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 at Luleå University of Technology (roughly, UK: Senior Lecturer // US: Associate Professor) 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, or mathematical relativity. I am particularly interested in geometric inequalities for black holes, and the problem of quasi-local mass. Check out my publications for some examples of work on both topics.
My emails are always open to questions, comments, potential collaborations or anything else really :)
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.
Recent News:
• New preprint on arXiv! A Volume-Renormalized Mass for Asymptotically Hyperbolic Manifolds (with Mattias Dahl and Klaus Kröncke).
• I attended the workshop Einstein Spaces and Special Geometry at the Mittag-Leffler Institute. My talk on our recent preprint can be found on the website.
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.
Email me at stephen dot mccormick at ltu.se.
Publications
Below is a list of my publications, which can also be found on Google Scholar.
- 2023 (preprint) -- A Volume-Renormalized Mass for Asymptotically Hyperbolic Manifolds. (With with M. Dahl and K. Kröncke)
arxiv.org/abs/2307.06196 - 2022 -- Quasi-local Penrose inequalities with electric charge, Int. Math. Res. Not. rnab215. (With P.-N. Chen)
https://doi.org/10.1093/imrn/rnab215 (arXiv link:2002.04557) - 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)
https://doi.org/10.1090/tran/8297 (arXiv link:1911.12343) - 2021 -- The Hilbert manifold of asymptotically flat metric extensions, Gen. Relativ. Gravit. 53(14).
https://doi.org/10.1007/s10714-021-02785-4 (Open Access) - 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 (arXiv link: 1805.09792) - 2019 -- On the charged Riemannian Penrose inequality with charged matter, Class. Quantum Gravity, 37(1).
doi.org/10.1088/1361-6382/ab50a8 (arXiv link:1907.07967) - 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 arXiv link: 1902.02284) - 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 (arXiv link:1701.04805) - 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 (arXiv link:1802.03331) - 2018 -- On a Minkowski-like inequality for asymptotically flat static manifolds, Proc. Am. Math. Soc. 146
doi.org/10.1090/proc/14047 (arXiv link:1709.06550) -
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 (arXiv link:1612.05241) - 2017 -- The asymptotically flat scalar-flat Yamabe problem with boundary, J. Geom. Anal. 27(3)
doi.org/10.1007/s12220-017-9760-0 (Open Access) - 2015 -- A note on mass-minimising extensions, Gen. Rel. Grav. 47(12).
DOI: 10.1007/s10714-015-1993-2 (Open Access) - 2014 -- First law of black hole mechanics as a condition for stationarity, Phys. Rev. D 90.
DOI: 10.1103/PhysRevD.90.104034 (arXiv link:1406.7480) - 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 (Open Access)
Teaching
I will try to maintain this section with only up-to-date teaching information in Luleå.In period 1 (2023-2024), I am teaching M0047M (Differential calculus).
Current students are directed to the Canvas page.
My lecture slides (typos and all) are available here: bit.ly/Math1-2023. For people outside of LTU, you might need to request access but I will grant it.
(One day I will try to get all my slides formatted in a more presentable way and organised better for sharing)
In period 2 (2023-2024), I am teaching M0048M (Linear Algebra and Integral Calculus).
PhD/Masters/Research Opportunities
There is no general funding available to support research positions, so these will only be available when explicitly advertised.
There are however various national and international schemes designed to externally fund PhD and postdoctoral positions. If someone would like to apply to funding through such a scheme to work in geometric analysis or mathematical general relativity, then I would be happy to discuss that. There are also some possibilities within Sweden to attract strong international postdocs.
Masters programs at LTU can be found here. Although we do not have a specific Master's programme in mathematics, if there is interest then please contact me nevertheless to discuss possibilities.
Other
Below are some other documents that you might be looking for.Assorted Documents
