Time: 16:15-17:45

Location: Mondi 2

Speaker: Sadashige Ishida (Wojtan group)
Title: Area formula for spherical polygons via prequantum bundles

Abstract: Symplectic and contact geometry were introduced to geometrically describe dynamical systems. Beyond the original motivation, they can sometimes offer powerful tools to study purely geometric problems. I will talk about an interesting instance. 

A spherical polygon is a closed piecewise geodesic on S^2. Practical situations in many fields like fluid dynamics, electromagnetism, and light transport theory require computing the surface area enclosed by a spherical polygon. Classically, the Gauss-Bonnet theorem gives an area formula, but this formula has assumptions that render it unavailable in certain situations.

I will explain how an interplay between symplectic and contact geometry helps us find a more widely applicable formula. Via a "prequantum bundle", a  preliminary setup to quantize classical dynamics, I generalize the classical formula to a somewhat quantum version.

I intend to make this talk for a general math audience. Some familiarity with differential topology is helpful, but I assume no prior knowledge of quantum mechanics or symplectic/contact geometry.

Speaker: Francesco Pedrotti (Maas group)
Title: Local conditions for global convergence of gradient flows

Abstract: Gradient flows and their discretizations are widely used methods to look for a minimizer of a given functional. However, it is often not easy to establish convergence to a global minimum. In this talk we discuss a recent new family of local criteria that can be used for this purpose in the setting of lower semicontinuous functionals on complete metric spaces. Based on joint work with Jan Maas and Lorenzo Dello Schiavo.