The goal of the programme is to bring together doctoral students, young researchers, and established experts who work on the overlap of geometric analysis and mathematical relativity. The recent developments in the area, and the new techniques that are proving to be particularly successful will be discussed. Above all, the programme seeks to support existing collaborations and to inspire new ones.

The following topics have been seeing a surge of activity following spectacular recent breakthroughs. They form the thematic center of the programme:

• Geometry of initial data sets

New notions of mass, quasi-local mass, and center of mass, as well as new proofs of the positive energy theorem yield deep insights to the geometry of initial data for the Einstein equations. The incompatibility of some of these notions raises difficult new questions that are being explored. Important themes here also include new initial data singularity theorems based on topological properties, and progress on the geometry of stationary black hole initial data.

• Construction of initial data sets 

New gluing techniques for the constraint equations and progress on the solution of the classical conformal method allow for the construction of asymptotically flat and asymptotically hyperbolic initial data sets with surprising properties. New results on initial data with positive cosmological constant show a rich structure, including non-uniqueness and bifurcation phenomena, which deserves to be further explored.

• Scalar Curvature 

The spectacular recent results on scalar curvature rigidity and the discovery of global effects of scalar curvature on the large scale isoperimetric structure of a Riemannian manifold have given new impetus to this classical field and have opened avenues for future research.

A summer school will be part of the ESI Programme and will take place in the week before the conference, July 17 – July 21, 2017. See the web site of the Summer School for more details. Schedule (pdf)

A conference will take place from July 24 – July 28, 2017: Schedule (pdf)

Further Lectures:

• Talk Martin Reiris (U de la Republica, Montevideo): A classification of static and stationary solutions to Einstein field equations obtained by the application of novel techniques in comparison geometry

      July 31, 2017, 1:00 p.m., Announcement (pdf)

• Talk Katharina Rademacher (KTH Stockholm): Strong Cosmic Censorship and the initial singularity in Bianchi spacetimes

       August 2, 2017, 3:30 p.m., Announcement (pdf) 

• Talk Marcus Khuri (State U New York, Stony Brook): Existence and Uniqueness for Near-Horizon Geometries in the Cosmological Setting

       August 4, 2017, 1:00   p.m., Announcement (pdf)

 

• Talk Eric Woolgar (U of Alberta, Edmonton): Lorentzian Bakry-Emery Theory,

       August 7, 2017, 1:00 p.m., Announcement (pdf)

 

• Talk Annegret Burtscher (U Bonn): On the asymptotic behavior of static perfect fluids

       August 9, 2017, 3:30 p.m., Announcement (pdf)

 

• Talk Gilbert Weinstein (Ariel U): Bi-axisymmetric Stationary Solutions to the Vacuum Einstein Equation with Non-spherical Horizons

       August 10, 2017, 3:30 p.m., Announcement (pdf)

 

• Talk Peter Topping (U of Warwick): Ricci Flow and Ricci Limit Spaces
  August 11, 2017, 1:00 p.m., Announcement (pdf)

 

• Talk Luc Nguyen (Oxford U): Existence and uniqueness of Green's functions to a nonlinear Yamabe problem
  August 14, 2017, 1:00 p.m., Announcement (pdf)
   
• Talk Stefan Haller (U Vienna): The heat equation on filtered manifolds
  August 21, 2017, 3:30 p.m., Announcement (pdf)
   
• Talk Hubert Bray (Duke U): Flatly Foliated Relativity: A Stepping Stone between Special and General Relativity

       August 22, 2017, 3:30 p.m., Announcement (pdf)

 

 

• Talk Volker Branding (U Vienna): The supersymmetric nonlinear sigma model: Harmonic maps coupled to spinor fields

       August 23, 2017, 3:30 p.m., Announcement (pdf)
 

 

• Talk Juan Valiente-Kroon (Queen Mary College, London): On the construction of anti-de Sitter-like spacetimes

       August 24, 2017, 3:30 p.m., Announcement (pdf)
 

• Talk Jérémie Joudioux (U Vienna): The stability of Minkowski space as a solution to the Einstein-Vlasov system

       August 25, 2017, 1:00 p.m., Announcement (pdf)
 

• Talk Håkan Andréasson (U Chalmers): Approximating gravitational collapse for dust with Vlasov matter

       September 6, 2017, 3:30 p.m., Announcement (pdf)
 

• Talk Tim-Torben Paetz (U Vienna): Analysis of a Bianchi-ike equation satisfied by the Mars-Simon tensor

       September 8, 2017, 1:00 p.m., Announcement (pdf)

And a workshop "Advances in General Relativity" will take place from August 28 – September 1, 2017. Schedule (pdf) [updated August 29, 2017] Venue for MONDAY AFTERNOON (August 28, 2017) of the workshop, the conference and the summer school in July: Lise Meitner Lecture Hall, 1st floor, Faculty of Physics, Strudlhofgasse 4, 1090 Vienna, (map)