Workshop on Symmetric Spaces, Their Generalizations, and Special Functions

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This award will support participation by U.S.-based mathematicians, especially graduate students and other early-career researchers, in the upcoming international workshop and conference on Symmetric Spaces, Their Generalizations, and Special Functions, which will be held at the University of Ottawa from May 14 until May 17, 2020. The goal of the workshop is to foster the international collaboration of researchers in several areas connected to representation theory and algebraic combinatorics, including Lie superalgebras, quantized enveloping algebras, and algebraic combinatorics. The rationale for this activity is recent advancements that indicate new links between the aforementioned areas, and its goal is to investigate open problems that are spawned by these advancements and examine new strategies for solving them. The workshop will also have a substantial pedagogical component in the form of three mini-courses that will cover background and recent exciting progress in its focus areas. These mini-courses will be accessible for non-experts, including graduate students and junior researchers.Recent results hint at a new and promising connection between quantized symmetric spaces and interpolation polynomials. A natural and important problem that lies at the intersection of the aforementioned areas is to define and investigate the properties of q-deformations of Capelli operators in a uniform way. In addition, for (non-quantized) symmetric spaces of Lie superalgebras that are associated to BC-type root systems, an analogous relation between invariant differential operators and interpolation polynomials is yet to be established. We hope that the conference will provide an environment for experts to exchange their ideas for these interdisciplinary problems. The website for the workshop is http://www.fields.utoronto.ca/activities/19-20/symmetric-spaces.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.