Stacey Law
Research & about me
Currently, I am an Assistant Professor in Algebra in the School of Mathematics at the University of Birmingham.
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.
* * *
I am organising Symmetric groups & Lie-theoretic friends, a 2-day workshop which will be 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. Please visit the workshop website to register and find out more!
Papers
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
Here are some of my invited talks and activities:
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.
Workshop: Counting conjectures and beyond, 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.
Mathematics Virtual Seminar, Royal Holloway University of London, UK, October 2020.
Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany, February 2020.
Algebra and Number Theory Seminar, Queen Mary University of London, UK, October 2019.
ALGB Seminar, Vrije Universiteit Brussel, Belgium, May 2019.
Algebra Seminar, University of Aberdeen, UK, April 2019.
Seminars in Groups and Representations, TU Kaiserslautern, Germany, November 2018.
Pure Seminar Series, Newcastle University, UK, October 2018.
Department of Mathematics & Statistics Colloquium, Maynooth University, Ireland, April 2018.
Pure Mathematics Research Seminar, University of East Anglia, UK, April 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
Year 2/3 module: Algebra & Combinatorics 2 (Algebra half), 20 lectures (2024–).
Year 3 module: Research Skills in Mathematics, project supervisor.
Year 4 module: Project in Mathematics, project supervisor.
University of Cambridge:
Part III course: Representation Theory of Symmetric Groups, 24 lectures (2021–23).
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
I completed my undergraduate and graduate studies at Trinity College, 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.
My Erdős number is 4 (Giannelli - Olsson - Balog or Long - Narayanan - Bollobás).
Contact Information
School of MathematicsWatson BuildingUniversity of BirminghamEdgbastonBirminghamB15 2TTUK
Email: s DOT law AT bham DOT ac DOT uk