Monday, October 29, 2018
10/29/2018 - 2:30pm
The localization theorem, which has played a central role in representation theory since its discovery in the 1980s, identifies a regular block of Category O for a semisimple Lie algebra with certain D-modules on its flag variety. In this talk we will explain work in progress which produces a similar picture for the Virasoro algebra and more generally for affine W-algebras. Some new purely algebraic input is (i) a version of the Feigin-Fuchs duality between Verma modules for Vir at central charges c and 26 - c, which applies to all smooth representations and other affine W-algebras, (i)’ BRST reduction functors for affine W algebras, and (ii) a linkage principle for representations in category O of a W-algebra. As geometric input, we will explain how to (i) adapt the Beilinson-Drinfeld construction of vertex algebras via factorization spaces to also produce representations and in particular (ii) develop a factorizable version of affine Borel–Weil–Bott.
10/29/2018 - 4:15pm
This introductory lecture will describe results about counting rational points on certain
non-algebraic sets and sketch how they can be used to attack certain problems in
diophantine geometry and functional transcendence.
10 Hillhouse AvenueNew Haven, CT 06520