Personal Home Page of Owen Barrett

I recently received my Bachelor of Science and Master of Science in mathematics from Yale University. Beginning in the fall, I will begin to pursue a Ph.D. in mathematics at the University of Chicago. You can email me at owen.barrett@yale.edu. Here's a pdf of my CV.

My research is motivated by a desire to understand how arithmetic flows between different areas. Questions that interest me pertain to the spectrum of the Laplacian on arithmetic manifolds, the Arthur-Selberg trace formula, Weyl's law, quantum unique ergodicity, automorphic forms and L-functions on GL(n), modularity of Galois representations and other kinds of automorphy. My current projects are in the analytic theory of GL(2) L-functions.


2015 M.S./B.S. Mathematics, Yale University, New Haven, CT.


  1. (with B. McDonald, S.J. Miller, P. Ryan, C.L. Turnage-Butterbaugh, and K. Winsor) Gaps between zeros of GL(2) L-functions, J. Math. Anal. Appl. 429 (2015) 204–232. doi:10.1016/j.jmaa.2015.04.007
  2. An excised orthogonal model for families of cusp forms. In preparation.
  3. One-level density for families of cusp forms of prime power level. In preparation.

Expository writing

Here's an introduction to Kac-Moody algebras that I wrote. I tried to to emphasize the conceptual similarity between the basic construction and structure of Kac-Moody algebras and that of classical finite-dimensional Lie algebras.

I wrote the essay The Spectrum of the Laplacian on Γ\H & the Trace Formula to satisfy a graduation requirement at Yale. It is on the spectral theory of GL(2) automorphic forms, the Selberg trace formula, and includes discussions of the spectrum of the Laplacian on PSL(2, Z)\H, the Ramanujan conjecture, Weyl's law, quantum ergodicity, and Duke's theorem. Peng Zhao was my very generous supervisor.

Talks & Visits

Mar Lowest zeros of twisted GL(2) L-functions & arithmetic matrix ensembles.
Algebra and Number Theory Seminar, Yale University, New Haven, 26 March 2015.

Lowest zeros of GL(2) L-functions & arithmetic matrix ensembles.
29th Automorphic Forms Workshop, University of Michigan, Ann Arbor, 2 March 2015.
abstract  ·  slides

Large gaps between zeros of GL(2) L-functions (presented with K. Winsor).
29th Automorphic Forms Workshop, University of Michigan, Ann Arbor, 2 March 2015.
abstract  ·  slides
Sep Large gaps between zeros of GL(2) L-functions (presented with B. McDonald, P. Ryan).
Conférence de théorie des nombres Québec-Maine, Université Laval, Québec, 28 September 2014.
abstract  ·  slides
Aug Large gaps between zeros of GL(2) L-functions (presented with K. Winsor)
Young Mathematicians Conference, The Ohio State University, 22 August 2014.
abstract  ·  slides
July Large gaps between zeros of GL(2) L-functions (presented with P. Ryan and K. Winsor)
REU Mini-conference 2014, Yale University, 25 July 2014.
abstract  ·  slides  ·  photo
Dec Chern Institute visiting scholar.
Joined J.W. Hoffman during his visit to Nankai at the invitation of Lei Fu.
Dec 18–31, 2013. Chern Institute at Nankai University, Nankai, Tianjin, China.


In summer 2014, I was part of Steven J. Miller's PANTHers group, the probability and number group at the SMALL REU at Williams College. The projects above were started during the REU. Here's a group photo of all of us, taken by Cesar Silva.
In summer 2013, I worked under J.W. Hoffman at the LSU REU. Our project was in arithmetic algebraic geometry; we studied character sums using supercomputers. Our work was joint with J. Geiger, G. Muller, P. Thompson, and C. Winterer. Our final report is available here. Data for these experiments are available upon request.


Oct Number Theory class at Sprout at Yale.
Sprout at Yale is three-week enrichment program for kids in grades 7–12 held on Saturdays. I taught a core class that met each Saturday for 80 minutes with 25 students in grades 8–12. We proved the coincidence of irreducible and prime numbers, and the infinitude of primes. We discussed famous theorems and open problems in number theory, such as twin primes and bounded gaps between primes.


I own a lever espresso machine and enjoy making and drinking espresso with my friends. Here's a photo of a shot I pulled with Counter Culture Coffee's Equilibrium blend.