My research lies at the intersection of general relativity, differential geometry and hyperbolic PDEs. I am very interested in studying PDEs derived from theories of higher dimensional gravity, string theory, particle physics and cosmology. My contact details are email@example.com.
- 2015 – 2020: PhD in Mathematics under Dr Pieter Blue at the University of Edinburgh through MIGSAA. Here is my thesis.
- 2010 – 2014: BA and MMath (Part III) at Newnham College, University of Cambridge.
- Global stability of spacetimes with supersymmetric compactifications, with Lars Andersson (AEI), Pieter Blue (Edinburgh) and Shing-Tung Yau (Harvard)
- Stabilizing relativistic fluids on spacetimes with non-accelerated expansion, with David Fajman (Vienna) and Todd Oliynyk (Monash), accepted by CMP.
- Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds, with Philippe LeFloch (Sorbonne-UPMC) and Shijie Dong (Fudan), Annales Henri Poincaré (2020)
- Attractors of the Einstein-Klein-Gordon system, with David Fajman (Vienna), Communications in PDE (2020).
- Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities, with Shijie Dong (Fudan), Journal of Differential Equations Vol. 269 Issue 9 (2020) 7470-7497.
- The Weak Null Condition and Kaluza-Klein Spacetimes, J. Hyperbolic Differ. Equ. Vol. 15, No. 2 (2018) 219-258.
- December 2020, Junior Analysis e-Seminar, Imperial College London.
- November 2020, Seminar in Loughborough as part of the LMS Hyperbolic Network.
- October 2020, Lightening talk at “Advances in Computational Relativity”, ICERM, Brown University.
- June 2020, Maxwell Analysis e-Seminar, University of Edinburgh and Heriot Watt University. Slides here.
- June 2020, Relativity e-Seminar, University of Vienna. Slides here.
- March 2020, General Relativity Seminar, University of Cambridge. Slides here.
- February 2020, 10th Central European Relativity Seminar, AEI Golm. Slides here.
- February 2020, Geometric Analysis Seminar, University of Tübingen. Blackboard talk.
- September 2019, PDE Seminar, Vanderbilt University. Slides here.
- March 2019, Differential Geometry Seminar, University of Potsdam. Slides here.
- March 2019, Geometry and Analysis Seminar, Queen Mary University of London. Slides here.
- March 2019, Analysis Seminar, University of Leeds. Slides here.
- February 2019, 9th Central European Relativity Seminar, Kraków. Slides here.
- January 2019, Relativity Seminar, University of Vienna. Blackboard talk.
- May 2018, PDE CDT Seminar, University of Oxford. Slides here.
- April 2018, 3rd Meeting of the LMS Hyperbolic Network, ICMS, Edinburgh. Slides here (also happily 3 of the 6 speakers were women).
- March 2018, Relativity Seminar, University of Vienna. Slides here.
- February 2018, 8th Central European Relativity Seminar, Brno, Czech Republic. Slides here.
- November 2017, Junior WIC Geometric Analysis seminar, University of Cambridge. Slides here.
- April 2017, Colloquium of the UK CDTs in Analysis, ICMS, Edinburgh.
Invited research visits:
- 2022, ESI Programme on “Mathematical Perspectives of Gravitation beyond the Vacuum Regime”, Austria.
- 2021, Workshop “Mathematical Aspects of General Relativity”, Oberwolfach.
- 2020, “Hyperbolic Differential Equations in Geometry and Physics” at the MATRIX research institute, Australia.
- 2019, Institut Mittag-Leffler fellowship (2 month visit), Sweden.
- 2018 – 2019: 6 month research visit to the Gravitational Physics group at the University of Vienna working under Associate Professor David Fajman.
- 2017 – 2018: 3 research visits (totalling 8 months) to Sorbonne-UPMC, Paris working under Professor Philippe LeFloch.
Other talks (ie, things I find interesting, presentations of other papers, layman or informal talks):
- October 2020 — present, co-organising the DAMTP GR Journal Club
- March 2020, Edinburgh Mathematical Physics Group (EMPG) Seminar and Preseminar
- An introduction to the Initial Value Problem in General Relativity, slides here.
- Semester 2, 2020, I organised a Microlocal Analysis Reading Group, superbly named #MARG, which sadly was cut short due to the virus :(
- January 2020, Postgraduate Colloquium, University of Edinburgh.
- How to track your cat: the maths behind GPS, slides here.
- January 2019, Gravity Lunchtime Seminar, University of Vienna.
