About Me
I like to say that I'm a mathematician who pretends to be a physicist sometimes, although I'd never convince the physicists of that.I'm a universitetslektor (Senior Lecturer/Associate Professor) at Luleå University of Technology working geometric analysis, which is essentially the intersection of PDEs and Riemannian geometry.
Most of my research is motivated by general relativity, where the application of geometric analysis to such problems is often described as the field of mathematical general relativity. I am particularly interested in geometric inequalities for black holes, and the problem of quasi-local mass.
Prior to moving to Luleå, I spent some time working at Uppsala University and KTH Royal Institute of Technology in Stockholm, inlcuding some time while I was formally employed by the University of Regensburg (Germany). Although I am originally from Scotland, I moved to Australia when I was a kid and completed all my studies there including my PhD at Monash Universty under the supervision of Robert Bartnik. Before moving to Sweden I also held my first academic position in Australia, at the University of New England.
Email me at stephen dot mccormick at ltu.se.
Recent News:
New preprint on arXiv: The Volume-Renormalized Mass from a Hamiltonian Perspective (with Mattias Dahl and Klaus Kröncke).
• Dec 2024 - I have recieved funding from the Kempe Foundation, which will allow me to recruit a postdoc.
Find Me Online
You can find me here on Google Scholar or arXiv. You can also follow me on Twitter (@Quasilocal) where I try to post light-hearted mathematics and physics but inevitably get sucked into discussions on current issues.
Publications
Below is a list of my publications, which can also be found on Google Scholar.
- 20XX (preprint) -- The Volume-Renormalized Mass from a Hamiltonian Perspective. (With with M. Dahl and K. Kröncke)
(With with M. Dahl and K. Kröncke)
arxiv.org/abs/2506.11841 - 20XX (preprint) -- A Volume-Renormalized Mass for Asymptotically Hyperbolic Manifolds. (With with M. Dahl and K. Kröncke)
arxiv.org/abs/2307.06196 - 2025 -- V-static metrics and the volume-renormalised mass, J. Geom. Anal. 35(110)
doi.org/10.1007/s12220-025-01939-z - 2024 -- Fill-ins with scalar curvature lower bounds and applications to positive mass theorems, Ann. Glob. Anal. Geom. 65(26).
doi.org/10.1007/s10455-024-09956-x - 2024 -- An Overview of Bartnik's Quasi-Local Mass, Beijing J. Pure Appl. Math. 1(2).
dx.doi.org/10.4310/BPAM.2024.v1.n2.a2 - 2022 -- Quasi-local Penrose inequalities with electric charge, Int. Math. Res. Not. rnab215. (With P.-N. Chen)
https://doi.org/10.1093/imrn/rnab215 - 2021 -- Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space, Trans. Amer. Math. Soc. 374. (With A. Alaee and A. J. Cabrera Pacheco)
doi.org/10.1090/tran/8297 - 2021 -- The Hilbert manifold of asymptotically flat metric extensions, Gen. Relativ. Gravit. 53(14).
doi.org/10.1007/s10714-021-02785-4 - 2020 -- Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions, Pacific J. Math. 304(2).
doi.org/10.2140/pjm.2020.304.629 - 2019 -- On the charged Riemannian Penrose inequality with charged matter, Class. Quantum Gravity, 37(1).
doi.org/10.1088/1361-6382/ab50a8 - 2019 -- On the evolution of the spacetime Bartnik mass, Pure Appl. Math. Q. 15(3). (With P. Miao. Special issue in honour of Robert Bartnik.)
doi.org/10.4310/PAMQ.2019.v15.n3.a6 - 2019 -- On a Penrose-like inequality in dimensions less than eight, Int. Math. Res. Not. 2019(7). (With P. Miao)
doi.org/10.1093/imrn/rnx181 - 2018 -- Asymptotically hyperbolic extensions and an analogue of the Bartnik mass, J. Geom. Phys. 132. (With A. J. Cabrera Pacheco, and C. Cederbaum)
doi.org/10.1016/j.geomphys.2018.06.010 - 2018 -- On a Minkowski-like inequality for asymptotically flat static manifolds, Proc. Am. Math. Soc. 146
doi.org/10.1090/proc/14047 -
2017 -- Asymptotically flat extensions of CMC Bartnik data, Class. Quantum grav. 34(10) (With A. J. Cabrera Pacheco, C. Cederbaum, and P. Miao)
doi.org/10.1088/1361-6382/aa6921 - 2017 -- The asymptotically flat scalar-flat Yamabe problem with boundary, J. Geom. Anal. 27(3)
doi.org/10.1007/s12220-017-9760-0 - 2015 -- A note on mass-minimising extensions, Gen. Rel. Grav. 47(12).
DOI: 10.1007/s10714-015-1993-2 - 2014 -- First law of black hole mechanics as a condition for stationarity, Phys. Rev. D 90.
DOI: 10.1103/PhysRevD.90.104034 - 2014 -- The phase space for the Einstein-Yang-Mills equations and the first law of black hole thermodynamics, Adv. Theor. Math. Phys. 18.
DOI: 10.4310/ATMP.2014.v18.n4.a2
Teaching
Current students are directed to Canvas for course teaching information
I will not maintain up-to-date teaching information here, but each term I usually am teaching one of the four core math courses at LTU -- most often if it is the X-th quarter/term (LP X) then I will be teaching one instance of Math X, for X=1, 2, 3, 4. As of 2024, I am responsible for M0018M - Linear Analysis.
I will hopefully clean up my lecture notes and slides at some point in the near future to make them available here. [Under Construction]
Since I find it a little difficult to find all the courses we actually offer in math, I collected (hopefully) most of them here. I excluded a few specific ones such as bridging courses and courses specifically for teacher training. I also left off courses for the 3-year programmes where similar courses exist for the 5-year programmes, and probably a few others here and there. Swedish names are used here.
Click here to expand the course list
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M0065M Envariabelanalys 1
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M0066M Envariabelanalys 2
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M0067M Linjär algebra
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M0068M Flervariabelanalys
- M0009M Diskret matematik
- M0064M Kombinatorik
- M0018M Linjär analys
- M0014M Matematisk fysik
- M0054M Komplex analys
- M7010M Funktionalanalys
- M7018M Tillämpad matematik
- M7026M Analysens grunder
Postdoc / PhD / Masters Opportunities
There is no general funding available to support research positions. The will be advertised when they are available. However, I am happy to support external applications to fund research positions.
Postdoc Positions
There are some funding schemes in Sweden to support postdoc positions for researchers, usually from abroad to encourage internationalisation. If a suitable candidate with a geometric analysis background is interested in such a position, I'd be happy to work together on a proposal. Please contact me if you would like to know more.
Otherwise, there are not too many opportunities for postdoc positions here.
PhD Positions
PhD positions in mathematics are unfortunately very difficult to finance in Sweden for a variety of reasons. If a PhD position becomes available though. it will be advertised here.
It is even difficult to support a PhD project even if the PhD candidate has their own external funding due to various rules an regulations. This is not impossible, but there are very strict rules around what external funding is sufficient to create a PhD position.
Masters Supervision
Although we do not have a masters programme in mathematics at LTU, I am available for supervision for local students in related programmes (eg. Y-programmet). I may also be able to work with masters students from other universities on a case-by-case basis, depending on local rules and funding available for visits.
Other
Below are some other documents that you might be looking for.Assorted Documents
