Wednesday Seminar
Organizer:Masa-Hiko Saito & Takuro Mochizuki
Date: May 15 (Wed), 10:00--12:00
Venue: Room 110, RIMS, Kyoto University
Speaker: Motohico Mulase (UC Davis, RIMS Kyoto University)
Title: "From Zeta(3) to Mirror Symmetry"
Abstract: The Riemann Zeta function is the most mysterious function in mathematics. This talk focuses on its special values. In the first part, I will explain my own unexpected encounter with some special values of Zeta. Topological recursion and moduli spaces of curves are behind the scene, which gives a new understanding of the Kontsevich proof of the Witten conjecture. Then I will present recent discoveries associated with Zeta(3) in the context of algebraic geometry and differential equations. Apéry's irrationality proof of Zeta(3) is the source of our inspiration. Apéry discovered a mysterious integer sequence in his proof. Later it was noticed that these numbers have direct relevance to mirror symmetry of a particular Fano 3-fold and its mirror Landau-Ginzburg model. I will report what has been proven in this direction. In the discussion part, I will formulate what seems to be true. Still we do not know the whole story.
Date: May 22 (Wed), 10:00--12:00am (JST)
Venue: Room206, RIMS, Kyoto University
Speaker: Laura Schaposnik Massolo (University of Illinois at Chicago)
Title: Higgs bundles and the Hitchin fibration, old and new
Abstract: During the first half of the talk we will introduce Higgs bundles and their integrable system, focusing on how they can both be described in terms of spectral data. After describing some dualities they satisfy (not only from mirror symmetry but also via other correspondences such as low-rank isogenies), we will then focus on different methods to understand the Hitchin fibration and specially its singular fibres (monodromy, isogenies, cayley correspondences).
Date: May 29 (Wed), 10:00--12:00
Venue: Room 111, RIMS, Kyoto University
Speaker: Motohico Mulase (UC Davis, RIMS Kyoto University)
Title: "Discontinuous and Biholomorphic?" "
Abstract: How can we define a global higher order differential operator on a compact Riemann surface? This naïve question leads us to encountering the half-canonical sheaf and the concept of *opers*. They are connections in holomorphic vector bundles, but form only a very thin slice of the moduli space of connections. This slice forms a holomorphic Lagrangian subvariety of the moduli space, which is a holomorphic symplectic manifold. Are there other Lagrangians in this symplectic space, and if so, can we realize the moduli space as the total space of an analytic family of disjoint Lagrangians? This is the Lagrangian foliation conjecture of Carols Simpson. Very recently, an amazing proof was discovered for the case of SL(2) connections by a starting postdoctoral scholar. I will present several exciting moments of discoveries of the key facts appearing in this new result.