Michael Magee
email: michael(dot)r(dot)magee(AT)durham(dot)ac(dot)uk

About me
I'm currently an Assistant Professor at Durham University.
I obtained my Ph.D. in 2014 under the supervision of Alex Gamburd at U.C. Santa Cruz, and had postdoctoral positions at I.A.S. Princeton and Yale University.
I'm interested in problems in number theory, dynamics, and geometry.
I am from Northern Ireland.
9. Automorphism-invariant positive definite functions on free groups. (With Benoît Collins and Doron Puder)
Submitted arXiv
8. Explicit spectral gaps for random covers of Riemann surfaces. (With Frédéric Naud)
7. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n). (With Doron Puder)
Submitted arXiv
6. Surface words are determined by word measures on groups. (With Doron Puder)
Submitted arXiv
5. Kesten-McKay law for the Markoff surface mod p. (With Matthew de Courcy-Ireland)
Submitted arXiv
4. Counting saddle connections in a homology class modulo q. (With Rene Rühr)
Contains an appendix by Rodolfo Gutiérrez-Romo
Submitted arXiv
3. The cycle structure of a Markoff automorphism over finite fields. (With Alois Cerbu, Elijah Gunther and Luke Peilen)
Submitted arXiv
2. On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials.
Submitted arXiv
1. An asymptotic formula for integer points on Markoff-Hurwitz varieties. (With Alex Gamburd and Ryan Ronan)
Submitted arXiv
One hour talk. Talk
Journal Articles
5. Matrix group integrals, surfaces, and mapping class groups I: U(n) (With Doron Puder)
Inventiones mathematicae, 2019. arXiv Journal
Two 45 minute talks: Talk 1 (Background and basic results) Talk 2 (Overview of main results and issues involved)
4. Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes.
I.M.R.N., 2018. arXiv Journal
3. Uniform congruence counting for Schottky semigroups in SL_2(Z). (With Hee Oh and Dale Winter)
Appendix to above: Thermodynamic expansion to arbitrary moduli. (With Jean Bourgain and Alex Kontorovich)
Crelle's Journal, 2017. arXiv Journal
2. Arithmetic, zeros, and nodal domains on the sphere.
Communications in Mathematical Physics, 2015. arXiv Journal
1. Quantitative spectral gap for thin groups of hyperbolic isometries.
Journal of the European Mathematical Society, 2015. arXiv Journal
Work not intended for publication
(i) Word measures on unitary groups. (With Doron Puder).
No longer intended to be published arXiv
The results of this preprint have now been significantly improved in the paper 'Matrix group integrals, surfaces, and mapping class groups I: U(n)'. On the other hand, this paper contains useful extra background on the more recent results.
Past teaching
Complex Analysis. Durham, Epiphany 2018, 2019, Michaelmas 2018
Group expansion and number theory. Yale, Spring 2017.
Number Theory. Yale, Spring 2017.
Linear Algebra with Applications. Yale, Fall 2016.
Introduction to Functional Analysis. Yale, Spring 2016.
Spectral Geometry. Yale, Spring 2016.
Ordinary Differential Equations. Yale, Fall 2015.