Department of Mathematics - College of Natural Sciences Colorado State University

The Banff International Research Station hosted the "Lifting Problems and Galois Theory"



The Banff International Research Station hosted the "Lifting Problems and Galois Theory" workshop from August 16th to August 21st, 2015. Colorado State University Professor Rachel Pries was a co-organizer for the workshop. Other co-organizers included: Frauke Bleher, University of Iowa; Ted Chinburg, University of Pennsylvania; and Andrew Obus, University of Virginia.

Galois Theory is the study of symmetries of systems of equations. This workshop focused on the recent advances in this field. Galois discovered that the symmetries of equations limit the ways in which one can write down explicit expressions for their solutions. This principle has had broad implications in algebra and geometry. One of the goals of this workshop included a study of so-called inverse problems, asking which sets of symmetries can arise from particular kinds of systems of equations. Another goal was to study lifting problems, having to do with determining when one can refine the coefficients of systems of equations without changing their symmetries.

The aim of the workshop was to bring together researchers and advanced Ph.D. students working on Galois Theory in order to advance this field. The lifting problems for curves, the focus of the workshop, has been a central topic in algebraic geometry since the work of Grothendieck, Deligne, and Mumford, and others on etale fundamental groups and moduli spaces of curves. The subject is undergoing rapid change due to the introduction of new techniques, as in the proof of the Oort conjecture.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-U.S.-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 TecnologĂ­a (CONACYT).

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