A symplectic morning with Bernhelm Boos-Bavnbeck and Chaofeng Zhu

21.07.2023, 10:30 Uhr  –  Room 2.22 of Building 9 & zoom
Arbeitsgruppenseminar Analysis

Bernhelm Booss-Bavnbeck (Roskilde,Danemark), Chaofeng Zhu (Nankai,China)

10:30 Uhr Bernhelm Booss-Bavnbeck (Roskilde,Danemark)

Title: The Calderón Projection for Elliptic Differential Operators on Manifolds with Boundary:
Concept, Meaning, and Deformation Properties

Abstract: A key result in spectral geometry is the calculation of the spectral flow
of a curve of elliptic boundary value problems over a smooth compact manifold
with boundary (belonging to the realm of functional analysis) by the Maslov index
of related curves of Lagrangian subspaces over the boundary (belonging to the
realm of symplectic geometry). I shall explain obstructions of a general validity
of this Spectral Flow Theorem and how to overcome these obstructions by natural
assumptions regarding the inner weak unique continuation property (UCP) that
imply the continuity of families of Calderón projections. I shall give details of a
simple proof of that crucial continuity. This is joint work with Chaofeng Zhu.

11:30 Uhr Chaofeng Zhu (Nankai,China)

Title: Global Mountain Pass Points and Applications to Minimal Period Problems in Hamiltonian Systems

Abstract: In this talk, we introduce the notion of the global mountain pass points. Then we show that under certain conditions,  there exists either a non-trivial minimal point or a global mountain pass point. As an application, we show that for each a strictly convex  super-linear autonomous Hamiltonian system with broken  symmetry has a periodic orbit with minimal period.