Lars Andersson
Wintersemester 2016/17
In diesem Seminar werden Themen aus den Bereichen der Differentialgeometrie und der Allgemeinen Relativitätstheorie besprochen. Interessenten sind herzlich willkommen.
Dienstags, 16:15
Campus Golm, Haus 9, Raum 0.14
| Datum | Vortrag | Referent | Inhalt |
| 18.10.16 | Supersymmetry and the Duistermaat-Heckmann-formula in finite dimensions | Florian Hanisch | The first session of the seminar will consist of 2 parts: 1) Discussion of the program for the semester. 2) Talk by F. Hanisch: Supersymmetry and the Duistermaat-Heckmann-formula in finite dimensions Abstract: We will review (and extend) our disussion from last term and describe a proof of the localization formula by Duistermaat and Heckmann in the finite-dimensional case based upon techniques from supersymmetry/-geometry. |
| 01.11.16 | Lagrangian and Hamiltonian field theory | Florian Hanisch | We will briefly review some basic ideas of the Lagrangian and the Hamiltonian approach to classical field theory, including some examples.
We will keep the talk at an elementary level (sometimes with a reduced level of mathematical rigor) and only indicate where more sophisticated concepts (e.g. jet bundles or infinite-dimensional manifolds) would enter the game.
Some standard examples will be included. This talk will serve as a sort of starting point of a series of talks/discussions of conserved charges in (super)gravity and related concepts. |
| 15.11.16 | Action principles and conserved currents | Lars Andersson | I will introduce, and give examples of, the notions of symplectic potential current, symplectic current, and Noether current for a Lagrangian field theory with local symmetries. References: Lee and Wald, Local symmetries and constraints, JMP 1990 Iyer and Wald, Some properties of the Noether charge and a proposal for black hole entropy, PRD 1994 |
| 22.11.16 | A short introduction to the basics of the Noether theorem and its application | Michael Jung | I will start with an infinitesimal symmetry transformation as a diffeomorphism and derive the Noether-current.
The setting is a compact domain in the flat space and just with one scalar field and one derivative, but I will explain briefly how to apply this for more scalar fields and derivatives of higher order. Afterwards I will deduce the Noether current for the Lagrangian as scalar density. |
| 29.11.16 | Action principles and conserved currents, continued | Lars Andersson | I will introduce the notions of Noether current and Noether charge for a Lagrangian field theory. References: Lee and Wald, Local symmetries and constraints, JMP 1990 Iyer and Wald, Some properties of the Noether charge and a proposal for black hole entropy, PRD 1994 |
| 13.12.16 | Higher conserved currents | Igor Khavkine | A conserved current for a PDE in $n$-variables can be thought of as a field dependent $(n-1)$-form that is closed on solutions. A similar definition can also be made in other form degrees. A field dependent $(n-p)$-form that is closed on solutions is called a higher current (or $p$-current). It is well known that, for variational PDEs, conserved currents (1-currents) correspond to symmetries via Noether's theorem. I will discuss a generalization of this result, which relates higher conserved currents to "higher stage symmetries". For simplicity, I will concentrate on the case of linear equations. |
| 31.01.17 | Introduction to Supergravity | Olof Ahlen | Supersymmetry has been a very active research area in both elementary particle physics as well as models for quantum gravity. In this talk, I will outline the motivation for analyzing supersymmetric field theories and briefly explain the relationship between local supersymmetry and theories of gravity. |