Geometric Analysis Days: Intersections of Geometric Analysis and Mathematical Relativity
Queen Mary University of London
30-31 October 2018
The Conference
October 2018
Tues 30th Oct 12:00-17:00. Wed 31st Oct 09:00-14:00
This two-day conference will bring together researchers in Geometric Analysis and Mathematical relativity with a focus on exploring intersections between the two fields. The event will feature five talks by experts in the field from the UK, USA and Europe.
Postgraduate students, postdoctoral associates and early-career researchers are encouraged to attend and there is limited funding available to support UK-based PhD students. Please indicate if you require support after registering by sending an email to s.beheshti@qmul.ac.uk.
On both days of the conference, lunch will be provided. The registration deadline to be included in the lunch plans is Thursday 25 October 2018.
Speakers
Shabnam Beheshti
QMUL
United Kingdom
Annegret Burtscher
Radboud University
The Netherlands
Jan Metzger
University of Potsdam
Germany
Hans Ringström
KTH
Sweden
Christina Sormani
CUNY
United States
Programme
Please note that the second day of the programme will be held entirely in Queens W316.
Tuesday 30 October
12:00 - 14:00 Lunch and Discussion, Queens Building, Room E304
14:15 - 15:15 Christina Sormani, Graduate Centre, Room 114
Spacetime Intrinsic Flat Convergence
The spacetime intrinsic flat convergence has been developed in joint work with Carlos Vega and Anna Sakovich. As a first step we convert a spacetime manifold into a metric space using the null distance (defined jointly with Vega) and the cosmological time function (Wald-Yip and Andersson-Galloway-Howard). For nice enough spacetimes the metric space is an integral current space and encodes causality. We are then able to define the intrinsic flat limits of these nice spacetimes. In upcoming work with Vega we apply this to study big bang spacetimes where the cosmological time function becomes a distance from a big bang point, and in upcoming work with Sakovich we apply this to future maximal developments of initial data sets.
15:15 - 15:30 Q&A
15:30 - 16:00 Coffee/Tea Break
16:00 - 17:00 Hans Ringström, Graduate Centre, Room 114
Linear Systems of Wave Equations on Cosmological Backgrounds
with Convergent Asymptotics
Studying linear systems of wave equations on a fixed background geometry is often a first step towards understanding the non-linear setting. The talk describes a theory for linear systems of wave equations on a class of cosmological backgrounds. The main result of the theory is optimal energy estimates. However, it also gives conclusions concerning the asymptotics of solutions, sometimes even a homeomorphism between initial data and asymptotic data.
17:00 - 17:15 Q&A
17:30 - close Walk and Pub Dinner at The Approach Tavern: friends & family welcome!
Wednesday 31 October
08:45 - 09:00 Coffee/Tea (and all talks), Queens Building, Room W316
09:00 - 10:00 Shabnam Beheshti
Open Questions (and Suggestions) in Relativistic Viscous Hydrodynamics
It is known that viscous effects lead to nontrivial dynamical behaviour in homogeneous cosmological models such as FLRW and Bianchi spacetimes. Recent progress in well-posedness of certain Einstein-Navier-Stokes systems motivates revisiting a model first proposed by Lichnerowicz in 1967. We investigate the role of dynamic velocity in a cosmological background, suggesting that the additional degree of freedom afforded by the associated fluid index may play a geometric role in the evolution of the fluid. The talk is aimed at a diverse mathematics/physics audience. and postgraduates are welcome.
10:00 - 10:15 Q&A
10:15 - 11:15 Jan Metzger
The Willmore Functional and Ambient Scalar Curvature
11:15 - 11:30 Q&A
11:30 - 12:30 Annegret Burtscher
Perfect Fluids in General Relativity
Perfect fluids in general relativity are commonly used to model stellar structures in astrophysics. In the static, asymptotically flat case, spherical symmetry is essentially inherent. We review some results about this special setting for different equations of state. Moreover, we show how certain static solutions can be suitably perturbed and serve as initial data for the Einstein equations leading to trapped surfaces during evolution. Such results are directly related to black hole formation.
12:30 - 12:45 Q&A
12:45 - 14:00 Lunch at Verdi's
Sponsors
Meeting made possible with support from the LMS Scheme 9 Celebrating New Appointments Grant for S. Beheshti, EPSRC Grant for R. Buzano and support from the School of Mathematical Sciences, Queen Mary University of London for both co-corganisers.