Conference: Geometric representation theory and moduli spaces

This award supports participation in a three-day workshop on recent advances in geometric representation theory and moduli spaces to be held October 20-22, 2023 at the University of North Carolina, Chapel Hill. The workshop will focus on recent advances in geometric representation theory (the theory of symmetries) and moduli spaces in algebraic geometry (the study of zeroes of polynomial equations). The workshop will consist of ten to twelve talks spread over three days, allowing plenty of time for additional discussions. Participation of graduate students and postdocs will be encouraged. Spaces that parameterize geometric objects are known as moduli spaces, and are central to the study of algebraic geometry and representation theory. There have been many recent developments on moduli space theory, perhaps the most significant is the emphasis of general stack theoretic results over traditional Geometric Invariant Theory based approaches to moduli space theory. Moduli stacks of bundles over curves are closely related to the theory of conformal blocks and the geometric Langlands program. A recent development has been a twisted theory of conformal blocks. There have been a series on recent developments in the geometric Langlands program, and connections with arithmetic are getting more apparent. Affine flag varieties (including affine Grassmannians and semi-infinite flag manifolds) are known to be related to representation theory of affine Lie algebras, quantum groups, and algebraic groups. The workshop will focus on these topics, and bring together experts in these areas, with an emphasis on the work of younger mathematicians. The workshop website is https://tarheels.live/grtm/. 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.