Wushi Goldring: A trio of algebraicity-geometricity programs: Langlands, Griffiths–Schmid and G-Zips, Mini-course, Part III

My work has been focused on three interrelated, conjectural themes/programs: (i) the connections between automorphic representations and algebraic geometry, as pioneered by Langlands and elaborated by others, especially Deligne–Serre, (ii) the search for an algebraic framework for Griffiths–Schmid manifolds, as pioneered by Griffiths–Schmid, Carayol, and Green–Griffiths–Kerr, and (iii) the geometricity of G-Zips via the analogy with Mumford–Tate domains, introduced in my recent papers and preprints with my coauthors.

I will explain the basic conjectures and open problems pertaining to each theme and how they are connected to one another. I will also illustrate how, like many speculative programs, the philosophy underlying them has lead — and continues to lead — to concrete results in a number of different areas. This is based on joint works with Y. Brunebarbe, J.-S. Koskivirta and B. Stroh.