Geometrical Aspects of Mathematical Relativity Masterclass
Copenhagen Centre for Geometry & Topology (GeoTop),
University of Copenhagen
16-20 June 2025
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The event will consist of three minicourses by our speakers, highlighting the various geometrical approaches to Einstein's theory of general relativity. In particular, the topics will include singularity theorems, topology of blackholes, constraint equations, connections between scalar curvature and mass of asymptotically flat spacetimes, and more. The target audience will be young researchers and students with a background in differential geometry or working in the field.
Title: Black holes: singularities, topology, and rigidity
Course description: The course will begin by developing the basic causal theory of spacetime. This will lead up to a discussion and proof of the famous Penrose singularity theorem, which was motivated by the issues of gravitational collapse and black hole formation, and for which Sir Roger Penrose was awarded half the Nobel Prize in Physics in 2020. We will then turn our attention to various fundamental properties of black holes. A significant part of this will depend on the more recent study of marginally outer trapped surfaces (MOTS), which are often used to model the surface of a black hole.
Title: A Tour of the Positive Mass Theorem
Course description: The Positive Mass Theorem is a fundamental result in general relativity and differential geometry. It states that, under certain conditions, the total mass (or energy) of an isolated gravitational system is non-negative and is zero only when the spacetime is either completely flat (Minkowski space) or a pure gravitational wave. We will begin with some background material, including minimal hypersurfaces and their generalizations in general relativity, and discuss the geometric proofs of the Positive Mass Theorem for asymptotically flat initial data sets.
The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue. More detailed information about the rooms will be posted here as the date of the masterclass is approached.
Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.
A journey planner in English is available.
More information on the "find us" webpage.
