking extension of the range of applications. The workshop will bring together a diverse group of experts with the goal of exploring existing and emerging applications of the moving frame method to differential equations and integrable systems in physics, to computer vision and object recognition, medical imaging, broken object reconstruction, discrete and differential-difference equations, geometric numerical integration, and much more.

University of Saskatchewan

The Canadian Conference on Computational Geometry (CCCG) is a forum to disseminate and discuss new theoretical and applied results in discrete and computational geometry. CCCG focuses on the design of efficient algorithms, the development of software, and the study of the mathematical foundations of computational problems whose formulations involve geometric constraints. The field of computational geometry is motivated by problems from a broad range of application areas, as diverse as computer graphics and animation, computer vision, computer-aided design and manufacturing, geographic information systems, pattern recognition, wireless communications, robotics, protein folding, urban planning, graph drawing, or statistical analysis.

Mathématiques appliquées (en général),    Algorithmes

Birational geometry is a classical mathematic subject dating back to the late 1800s. It aims to classify geometric shapes by looking at the majority of their points and asks "if I remove some points from shape A and some other points from shape B, do they become the same shape?". This turns out to be a surprisingly difficult and fundamental mathematical question. Perhaps more surprising is that the classification of geometric shapes from birational geometry is related to the classification of abstract mathematical gadgets called derived categories, a formal language developed by prominent mathematicians in France in the 1960s. However, the relationship between derived categories and birational geometry remains unproven.

The possibility of using quantum mechanics to build computers that are both faster and more secure is an exciting technological leap. One of the most promising pathways to a robust architecture, referred to as topological quantum computing, has lead to fascinating research at the frontier of mathematics and physics. Properties of new, exotic states of matter can be understood - and hence implemented in practice - using tools that were developed by pure mathematicians in connection to surfaces and their curvature. This workshop is bringing together international experts to explore the intimate connections between such topological properties of quantum matter and the key resource of quantum computing: entanglement.

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

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

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

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

Théorie des groupes,    Théorie des nombres, arithmétique