Moduli Spaces: Birational Geometry and Wall Crossings (18w5084)

The Banff International Research Station will host the "Moduli Spaces: Birational Geometry and Wall Crossings" workshop from October 7th to October 12th, 2018.

A moduli space parametrizes geometric objects with similar structures and encodes in itself the geometry of all possible families of such objects. Moduli spaces play a significant role in the development of mathematics, dating back to the parameterization of linear subspaces in the 19th century and of Riemann surfaces in the 20th century. The moduli-theoretic approach has produced an abundance of results by exploiting the universality of moduli spaces. This allows one to establish properties of all parameterized objects at once by a single argument. Inspired by a number of recent advances, this workshop will focus on two aspects of moduli spaces: Birational geometry and Wall crossings.

When objects transition from being stable to unstable, one often obtains a birational transformation of the moduli space. When such a transition occurs, geometric invariants on the two sides of the transition often have fascinating yet mysterious correspondences. Such is the case with the phenomenon of wall crossings in enumerative geometry. Most mathematicians working in moduli theory only focus on one aspect of the entire story. By bringing experts in these fields together, we aim to inspire new ideas and achieve progress on open problems both in birational geometry and the study of wall crossings in enumerative invariants.

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).