Abstract:In the first part of the talk, I will give a survey of the proof of the Dowling-Wilson conjecture using the Schubert variety of a hyperplane arrangement. The Schubert variety of a hyperplane arrangement is an equivariant compactification of the vector group with finitely many orbits. In the second part of the talk, we will discuss a recent work of Colin Crowley characterizing Schubert...
Abstract:I will first give a brief introduction to T. Mochizuki's Theory of twistor D-modules. Then, we use it to study Kodaira-type vanishings. In particular, we will generalize Saito vanishing, and give a Kawamata-Viehweg type statement. As an application, we will also prove a Bott-type Vanishing using M. Saito's mixed Hodge module