Research
"Discovery is the priviledge of the child." (Grothndieck)
Research Interests
Geometric representation theory, more specifically, the geometric Langlands program and arithmetic of character varieties
I do my best not to publish in journals run by the big five publishing houses. To see why, read this, and if you are academic, consider avoiding these companies.
ArXiv Preprints
21. Counting points on character varieties (joint with Gyeonghyeon Nam, Bailey Whitbread, and Stefano Giannini, submitted)
20. Connections whose differential Galois group is reductive of maximal rank (joint with Dan Sage, undergoing revision)
Published Papers
I try to publish in journals which are open access, cheap, and associated with societies. You can see how successful I have been!
19. Arithmetic geometry of character varieties with regular monodromy, I (with G. Nam and Anna Puskas, Representation Theory 2025).
18. Character stacks are PORC count (with Nick Bridger, Journal of the Australian Mathematical Society, 2023)
17. Hypergeometric sheaves for classical groups via geometric Langlands (with Daxin Xu and Lingfei Yi, Transactions of the American Mathematical Society, 2023)
16. Airy sheaf for reductive groups (with Konstantin Jakob and Lingfei Yi, Proceedings of London Mathematical Society, 2022) - video
15. Geometric Langlands for Hypergeometric Sheaves (with Lingfei Yi, Transactions of the American Mathematical Society, 2021)
14. Rigid connections on the projective line via the Bruhat--Tits building (with Dan Sage, Proceedings of the London Mathematical Society, 2020)
13. On a geometric analog of a conjecture of Gross and Reeder (with Dan Sage, American Journal of Maths, 2019)
12. On the image of the parabolic Hitchin map (with David Baraglia, Quarterly Journal of Math, 2017)
11. Complete integrability of the parabolic Hitchin map (with David Baraglia and Rohith Varma, International Mathematical Research Notices, 2017)
10. Jordan decomposition for formal G-connections (with Samuel Weatherhog, Graduate Journal of Maths 2017)
9. Conductors in local geometric Langlands correspondence (Canadian Journal of Mathematics, Vol 69, no. 1, 2017, 107--126)
8. Preservation of depths in local geometric Langlands program (with Tsao-Hsien Chen, Transactions of the American Mathematical Society (2017), 1345--1364)
7. Compatibility of the Feigin-Frenkel Isomorphism and the Harish-Chandra Isomorphism for Jet algebras (Transactions of the American Mathematical Society (2016), 2019--2038)
6. Ramified Satake Isomorphisms for strongly parabolic characters (with Travis Schedler, 2014, Documenta Mathematica)
5. Geometrization of principal series representation of reductive groups (with Travis Schedler, 2013, Annals of Institute Fourier)
4. Geometrization of continuous characters of Z_p^* (with Clifton Cunningham, Pacific Journal of Mathematics, 2013)
3. Compatible intertwiners for representations of nilpotent groups (with Teru Thomas, Representation Theory, 2011)
2. Maximal representation dimension for finite p-groups (with Zinovy Reichstein and Shane Cernele, Journal of Group Theory, 2011)
1.Stacky abelianization of algebraic groups (PhD Thesis, Transformation Groups, 2009)
Incomplete Preprints- Not intended for publication
4. Langlands correspondence for a hypergeometric connection on the projective line (superseded by the paper with Lingfei Yi on hypergeometrics)
3. Stabilisers of eigenvectors of finite reflection groups (Results were generalised by in MPhil thesis of Sinead Wilson)
2. Universal property of K-theory and Homology (joint with Justin Noel) - See this paper where they give a definitive account of the universal property of K-theory.
1. Weil representation over finite field (Master's Thesis 2005)
Non-research notes published in the Gazette of the Australian Mathematical Society
4. Show me the money: what does your annual meeting registration fee cover? (2024)
3. Can we communicate mathematics better? (2023)
2. Interviews with Winners of AustMs Maryam Mirzakhani Award:
1. Meeting the Australian Parliament: a mathematician's experience (2019)