Workshop on Representation Theory, Combinatorics, and Geometry

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

The award will support participation of primarily early-career researchers in the Workshop on Representation Theory, Combinatorics, and Geometry, and the Distinguished Lecture Series "Virginia Mathematics Lectures" which will take place on October 19-21 and 22-24, 2019, respectively, at the University of Virginia. The workshop will consist of talks by leading experts on connections between quantum groups, quiver varieties, and canonical bases, as well as short talks by early-career participants. Participants will be exposed to exciting new directions in representation theory, geometry, and combinatorics, and will gain fodder for future projects. The diversity of mathematical researchers and areas represented at the workshop will foster new collaborations and new research projects. In more detail, Springer resolutions of nilpotent cones of semisimple Lie algebras provide a fertile ground for geometric representation theory. Maulik and Okounkov introduced a notion of stable envelope in the framework of symplectic resolutions (with Springer resolutions and quiver varieties as most important examples), and used it to provide a first geometric construction of R-matrices and a different construction of Yangians using the equivariant cohomology in a wide context. Their construction is intimately related to quantum cohomology of the symplectic resolutions. These subjects have played an important role in several areas of modern mathematics. Some of the most recent research directions (such as i-quiver varieties) have emerged only in the last year or so, and are currently aligning with Maulik-Okounkov's theory. The events at University of Virginia will provide a timely platform for exchange of emerging new ideas that will facilitate their further development. The website of the workshop is http://math.virginia.edu/ims/workshop-fall-2018/. 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.