Derived, Birational, and Categorical Algebraic Geometry (21w5509)


(University of Alberta)

(University of South Carolina)

(Max Planck Institute for Mathematics)


The Banff International Research Station will host the "Derived, Birational, and Categorical Algebraic Geometry" workshop from November 14 to November 19, 2021.

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.

One avenue to pursue this connection is through a modern mathematical subject known as "derived algebraic geometry". This workshop brings together experts in birational geometry, derived categories, and derived algebraic geometry in an effort to connect the disciplines and more thoroughly understand this deep mathematical phenomenon.

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).