Welcome to my webpage! I'm a 4th year math PhD student at the University of Cambridge under the supervision of Professor Mihalis Dafermos, in the Cambridge Center for Analysis. I'm also Research Scholar at Trinity College.

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 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,
    to appear in Revista Matemática Iberoamericana
Talks and seminars


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)
Fall 2019     Princeton University (USA), invited by Yakov Shlapentokh-Rothman.
Fall 2018       Princeton University (USA), invited by Mihalis Dafermos.
Lent 2018     Microsoft Research Cambridge (UK), working with Neil Dalchau.
July 2017     Sainsbury Laboratory Cambridge (UK), working in the Jones group.
2017 – 2021 Research Scholarship 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)
2014 – 2016 Academic Merit Scholarship, Fundação Eugénio de Almeida (Portugal)
2012 2nd Place at the Portuguese Physics Olympiads


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)