Geometric Representation Theory and Low Dimensional Topology

University Of California-Riverside, Riverside CA

Investigators

Abstract

The conference "Geometric Representation Theory and Low Dimensional Topology" will take place at the International Centre for Mathematical Sciences in Edinburgh, Scotland, June 10-14, 2019. There will be a summer school June 3-7 with several lecture series to provide background material for early career participants in the conference. The overall goal of the conference is to study interactions between the two areas of mathematics in the title. "Topology" is the study of shapes that are allowed to stretch and bend. For example, a triangle and circle are considered to be topologically equivalent because one can be stretched into the other, and similarly a cube and sphere are considered topologically equivalent. "Low dimensional topology" studies shapes or objects in dimensions 2, 3, and 4, such as surfaces, or knotted loops in 3-dimensional space. This can be useful in other sciences; for example, DNA can be knotted, or the shape of the universe could have a nontrivial topology. "Representation theory" is the study of symmetries in mathematics, and at a concrete level, these symmetries often manifest themselves as solutions to systems of equations where the variables represent matrices instead of numbers. This mathematical area has also had applications in other sciences, such as symmetries of elementary particles in physics, or symmetries of molecules in chemistry. There are sophisticated mathematical techniques for taking certain spaces of solutions to polynomial equations and producing solutions to matrix equations, and recently low dimensional topology has been used to find solutions to the same equations, using completely different mathematical constructions. One of the goals of the conference is to understand this new phenomenon using ideas coming from mathematical physics. This award will fund participation of early career US scientists in this summer school and conference so they can learn about these exciting new ideas.More details about the conference are available at https://www.icms.org.uk/geometricrepresentation.php. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.