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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.

Prospective postdocs: I do not have direct access to research funds to hire a postdoc, however there are some schemes available to apply for funding to create positions. I would be happy to apply for such positions with a competitive candidate whose research aligns with my own.

If this interests you, please don't hesitate to contact me :)

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.

• June 2024 - New preprint on arXiv: arxiv.org/abs/2406.09101

• Paper accepted in Annals of Global Analysis and Geometry (updated in publications, below)

• I have been elected to the Swedish National Committee for Mathematics

• I'm looking forward to being a mentor at the British Isles Graduate Workshop V in Mathematical General Relativity, in July. ~~Applications are open for PhD candidates and postdocs to participage (see link).~~

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.

**20XX**(preprint) -- V-static metrics and the volume-renormalised mass

arxiv.org/abs/2406.09101**20XX**(preprint) -- A Volume-Renormalized Mass for Asymptotically Hyperbolic Manifolds. (*With with M. Dahl and K. Kröncke*)

arxiv.org/abs/2307.06196**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 Journal of Pure and Applied Mathematics

(To appear in a special issue in memory of Robert Bartnik).

(arXiv link: arxiv.org/abs/2401.05128)**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

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]

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.

Although we do not have a specific Master's programme in mathematics at LTU, I may be available for Master's supervision in a closely related subject.