Vorträge in der Woche 13.01.2025 bis 19.01.2025

Donnerstag, 16.01.2025: Rigidity and Monotonicity of the Hawking Energy on Hawking Surfaces

Alejandro Penuela Diaz (Universität Potsdam)

The Hawking energy is one of the simplest quasi-local energy definitions in general relativity. Despite its simplicity, the Hawking energy has faced challenges due to ambiguities when applied to general surfaces. In this talk, I will present my recent results demonstrating that the Hawking energy exhibits key physical and mathematical properties—non-negativity, rigidity, and monotonicity—when evaluated on Hawking surfaces, a class of critical surfaces of the Hawking functional. These results establish Hawking surfaces as useful tool for evaluating the Hawking energy and reinforce its potential as a meaningful tool for understanding gravitational phenomena.

Donnerstag, 16.01.2025: Toward a structure theory of disordered matrix product states

Dr. Eric Roon (Michigan State University, USA)

In 1992, Fannes, Nachtergaele, and Werner classified finitely correlated translation-invariant states on quantum spin chains and discovered that they admit a matrix product structure. Such matrix products states are simultaneously good approximations for general states, and natural candidates for ground states of specific local Hamiltonians. Following the observation by Vidal (2004) that matrix products states are ‘efficient,’ the theory took root and is now an indispensable tool in many-body physics and quantum simulation. Recent work in this direction by Movassagh—Schenker (2022) and Nelson—R. (2024) adapted this structure to states generated by disordered matrix products. Nelson—R. showed such disordered matrix product states are translation co-variant with respect to an ergodic map. However both works above only had a ‘one-way’ construction, not a classification. In this talk, I’ll report on some work in progress with Jeffrey Schenker where we study disordered translation co-variant states in the case that the underlying probability space is a compact Hausdorff space.

Freitag, 17.01.2025: Die Spektralsequenz von Atiyah und Hirzebruch

David Seez M.Sc. (Uni Tübingen)