Jiuzu Hong (UNC - Chapel Hill) will be delivering a four lecture series on geometric representation theory:
Title: Affine Grassmannians and Bun_G: A Parahoric Perspective
Abstract: Affine Grassmannians and Bun_G play a central role in geometric representation theory, geometric Langlands and algebraic geometry. Parahoric group schemes originated from Bruhat-Tits theory, and their global counterparts over algebraic curves called parahoric Bruhat-Tits group schemes were introduced more recently by Pappas-Rapoport and Heinloth.
All partial affine flag varieties can be viewed as affine Grassmannians of parahoric group schemes. This perspective has advantage of globalizing their geometry over an algebraic curve in the style of Beilinson-Drinfeld Grassmannians. This approach has led to interesting applications, including Zhu’s proof of the coherence conjecture of Pappas and Rapoport, and the determination of smooth loci of Schubert varieites in twisted affine Grassmannians by Besson and myself.
Moreover, the moduli of bundles over parahoric Bruhat-Tits group schemes generalizes parabolic Bun_G and Prym varieties. In fact, their non-abelian theta functions can be identified with (twisted) conformal blocks. This is my recent work joint with Damiolini, building on my earlier works with Kumar.
Details: All lectures will run on Fridays from 9:30 – 11:00, SMRI Seminar Room (Macleay Building A12 Room 301).
Friday 7 Feb, Lecture 1: Affine Grassmannians and Schubert varieties
Friday 14 Feb, Lecture 2: Loop groups and parahoric group schemes
Friday 21 Feb, Lecture 3: Global Schubert varieties
Friday 28 Feb, Lecture 4: Line bundles on moduli of parahoric bundles