Vorträge in der Woche 03.12.2018 bis 09.12.2018

Montag, 03.12.2018: Minimal Lagrangians and where to find them

Prof. Jason D. Lotay (UCL)

Vorkolloquium um 16 Uhr (moderiert von Lisa Hilken)"A short tour in complex projective space" Abstract: Complex projective space is a fundamental object in geometry. In this talk I will describe several key features of complex projective space which are relevant for my colloquium talk “Minimal Lagrangians and where to find them”. <br><br>Abstract: A classical problem going back to ancient Greece is to find the shortest curve in the plane enclosing a given area: the isoperimetric problem. A similar question is whether given a curve on a surface it can be deformed to a shortest one. Whilst the solutions to these classical problems are well-known, natural generalisations in higher dimensions are mostly unsolved. I will explain how this leads us to the study of minimal Lagrangians and the question of how to find them, which will take us to the interface between symplectic topology, Riemannian geometry and analysis of nonlinear PDEs, with links to theoretical physics.

Dienstag, 04.12.2018: Volumenwachstum in sphärischen Räumen

Julien Sessler

Dienstag, 04.12.2018: “All the world’s a stage”: actors’ skills for maths communication

Dr. Jason Lotay (UCL)

I will describe communication skills training we provide for PhD students at the London School of Geometry and Number Theory. In particular, I will discuss a course given by actors to help our PhD students become better communicators.

Donnerstag, 06.12.2018: Envelopes in Outer Space

Christian Steinhart (Universität des Saarlandes)

Culler-Vogtmann Space alias Outer Space CV_n is the moduli space of finite, metric graphs with marking. Analogue to the Thurston metric in Teichmüller space there exists a natural asymmetric Lipschitz-metric on CV_n which we will discuss during the talk. An interesting aspect of CV_n with this metric is, that geodesics are almost never unique. By using the envelope of two points, that is the set of all geodesics from A to B, we will construct a geodesic, which is piecewise unique. Furthermore dimension changes of envelopes determine the faces of reduced Outer Space, which implies that the isometry group of the reduced Outer Space is the isometry group of Outer Space.

Donnerstag, 06.12.2018: Existence of Multi-Time Dynamics in a Quantum Field Theory Model

Sascha Lill (Uni Tübingen)

In order to describe a Quantum-N-body system in the Schrödinger picture in a manifestly covariant way, one needs to introduce a separate time coordinate for each particle. The wave function therefore depends on N time coordinates ("Multi-Time wave function'') and the Schrödinger equation becomes a system of N Partial Differential Equations (PDEs). So far, a series of papers investigated the existence and uniqueness of solutions to the Multi-Time Schrödinger equation systems - but mostly on a non-rigorous level. In my master thesis, I could establish a proof of existence and uniqueness of a solution to the equations of motion for a Quantum Field Theory (QFT) toy model. This talk will concern about Multi-Time formalism in general, how to construct a solution to the equations of motion and how to show that this PDE system is actually solved.

Donnerstag, 06.12.2018: Die Mathematik von Evariste Galois

Prof. Dr. Ivo Radloff (Universität Tübingen)

Galois’ Name ist untrennbar verbunden mit der Antwort auf die Frage nach der Auflösbarkeit von Polynomen durch Radikale. Noch als Schüler entwickelte er die Theorie, die heute seinen Namen trägt, und legte sie Fourier und Cauchy vor. Die Anerkennung, die er sich erhoffte, blieb aus. Ein erhoffter Preis ging an Abel und Jacobi. Galois starb wenig später 1832 an den Folgen eines Duells, keine 21 Jahre alt. Im Vortrag geht es um Galois’ eigene Darstellung der Theorie und um seine tiefen, weniger bekannten Aussagen zur Modulargleichung, 2-fach transitiven auflösbaren Gruppen und algebraischen Integralen.