Will Osborne

About

• DPhil (PhD) Student, Mathematical Institute, Oxford

• Contact: will [dot] osborne [at] maths [dot] ox [dot] ac [dot] uk 

• Will Osborne | Mathematical Institute

Interests

• Representation theory

• Algebraic combinatorics

• Unitary representations of p-adic groups

• Graded affine Hecke algebras

Research

• Spin Representations of Finite Coxeter Groups and Generalisations of Saxl’s Conjecture (arxiv:2409.17540)

  • Yutong Chen, Felix Gu, and Will Osborne (Sept 2024)

  • Undergraduate project supervised by Prof. Dan Ciubotaru

  • Abstract: We present a natural generalisation of Saxl’s conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to certain tensor product decomposition problems in symmetric groups. We provide an alternative uniform description of the cuspidal family through spin representations, offering an equivalent conjecture formulation. Additionally, we generalise Saxl’s conjecture to finite Coxeter groups and prove it for the non-crystallographic cases. 

Awards

• Martingale Scholarship for Part C and DPhil Mathematics at Oxford

Talks

• (04/26) On Schur expansions of Schur P-functions, 7th Graduate Student Meeting in Algebraic Combinatorics, University of Bristol

• (10/24) Spin Representations for Coxeter Groups and Generalisations of Saxl's Conjecture,  Algebra Seminar, University of Oxford 

Attended Conferences

• (04/26) 7th Graduate Student Meeting in Algebraic Combinatorics 2026, University of Bristol

• (03/26) New developments in p-adic Representation Theory, University of Essen

• (07/25) Ring-Theoretic Aspects of Lie Theory, University of Edinburgh

• (09/24) ARTIN 62, Newcastle University

• (09/24) Groups and Representations, after Roger Carter, University of Warwick

• (09/24) Representations of p-adic Groups and the Langlands Correspondence, after Colin Bushnell, King's College London