Around Symmetries of K3 Surfaces (23w5065)

The Banff International Research Station will host the "Around Symmetries of K3 Surfaces" workshop in Banff from February 26 to March 3, 2023.

Workshop Files - Slides

Workshop Report - Click here to download

Algebraic geometers are mathematicians who study the geometry of polynomials. Some of their favorite objects are K3 surfaces as these surfaces have elegant properties yet are explicit enough to help them understand more general problems. But K3 surfaces are far from being simply important to algebraic geometry, their study has had important influence in several other fields. A classic example comes from the field of optics. When studying the propagation of electro-magnetic waves, such as light, in a crystal of aragonite, physicists have discovered that the wave surface, also known as Fresnel surface, can be described by a quartic equation. For many materials, Fresnel surfaces form a special case of K3 surfaces called Kummer surfaces. The example above is just one of the many instances where K3 surfaces pop up in nature---string theory is another example.

While the study of K3 surfaces has been very active over the last hundred years, many important problems remain unanswered even today concerning their symmetry and the way these surfaces are related to one another. There are today many young researchers who are focusing their energy on understanding the geometry of K3 surfaces and this workshop is a key ingredient in the diffusion of new ideas.

The main focus of this conference is to gather the experts on the most recent developments regarding the study of symmetries of K3 surfaces and the geometric conditions under which these surfaces are uniquely determined, in order to advance our understanding of these surfaces, with an eye toward several important open problems.

We will bring together experts from around the world who study both K3 surfaces from their intrinsic properties and from their characteristics as they vary in families. The two perspectives should mutually resonate and allow for even deeper results than those obtained when working in parallel.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).