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Research & about me
Research & about me
Currently, I am an Assistant Professor in Algebra in the School of Mathematics at the University of Birmingham. Here is my departmental webpage.
Before this, I was the Meggitt Research Fellow and Director of Studies in Pure Mathematics at Emmanuel College, Cambridge, as well as an Affiliated Lecturer at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.
Previously, I was an LMS Early Career Fellow at the University of Oxford, visiting Dr Karin Erdmann. I completed my PhD in Cambridge, under the supervision of Prof. Stuart Martin and mentorship of Dr Eugenio Giannelli.
My main research interests are in the representation theory of finite groups and algebraic combinatorics. I am particularly interested in the representation theory of symmetric groups and related algebras.
Papers
Papers
Minimal numbers of linear constituents in Sylow restrictions for symmetric groups (joint with B. Gustavsson), submitted. [arXiv]
On the number and sizes of double cosets of Sylow subgroups of the symmetric group (joint with P. Diaconis, E. Giannelli, R. Guralnick, G. Navarro, B. Sambale and H. Spink), submitted. [arXiv]
Degrees and prime power order zeros of characters of symmetric and alternating groups (joint with E. Giannelli and E. McDowell), accepted in Bulletin of the London Mathematical Society. [arXiv]
Sylow branching trees for symmetric groups (joint with E. Giannelli), accepted in Transactions of the American Mathematical Society. [arXiv]
Some stable plethysms (joint with Y. Okitani), Proceedings of the American Mathematical Society 151 (11) (2023), 4557–4564. [arXiv]
Positivity of Sylow branching coefficients for symmetric groups, Journal of Pure and Applied Algebra 227 (2023), doi:10.1016/j.jpaa.2023.107355. [arXiv]
On plethysms and Sylow branching coefficients (joint with Y. Okitani), Algebraic Combinatorics 6 (2) (2023), 321–357. [arXiv]
Sylow branching coefficients and a conjecture of Malle and Navarro (joint with E. Giannelli, J. Long and C. Vallejo), Bulletin of the London Mathematical Society 54 (2022), 552–567. [arXiv]
Torsion pairs and Ringel duality for Schur algebras (joint with K. Erdmann), Algebras and Representation Theory (2021), https://doi.org/10.1007/s10468-021-10098-y. [arXiv]
Linear characters of Sylow subgroups of symmetric groups (joint with E. Giannelli and J. Long), Journal of Algebra 584 (2021), 125–160. [arXiv]
Sylow branching coefficients for symmetric groups (joint with E. Giannelli), Journal of the London Mathematical Society (2) 103 (2021), 697–728. [arXiv]
On the p'-subgraph of the Young graph (joint with E. Giannelli and S. Martin), Algebras and Representation Theory 22 (2019), no. 3, 627–650. [arXiv]
On permutation characters and Sylow p-subgroups of Sn (joint with E. Giannelli), Journal of Algebra 506 (2018), 409–428. [arXiv]
Other written work:
On Problems in the Representation Theory of Symmetric Groups. PhD thesis (2019).
Topics in the Representation Theory of Schur algebras. Smith-Knight essay (2017).
Auslander-Reiten Theory. Part III essay, supervised by Prof. S. Martin (2015).
e^{π\sqrt{163}}: A brief foray into the theory of elliptic curves, the j-invariant and the modular equation. Yeats Prize essay, supervised by Prof. B. Green (2013).
Talks
Talks
Here are some of my invited talks and activities:
AGGITatE 2025: A conference on Groups, Representations and Cohomology, University of Essex, UK, August 2025.
LMS Midlands Regional Meeting & Workshop 2025: Groups in the Midlands, University of Lincoln, UK, June 2025.
Group Representation Theory, Universit\`a degli Studi di Firenze, Italy, June 2025.
Representation Theory Down Under, conference in special semester: "Modern perspectives in representation theory", Sydney Mathematical Research Institute, Australia, June 2025.
Representation Theory in City: Geometry, Combinatorics and Springer Theory, City St George's, University of London, UK, May 2025.
