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Nicolas Templier
Associate Professor
Departments/Programs
 Mathematics
Graduate Fields
 Mathematics
Research
Automorphic forms
A major theme in my work has been to show instances of randomness in number theory. A guiding principle is that when an answer to a given problem is difficult (e.g. finding prime numbers), it exhibits randomness according to some probabilistic law (e.g. prime numbers seem to distribute according to the Poisson process).
Families of automorphic representations are central to the resolution of certain algebraic and asymptotic questions. I am interested in the arithmetic statistics of families, the KatzSarnak heuristics, arithmetic quantum chaos and padic families of automorphic forms.
I have been also working on the asymptotic properties of special functions motivated by periods and central values. Symplectic geometry and integrable systems provide the relevant tools to investigate the Bessel, Airy and hypergeometric functions and their generalizations notably arising from branching laws of Lie groups representations. In this direction I recently proved the mirror symmetry conjecture for minuscule flag varieties.
Courses
Spring 2021
Publications

On the Ramanujan conjecture for automorphic forms over function fields I. Geometry. (with W. Sawin), Journal of the AMS.
 Families of Lfunctions and their symmetry (with P. Sarnak and S.W. Shin), proceedings of Simons symposium on the trace formula, SpringerVerlag (2016).
 SatoTate theorem for families and lowlying zeros of automorphic Lfunctions (with S.W. Shin), Invent. Math., 203 no.1 (2016), 1177.
 Hybrid supnorm bounds for HeckeMaass cusp forms, J. Eur. Math. Soc. 17 no.8 (2015), 20692082.
 Large values of modular forms, Cambridge Journal of Mathematics, 2 no.1 (2014), 91–116.
 A nonsplit sum of coefficients of modular forms, Duke Math. J., 157 no.1 (2011), 109–165.