Time: Monday 4 pm

Location: Krieger 308

Organizer(s): Jacob Bernstein and Yi Wang

Date |
Speaker |
Title |
Abstract |

(Imperial) Special Seminar |
Global nonlinear stability of Minkowski space for Einstein--Vlasov systems | Global nonlinear stability of Minkowski space for the massive and massless Einstein--Vlasov systems. Abstract: The Einstein--Vlasov system describes an ensemble of collisionless particles interacting via gravity, as modelled by general relativity. Under the assumption that all particles have equal mass there are two qualitatively different cases according to whether this mass is zero or nonzero. I will present two theorems concerning the global dispersive properties of small data solutions in both cases. The massive case is joint work with Hans Lindblad. | |

(UC Santa Barbara) |
Min-max theory for constant mean curvature (CMC) hypersurfaces | In this talk, I will present constructions of closed CMC hypersurfaces using min-max method. In particular, given any closed Riemannian manifold, I will show the existence of closed CMC hypersurfaces of any prescribed mean curvature. This is a joint work with Jonathan Zhu. | |

(Yale U) |
A variational approach to axially symmetric Maxwell perturbations of Kerr-de Sitter black holes | The Kerr-de Sitter black hole family is a solution of Einstein's equations of general relativity with a positive cosmological constant. After reviewing some background on these spacetimes, we shall discuss the proof that there exits a phase space of canonical variables for the (unconstrained) axially symmetric Maxwell's equations propagating on Kerr-de Sitter, such that their motion is restricted to the level sets of a positive-definite Hamiltonian, despite the ergo-region. If time permits, we shall discuss the equivalent results for the corresponding fully coupled (and constrained) Einstein-Maxwell initial value problem. | |

(UC Santa Cruz) |
Hypersurfaces in hyperbolic space | In this talk I will report our recent works on convex hypersurfaces in hyperbolic space. I will talk on nonnegatively curved immersed as well as Ricci nonnegative embedded hypersurfaces in hypersurfaces in hyperbolic space. | |

(UC Berkeley) |
Non-linear stability of Kerr-de Sitter black holes | I will explain some ideas behind the proof of the global stability of the Kerr-de Sitter family of black holes as solutions of the initial value problem for the Einstein vacuum equations when the cosmological constant is positive. I will explain the general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations, and thus how our solution scheme finds a suitable gauge, within a carefully chosen finite-dimensional family of gauges, in which we can find the global solution. I will also address the issue of finding the mass and the angular momentum of the final black hole. This talk is based on joint work with AndrĂ¡s Vasy. | |

(JHU) |
Hausdorff stability of round spheres under small-entropy perturbation | Colding-Minicozzi introduced the entropy functional on the space of all hypersurfaces in the Euclidean space when studying generic singularities of mean curvature flow. It is a measure of complexity of hypersurfaces. Bernstein-Wang proved that round spheres $\mathbb S^n$ minimize entropy among all closed hypersurfaces for $n\leq6$, and the result is generalized to all dimensions by Zhu. Bernstein-Wang later also proved that the round 2-sphere is actually Hausdorff stable under small-entropy perturbations. I will present in this talk the generalization of the Hausdorff stability to round hyper-spheres in all dimensions. | |

(Ryukoku U) |
An exterior nonlinear elliptic problem with a dynamical boundary condition | We consider the nonnegative solution of a semilinear elliptic equation with a dynamical boundary condition. Several results on existence, nonexistence and large-time behavior of small solutions were obtained before for the half-space case. In this talk we study the effects of the change of the domain from the half-space to the exterior of the unit ball. We obtain the critical exponent with respect to the existence of solutions and the decay rate of small global-in-time solutions. Furthermore, we show that local solvability is equivalent to global solvability. This talk is based on the joint work with M. Fila (Comenius Univ.) and K. Ishige (Tohoku Univ.). | |

(Minnesota) |
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(Northwestern) |
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(U Chicago) |
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(U Missouri) |
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(U Autonoma de Madrid) |
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(Imperial) |

Archive of Analysis Seminar:

Spring 2017 Fall 2016 Spring 2016 Fall 2015 Spring 2015 Fall 2014 Spring 2014 Fall 2013