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 geometry, dynamics, and number theory.
I am from Northern Ireland.
Preprints
5. Explicit spectral gaps for random covers of Riemann surfaces. (With Frédéric Naud)
Submitted
4. Automorphism-invariant positive definite functions on free groups. (With Benoît Collins and Doron Puder)
Submitted
3. Matrix group integrals, surfaces, and mapping class groups II: O(n) and Sp(n). (With Doron Puder)
Submitted
2. Surface words are determined by word measures on groups. (With Doron Puder)
Submitted
1. Kesten-McKay law for the Markoff surface mod p. (With Matthew de Courcy-Ireland)
Submitted
Journal Articles
9. On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials.
Compositio Mathematica, 2019.
8. The cycle structure of a Markoff automorphism over finite fields. (With Alois Cerbu, Elijah Gunther and Luke Peilen)
Journal of Number Theory, 2019.
7. An asymptotic formula for integer points on Markoff-Hurwitz varieties. (With Alex Gamburd and Ryan Ronan)
Annals of Mathematics, 2019. One hour talk
6. Counting saddle connections in a homology class modulo q. (With Rene Rühr)
Journal of Modern Dynamics, 2019. Contains an appendix by Rodolfo Gutiérrez-Romo
5. Matrix group integrals, surfaces, and mapping class groups I: U(n) (With Doron Puder)
Inventiones mathematicae, 2019. Two 45 minute talks: [Background] [Main results]
4. Counting one sided simple closed geodesics on Fuchsian thrice punctured projective planes.
I.M.R.N., 2018.
3. Uniform congruence counting for Schottky semigroups in SL_2(Z). (With Hee Oh and Dale Winter)
Crelle's Journal, 2017. Contains an appendix written with Jean Bourgain and Alex Kontorovich
2. Arithmetic, zeros, and nodal domains on the sphere.
Communications in Mathematical Physics, 2015.
1. Quantitative spectral gap for thin groups of hyperbolic isometries.
Journal of the European Mathematical Society, 2015.
Work not intended for publication
(i) Word measures on unitary groups. (With Doron Puder).
No longer intended to be published.
The results of this preprint are superseded by the paper 'Matrix group integrals, surfaces, and mapping class groups I: U(n)'.
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.