- July 2018, Paris Relativity Reading Group, Université Pierre-et-Marie-Curie.
- An introduction to Dafermos and Rodnianski’s r^p weighted method, introduced in this paper.
- April 2018, Postgraduate Colloquium, University of Edinburgh.
- March 2018, Postgraduate Colloquium, Heriot Watt University.
- The Cauchy Problem in GR and Kaluza Klein spacetimes.
- February 2018, Edinburgh Mathematical Physics Lunch Seminar.
- Late-time asymptotics on extremal and subextremal spacetimes (following this and related previous papers by those authors).
- March 2017, Mathematical Relativity Seminar, University of Edinburgh.
- Four talks on Lindblad and Rodnianski’s proof of the stability of Minkowski spacetime.
- March 2017, Edinburgh Mathematical Physics Lunch Seminar.
- Kaluza Klein spacetimes and stability questions.
- December 2016, Postgraduate Colloquium, University of Edinburgh.
- Understanding LIGO, slides here.
- July 2016, MIGSAA Presentation
- Nonlinear stability of Minkowski spacetime in high dimensions, slides here
- February 2016, Postgraduate Colloquium, Heriot Watt University
- Well-posedness of BSSN in d-dimensions, slides here
- November 2015, Geometry Club, Edinburgh University
- Minimal surfaces in general relativity, some notes here
- November 2013, Part III colloquiums, University of Cambridge
- Minimal surfaces in general relativity
- March 2014, Part III colloquiums, University of Cambridge
- Some PDE theory for the Einstein equations
- February 2013, ‘Tomorrow’s Mathematicians Today’ conference, University of Greenwich
- Tarski’s undefinability of truth. I was also voted best speaker by the fellow students!
Awards and funding:
- 2020, London Mathematical Society Early Career Fellowship to (now virtually) visit Prof. David Berman at QMUL from July – Sept (£3600).
- 2020, REWIRE Grant and Fellowship at University of Vienna (€200,000, declined).
- 2020, Henslow Junior Research Fellowship, Darwin College Cambridge (declined for Herschel Smith position).
- 2019, Laura Wisewell Travel Scholarship and MIGSAA special funding (£900).
- 2018, Sir William Darling Memorial Prize from University of Edinburgh for my maths outreach work (£1000).
- 2017, top level prize from the Edinburgh Maths department’s “Postgraduate Research Student Essay Prize” (£500).
- 2016-2019, funding received to attend conferences at: MSRI, IHP, IHES, Oberwolfach, Reading University, Warwick University, ETH Zurich.
- 2015, PhD positions with overseas-student funding from MIGSAA (a joint Analysis programme between UoE and HWU) and University of Cambridge (declined).
- 2014, Anne Clough Prize for excellent exam performance in mathematics, Newnham College, University of Cambridge.
- 2013, Marjorie Tunnicliffe Prize for excellent exam performance in mathematics, Newnham College, University of Cambridge.
- 2020-21 in Cambridge
- Analysis and Topology IB (2nd year)
- 2019-20 at Edinburgh
- Fundamentals of Pure Maths (2nd year), Geometry of General Relativity (4th year)
- 2018-19 at Edinburgh
- I did not teach this year, however I wrote some simple moving graphs to explain concepts in analysis: eg pointwise vs. uniform convergence.
- 2017-18 at Edinburgh
- Honours Analysis (3rd year), including private tutoring for this course (with my own revision notes including extra problems)
- Proofs and Problem Solving (1st year), Geometry of General Relativity (4th year), Advanced Methods in Applied Mathematics (4th year)
- Nominated four times for the “Best Student Who Tutors Award”, part of the student union awards (see what my students said about me here!)
- 2016-17 at Edinburgh
- Fundamentals of Pure Maths (2nd year), Proofs and Problem Solving (1st year), Honours Analysis (3rd year), Advanced Methods in Applied Mathematics (4th year)
- Nominated for the “Best Student Who Tutors Award”, part of the student union awards
- 2014-2015 at AIMS
- Tutor for about 80 Masters students
Other maths projects:
- A short 2 page summary of my first paper, awarded top-level prize in the Edinburgh Maths department’s “Postgraduate Research Student Essay Prize”.
- First year MIGSAA project on the non-linear stability of dimensional Minkowski spacetime for and some standard results about stationary solutions to the incompressible Navier Stokes equations.
- In my Part III essay I generalised the proof of local well-posedness of BSSN to high dimensions, for . This was actually not known before then.
- While working at AIMS-South Africa I wrote some notes and problems about dimensional analysis, 6 page PDF.
