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

Soon after Einstein postulated the General Theory of Relativity, he introduced what he called his "greatest mistake'', the so-called cosmological constant. Solutions of the Einstein equation with cosmological constant are now called Einstein manifolds, and despite Einstein's pessimistic view, play key roles both in mathematics and physics. Quasi-Einstein manifolds are generalizations of Einstein manifolds, which include not only Einstein manifolds but Ricci solitons, warped product Einstein manifolds, static Einstein manifolds, and other special manifolds. These are important in many areas of modern mathematical research, including Ricci flow, collapsed Gromov-Hausdorff limits, and general relativity. This workshop will examine progress in seemingly disparate fields which in fact share a common nexus, namely quasi-Einstein manifolds or the related notion of Bakry-Emery Ricci curvature. Problems to be discussed include the classification problem for near horizon geometries (of black holes), for Ricci solitons and for static Einstein metrics, as well as the fundamental gap problem for Laplace and Schroedinger operators, and the formulation and application of synthetic Bakry-Emery Ricci curvature.

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

What could be a bigger source of "big data" than the entire Universe? Researchers in statistics and computer science are developing new methods to analyse the "big data" that companies and governments want to understand. To test out these methods they need big datasets that everyone can share --- and new astronomical telescopes just happen to be gearing up to generate observations of billions of stars and galaxies that fit the bill. Insights from statistics will help astrophysicists to get the most out of these observations. The Astrostatistics 2023 workshop will bring together statisticians and astrophysicists to learn the technical languages of the two fields and identify how to work together to combine the excitement of space with big data.

Probability and Statistics, Game Theory,    Scientific Computing and Data Science