Vorträge in der Woche 08.11.2021 bis 14.11.2021

Dienstag, 09.11.2021: Willmore surfaces in \R^3

Dr. Nicolas Marque (Uni Potsdam)

When one considers a surface in \R^3, the mean curvature quickly appears as a node of geometric insight, tying itself to isoperimetry, elasticity, and regularity. From it one can naturally build a quadratic energy linked with the elastic properties of the surface: the Willmore energy. We will see how insights on Willmore informs our knowledge of the surface, and how its pecular behavior generates rich and surprising phenomena for its critical points: noncompact bubbling. If time allows, we will also look at situations where the aforementioned knowledges can be applied, notably to GR, or the sphere eversion.

Dienstag, 09.11.2021: Das Spektrum des Laplace-Operators

Claudius Kamp

Donnerstag, 11.11.2021: Quantum states at equilibrium: thermal states, tensor networks and area laws

Alvaro Alhambra (MPQ München)

The thermal or Gibbs state is one of the most ubiquitous states of quantum matter, which appears when quantum systems come to equilibrium with their surrounding environment. Beyond its wide interest for physics, it also notably appears in the study of computational complexity and algorithms. The most interesting and complex of these occur when the system at hand is composed of a large number of particles, such as in a regular lattice. In this talk, we will discuss how these states can be described classically, most notably through tensor network methods. Their effectiveness is related to how correlations are distributed in these systems at equilibrium. We also describe these through the so-called area law, which states that these correlations are localized within the system at hand. In doing so, we will illustrate one of the more successful ways of efficiently describing quantum states via classical algorithms.