Postgraduate Group Theory Conference (plenary speaker), University of Birmingham, UK, July 2024.
Perspectives in Representation Theory: satellite conference of the 9th European Congress of Mathematics, University of Coimbra, Portugal, July 2024.
75th British Mathematical Colloquium, Algebra Workshop speaker, University of Manchester, UK, June 2024.
Introduction to Modern Advances in Algebra (plenary speaker), University of Exeter, UK, February 2024.
New Approaches to Plethysm: Computation and Complexity – Focused Research Workshop, University of York, UK, August 2023.
Categorification in Representation Theory, University of Sydney, Australia, February 2023.
Representation Theory of Symmetric Groups and Related Algebras II, Institute for Mathematical Sciences, National University of Singapore, December 2022.
Workshop: Character Theory and Categorification, Mathematisches Forschungsinstitut Oberwolfach, Germany, August 2022.
Programme seminar: ‘Groups, representations and applications: new perspectives’, Isaac Newton Institute, UK, July 2022.
Colloquium and Conference in memory of Christine Bessenrodt, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Germany, July 2022.
Counting conjectures and beyond, workshop of "Groups, representations and applications: new perspectives", Isaac Newton Institute, UK, May 2022.
Combinatorics Seminar, University of California, Berkeley, USA, March 2022.
Representation Theory Seminar, Okinawa Institute of Science and Technology Graduate University, Japan, April 2021.
Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany, February 2020.
Seminars in Groups and Representations, TU Kaiserslautern, Germany, November 2018.
Groups & Their Applications: 14th ‘Triangle’ Meeting, University of Bristol, UK, February 2018.
Algebra Seminar, Lincoln University, UK, February 2018.
Representation Theory of Symmetric Groups and Related Algebras, Institute for Mathematical Sciences, National University of Singapore, December 2017.
and some of my contributed talks:
Representations in Lie Theory and Interactions, CIRM, France, November 2018.
Group Theory in Florence II, Università degli Studi di Firenze, Italy, September 2018.
Young Algebraists’ Conference, EPFL, Switzerland, June 2017.
Teaching
Teaching
Year 2/3 module: LI/LH Algebra & Combinatorics 2 (Algebra half), 20 lectures.
Year 3 module: Research Skills in Mathematics, project supervisor.
Year 4 module: Advanced Topics in Algebra, 10 lectures.
Year 4 module: Project in Mathematics, project supervisor.
University of Cambridge:
Part III course: Representation Theory of Symmetric Groups, 24 lectures (2021–23). Lecture notes taken by Leonard Tomczak in Lent 2023.
Undergraduate supervisions: IA Group Theory, IA Probability, IA Analysis I, IB Groups, Rings & Modules, II Graph Theory and II Representation Theory (2015–23).
Part III examples classes for Representation Theory (2017), Modular Representation Theory (2018).
Part III catch-up workshop on Rings & Modules (2016).
More
More
I previously organised:
Representation Theory in Birmingham, a 1-day workshop at the University of Birmingham on 19 May 2025, supported by Birmingham's School of Mathematics and a London Mathematical Society Scheme 9 Celebrating New Appointments Grant; and
Symmetric groups & Lie-theoretic friends, a 2-day workshop held at the University of Birmingham, 14-15 May 2024, on the representation theory of finite groups, in particular the symmetric groups, and their connections to Lie theory and wider topics.
Since October 2023, I have been running the University of Birmingham School of Mathematics' undergraduate summer research programme. Since January 2024, I have been co-organising the Algebra Seminar at Birmingham with David Hume.
I completed my undergraduate and graduate studies at Trinity College, Cambridge, where I was also an admissions interviewer and an undergraduate supervisor for mathematics.
In 2018-9, I co-organised the Junior Algebra Seminar at Cambridge with Richard Freeland, and was a co-organiser of the Postgraduate Group Theory Conference in 2017.
Contact Information
School of MathematicsWatson BuildingUniversity of BirminghamEdgbastonBirminghamB15 2TTUK
Email: s DOT law AT bham DOT ac DOT uk
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