Geometry and Topology seminar. Academic year 2018-2019.

This is the webpage of the seminar of the Research Cluster in Geometry at the Mathematics Department of the University of Luxembourg.

Unless otherwise specified, the seminar will be on Monday, 2-3pm and will take place in Room S-6A (MNO).

Here is a link to the seminars of former years.

Organizers: Clara Aldana, Clément Guérin, Vincent Pecastaing.

Next seminar

Upcoming seminars

Previous seminars

  • September 10, 2018: Julien Keller (Aix-Marseille University)
    Caution: Seminar on Monday. Time 15:00, Room S6A.

    Constant scalar curvature Kähler cone metrics

    We will explain what we think is a good definition of a constant scalar curvature Kähler metric with conic singularities. A construction of such special metrics over certain ruled manifolds will be given. To do so, we present a Fredholm alternative result for the Lichnerowicz operator. This also requires to study Hermitian-Einstein metrics on parabolic vector bundles with good regularity properties. Eventually, we will explain how these results fit in the logarithmic version of Yau-Tian-Donaldson conjecture that relates differential geometry to algebraic geometry. This is a joint work with Kai Zheng (Univ. of Warwick).

  • September 5, 2018: Amir Vig (University of California, Irvine)
    Caution: Seminar on Wednesday. Time 14:00, Room S6A.

    Spectral theory of the ellipse

    A famous inverse problem posed by Kac in the 1960s is to determine the shape of a drum from the set of resonant frequencies at which it vibrates. In this talk, I will discuss recent results in this direction pertaining to elliptical drumheads. In particular, I will outline a proof of “spectral rigidity” using a new parametrix for the wave propagator, which makes an interesting connection to billiards and Birkhoff s conjecture.