Staff Profile

Background:

I studied at Warwick and Imperial College London and I have been working at Newcastle since 2016. I enjoy teaching a range of subjects across the disciplines represented in our school.

Semester 1: MAS3901 Group Project

Semester 2: MAS3713/8713 Curves and Surfaces

Semester 2: MAS1613 Multivariable Calculus

• Properties of special Riemannian metrics (Einstein metrics and Ricci solitons)
• Numerical differential geometry

Recently, I've been working with Daniel Cole and Rachael Pirie from the School of Natural and Environmental Sciences on a project that applies ideas coming from differential geometry to the problems of molecular similarity searching. Our our second preprint is available here: https://arxiv.org/abs/2301.04424

I have been thinking about the canonical Einstein metric on a complex Grassmannian. A recent preprint is available here: https://arxiv.org/abs/2403.18757. This article will not be published but has been combined with work of Paul Schwahn and Uwe Semmelmann to produce a joint paper.

Paul, Uwe, and I have worked out the (second-order) deformation theory for SU(n)/SO(n) and SU(2n)/Sp(n). Our preprint is available here: https://arxiv.org/abs/2412.08770

I have contributed a short piece for a special edition of the journal Feminist Theory about the film Barbie. It is available here: https://doi.org/10.1177/14647001241291382

• Articles

  • Batat W, Hall SJ, Murphy T, Waldron J. Rigidity of SU_n-type symmetric spaces. International Mathematics Research Notices 2024, 2024(3), 2066-2098.
  • Hall SJ, Pirie R, Cole DJ. Riemannian geometry and molecular similarity I: spectrum of the Laplacian. Proceedings of the Royal Society A 2024, 480(2284), 20230343.
  • Hall SJ. Love must imagine the world: Quantum mechanics in Barbie. Feminist Theory 2024, epub ahead of print.
  • Batat W, Hall SJ, Murphy T. Destabilising compact warped product Einstein manifolds. Communications in Analysis and Geometry 2021, 29(5), 1061-1094.
  • Hall SJ, Murphy T, Waldron J. Compact Hermitian Symmetric Spaces, Coadjoint Orbits, and the Dynamical Stability of the Ricci Flow. The Journal of Geometric Analysis 2021, 31, 6195-6218.
  • Hall SJ. The canonical Einstein metric on G2 is dynamically unstable under the Ricci flow. Bulletin of the London Mathematical Society 2019, 51(3), 399-405.
  • Hall SJ, Murphy T. Bounding the first invariant eigenvalue of toric Kähler manifolds. Mathematical Research Letters 2017, 24(1), 67-81.
  • Hall SJ, Murphy T. Approximating Ricci solitons and quasi-Einstein metrics on toric surfaces. New York Journal of Mathematics 2016, 22, 615-635.
  • Batat W, Hall SJ, Jizany A, Murphy T. Conformally Kähler geometry and quasi-Einstein metrics. Muenster journal of Mathematics 2015, 8(1), 211-228.
  • Hall SJ, Haslhofer R, Siepmann M. The stability inequality for Ricci-flat cones. The Journal of Geometric Analysis 2014, 24(1), 472-494.
  • Hall SJ, Murphy T. On the spectrum of the Page and the Chen-LeBrun-Weber metrics. Annals of Global Analysis and Geometry 2014, 46(1), 87-101.
  • Hall SJ, Murphy T. Variation of complex structures and the stability of Kähler-Ricci solitons. Pacific Journal of Mathematics 2013, 265(2), 441-454.
  • Dancer AS, Hall SJ, Wang MY. Cohomogeneity one shrinking Ricci solitons: an analytic and numerical study. Asian Journal of Mathematics 2013, 17(1), 33-62.
  • Hall SJ, Murphy T. On the linear stability of Kaehler-Ricci solitons. Proceedings of the American Mathematical Society 2011, 139, 3327-3337.
  • Hall SJ. Computing Perelman's nu-functional. Differential geometry and its applications 2011, 29(3), 426-432.

• Book Chapter

  • Hall SJ, Murphy T. Bounding the invariant spectrum when the scalar curvature is non-negative. In: Van der Veken et. al, ed. Contemporary Mathematics: Geometry of Submanifolds. American Mathematical Society, 2020, pp.133-140.