Welcome to the Geometry Seminar of the Deparment of Geometry and Topology of the University of Granada. Here you can find information about the talks and events organized by the department.

Next talks

Chaos in higher-dimensional complex dynamics

University of Adelaida

I will report on new and recent work with Leandro Arosio (Universita di Roma, Tor Vergata) on chaos and other aspects of dynamics in certain highly symmetric complex manifolds. For example, we prove that for many linear algebraic groups G, chaotic automorphisms are generic among volume-preserving holomorphic automorphisms of G. I will start with some background on holomorphic dynamics in general, on chaos, and on the highly symmetric complex manifolds to which our results apply.

Seminario 1ª planta, IEMath-GR

An Integral Spectral Representation of the Massive Dirac Propagator in the Kerr Geometry in EF-type Coordinates

Universidad de Regensburg

We present an integral spectral representation of the massive Dirac propagator in the non-extreme Kerr geometry in horizon-penetrating coordinates, which describes the dynamics of Dirac particles outside and across the event horizon, up to the Cauchy horizon. To this end, we define the Kerr geometry in the Newman–Penrose formalism by means of a regular Carter tetrad in advanced Eddington–Finkelstein-type coordi- nates and the massive Dirac equation in a chiral Newman–Penrose dyad representation in Hamiltonian form. After showing the essential self-adjointness of the Hamiltonian, we compute the resolvent of this operator via the projector onto a finite-dimensional, invariant spectral eigenspace of the angular operator and the radial Green’s matrix stemming from Chandrasekhar’s separation of variables. Then, by applying Stone’s formula to the spectral measure of the Hamiltonian, that is, by expressing the spectral measure in terms of this resolvent, we obtain an explicit integral representation of the Dirac propagator from its formal spectral decomposition.

Aula A25, Facultad de Ciencias

Self-adjointness of the Dirac Hamiltonian for a Class of Non-uniformly Elliptic Mixed Initial-boundary Value Problems on Lorentzian Spacetimes.

Universidad de Regensburg

We introduce a new method of proof for the essential self-adjointness of the Dirac Hamiltonian for a specific class of non-uniformly elliptic mixed initial-boundary value problems for the Dirac equation on smooth, asymptotically flat Lorentzian spacetimes admitting a Killing field that is timelike near and tangential to the boundary, combining results from the theory of symmetric hyperbolic systems with near-boundary elliptic methods. Our results apply in particular to the situation that the spacetime includes horizons, on which the Hamiltonian in general fails to be elliptic.

Aula A25, Facultad de Ciencias

Realización de Grupos mediante espacios de Alexandroff

Universidad Complutense de Madrid

El problema de realización de grupos en la categorı́a topológica ha sido ampliamente estudiado a lo largo de los años. Una solución al problema para el caso de grupos finitos se basa en usar como espacios base espacios topológicos finitos. Sin embargo, este método no es válido para las categorı́as homotópica y homotópica punteada, las cuáles pueden resultar de gran interés para el caso de complejos celulares. En esta charla, dado un grupo \(G\) (no necesariamente finito), construiremos un espacio de Alexandroff (generalización natural de los espacios finitos) tal que su grupo de autohomeomorfismos, grupo de clases de homotopı́a de autoequivalencias homotópicas y su versión punteada sean isomorfos a \(G\). Por último, veremos qué relación hay con el problema clásico, planteado para complejos celulares, usando resultados de McCord, en los que se relacionan espacios de Alexandroff con complejos simpliciales.

Seminario 1ª planta, IEMath-GR

Ancient gradient flows of elliptic functionals and Morse index

MIT

We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, focusing on mean curvature flow for the talk. In all dimensions and codimensions, we classify ancient mean curvature flows in \(\mathbb{S}^n\) with low area: they are steady or canonically shrinking equators. In the mean curvature flow case in \(\mathbb{S}^3\), we classify ancient flows with more relaxed area bounds: they are steady or canonically shrinking equators or Clifford tori. In the embedded curve shortening case in \(\mathbb{S}^2\), we completely classify ancient flows of bounded length: they are steady or canonically shrinking equators. (Joint with Kyeongsu Choi.)

Seminario 1ª planta, IEMath-GR

Teoremas de semiespacio para superficies con curvatura media predeterminada

Universidad de Granada

Motivados por el teorema de semiespacio clásico de Hoffman y Meeks para superficies mínimas en \( \mathbb{R}^3\), el objetivo de esta charla es obtener resultados de tipo semiespacio para superficies inmersas en el espacio Euclideo \(\mathbb{R}^3\) cuya curvatura media viene dada por una función predeterminada dependiendo de su aplicación de Gauss.

Seminario 1ª planta, IEMath-GR

Visitors

Pontificia Universidad Católica de Chile

Despacho: Iemath

Universidade Federal de São Carlos

Despacho: IEMath, B1-4

Univerza v Ljubljani

Despacho: Planta baja, nº 5

University of Adelaida

Despacho: Despacho visitantes

Next visitors

Universidad de Regensburg

Despacho: IEMath, despacho D9

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