Spaces of Manifolds: Algebraic and Geometric Approaches (23w5017)


(University of Toronto)

(Karlsruhe Institute of Technology)

Mona Merling (University of Pennsylvania)

Tom Goodwillie (Brown University)


The Banff International Research Station will host the “Spaces of Manifolds: Algebraic and Geometric Approaches” workshop in Banff from November 26 to December 1, 2023.

The concept of a manifold in mathematics corresponds approximately to the everyday idea of a smooth surface --- think of soap bubbles or sheets of fabric --- except that it can have any number of dimensions. A question that lies at the origin of topology, the mathematics of shape, is: can we write down a list of all manifolds? At first, such a classification was attempted through numerical invariants. Over time, the focus of algebraic topology has shifted from using numerical invariants to the algebraic objects underlying them, and then ascended further to studying moduli spaces. This workshop concerns recent breakthroughs in this philosophy for studying of manifolds, combining higher-algebraic methods with novel geometric techniques.p

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), and Alberta’s Advanced Education and Technology.