ABOUT ME
Welcome to my webpage! I'm a 3rd year math PhD student at the University of Cambridge under the supervision of Professor Mihalis Dafermos, in the Cambridge Center for Analysis.
I work on Mathematical General Relativity, but I am also interested in related areas, such as hyperbolic PDEs and Geometric Analysis.
You can reach me by email at rita.t.costa at dpmms.cam.ac.uk. You can also find me in D0.10 at the Center for Mathematical Sciences.
RESEARCH
My research is focused on the Kerr family of black holes, a two-parameter family of rotating axisymmetric black holes that solves the vacuum Einstein equations.
Research papers
-
Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range
|a|<M: frequency space analysis, with Yakov Shlapentokh-Rothman -
Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes,
Communications in Mathematical Physics, 378(1), 705-781 - Numerical evidence towards a positive answer to Morrey's problem, with André Guerra
Talks and seminars
- C.A.K.E. seminar, University of Cambridge, 11 March 2020.
- LMS Hyperbolic Network meeting, Loughborough University, 18 February 2020.
- Junior Analysis Seminar, Imperial College London, 31 January 2020.
- General Relativity Seminar, University of Cambridge, 17 January 2020.
- Mathematical Relativity Seminar, Instituto Superior Técnico, 3 January 2020.
- Invited talk during program "General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein", Mittag-Lefler Institute, 12 December 2019.
- Analysis Seminar, Princeton University, 23 September 2019.
CURRICULUM VITAE
Education
| 2017 – 2021 | PhD in Mathematical Analysis at the University of Cambridge (UK) |
| 2016 – 2017 | Part III in Pure Mathematics at the University of Cambridge (UK) |
| 2013 – 2016 | BSc in Engineering Physics at Instituto Superior Técnico (Portugal) |
Visits
| Fall 2018 | Princeton University (USA), invited by Mihalis Dafermos. |
| Fall 2019 | Princeton University (USA), invited by Yakov Shlapentokh-Rothman. |
Awards
| 2017 – 2021 | Research Scholar at Trinity College (UK) & EPSRC PhD Scholarship (UK) |
| 2016 – 2017 | Trinity Studentship in Mathematics, Trinity College (UK) |
| 2015 – 2016 | Scholarship New Talents in Mathematics, Fundação Calouste Gulbenkian (Portugal) |
TEACHING
| Lent 2020 | Part III Black Holes (example classes) |
| Lent 2020 | Part II Analysis of Functions (supervisor at St Edmund, Girton and Homerton colleges) |
| Lent 2019 | Part II Differential Geometry (supervisor at Homerton, Pembroke and Queens colleges) |