Originally motivated in part by this TED talk, I am actively involved with making mathematics accessible to underprivileged and underrepresented groups.
- I helped run a Maths Circle teacher training session for 35 teachers, plus the Maths Circle in the afternoon (235 parents and kids!), on February 29.
- I helped organise and/or present at two Virtual Maths Circles on August 5 (over 100+ participants) and on October 3 (over 150+ participants)
- I gave a talk about “Life as a PhD student” to a group of 30 female undergraduates for the Piscopia Initiative which aims to promote female students doing PhDs.
In Edinburgh in 2019:
- I helped run Maths Circle teacher training sessions for about 45 teachers on both March 2 and December 14, as well as assist at the Maths Circles on March 2, October 12 and December 14.
- I co-wrote a successful small grant proposal (£1450) for Widening Participation in the Maths Circles awarded by the Edinburgh University’s Principal’s Teaching Award Scheme (PTAS).
- I was a helper at one of the Royal Institution Mathematics Masterclass events on May 18.
- This is a picture of me doing a stand-up comedy routine about the electroweak theory of particle physics at the Glasgow Bright Club, as part of Glasgow Science Week. I also performed the same routine at the 49th Edinburgh Bright Club. You can watch the videos here and here!
- We successfully received another grant from the Glasgow Mathematical Journal Trust that will support the Maths Circle for the next 4 years
- I helped at a small Maths Circle event on October 5 as part of Maths Week Scotland, to reach out to different communities in Edinburgh.
In Edinburgh in 2018:
- Using our first grant from the Glasgow Mathematical Journal Trust, we began to spread the Maths Circle word out, particularly to underprivileged or far-away schools. I helped run a training session for teachers, as well as assist at the Maths Circle, on 10th March.
- We received a £500 grant from the Edinburgh City Council to develop our Maths Circle resources to loan out to schools and I have been significantly involved in producing these resources.
- I was awarded the Sir William Darling Memorial Prize (and an award of £1000) by Edinburgh University for my maths outreach work in founding the Edinburgh Maths Circle. The prize recognises “such student who has done in any year most to advance or enhance the reputation [through conduct, example, scholarship or pre-eminence in sport] of the University”.
In Edinburgh in 2017:
- I wrote an interactive problem and a poster explaining the maths (and relativity) behind GPS for the Edinburgh International Science Festival.
- I wrote a problem about different types of map projections for a Maths Escape Room, for the Edinburgh University Innovative Learning Week.
- I helped organise, write problems for and run four Maths Circles in Edinburgh on 18th March, 6th May, 16th September (a record 400 parents and children for this one!) and 25th November.
- We were awarded a £1200 grant from the Glasgow Mathematical Journal Trust to keep running the Maths Circles.
- This is a picture of me giving a stand-up comedy performance about Black Holes at the 43rd Edinburgh Bright Club, held at the Stand comedy club in Edinburgh, see the video here!
- My former college Newnham has a Wall of Women page where I appear talking about AIMS.
In Edinburgh in 2016:
- Inspired by a similar event in Cambridge, I started the Edinburgh Maths Circle which has been very successful (averaging 200 attendees at each Circle).
- I helped organise, write problems for and run three of these Maths Circles on 28th May, 10th September and 3rd December.
- I made a poster about the physics behind building cathedrals for the Edinburgh International Science Festival.
In South Africa from 2014-2015:
- I was a tutor at AIMS South Africa for 1 year, teaching and mentoring around 60 underprivileged students from 19 African countries, as they completed their Masters program. Here is a picture of me and some of my incredible students on graduation day.
- Writing CVs and Statements, 4 page PDF which I wrote for AIMS students, but could be applicable for others.
- I gave a talk at my former high-school about what a degree in maths can do for you.
In undergrad at Cambridge:
- I helped at Cambridge Maths Circle events (2010-14).
- I did a summer internship (2011) at NRICH, writing problems and other mathematics material.
- In my second year (2012) I co-founded with Anna Seigal the Emmy Noether Society for female mathematicians at Cambridge University.
- I helped organise many events for the Emmy Noether Society.
- I appeared in a PDF about Former Students given to new Cambridge maths students.
- I taught a small group of 9/10-year-old students for a lunchtime Maths Club (2013).
- I made a poster (2014) about famous female mathematicians and another poster about the Emmy Noether Society for an open day at Cambridge University.
- I organised a Wikipedia Women in Maths Editathon (2014) at Cambridge to improve Wikipedia articles about female mathematicians.