Nicolas Templier

Professor

509 Malott Hall
npt27@cornell.edu
607/2553443

Education

Ph.D. (2008) Montpellier University

Departments and programs

Mathematics

Affiliated Colleges

College of Arts and Sciences

Academic interests

Algebra
Analysis
Geometry

Research Focus

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 have been working on the arithmetic statistics of families, the Katz-Sarnak heuristics, arithmetic quantum chaos, and families of central L-values.

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 proved the mirror symmetry conjecture for minuscule flag varieties.

Affiliations

Member of the AMS. Member of IEEE.

Publications

A. Shankar, A. Södergren, and N. T., Central values of zeta functions of non-Galois cubic fields, Invent. Math., (2025).
T. Lam and N. T., The mirror conjecture for minuscule flag varieties, Duke Math. J., 173 no.1 (2024), 75-175.
W. Sawin and N. T., On the Ramanujan conjecture for automorphic forms over function fields I. Geometry, Journal of the AMS, 34 no.3 (2021), 653—746.
J. Matz and N. T., Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n), Algebra & Number Theory, 15 no.6 (2021), 1343-1428.
J.L. Kim, S.W. Shin, and N. T., Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families, Adv. Math., 362 (2020), 106955.
F. Brumley and N. T., Large values of cusp forms on GL(n), Selecta Math., 26 no.4 (2020), Article number: 63.
N. T., Voronoi summation for GL(2), Representation Theory, Automorphic Forms & Complex Geometry, A Tribute to Wilfried Schmid, International Press (2020), 163-196.
P. Sarnak, S.W. Shin, and N. T., Families of L-functions and their symmetry, proceedings of Simons symposium on the trace formula, Springer-Verlag (2016).
S.W. Shin and N. T., Sato-Tate theorem for families and low-lying zeros of automorphic L-functions, Invent. Math., 203 no.1 (2016), 1-177.
N. T., Hybrid sup-norm bounds for Hecke-Maass cusp forms, J. Eur. Math. Soc. 17 no.8 (2015), 2069--2082.
S.W. Shin and N. T., On fields of rationality for automorphic representations, Compos. Math., 150 no.12 (2014), 2003-2053.
N. T., Large values of modular forms, Cambridge Journal of Mathematics, 2 no.1 (2014), 91–116.
R. Holowinsky and N. T., First moment of Rankin-Selberg central L-values and subconvexity in the level aspect, The Ramanujan J., 33 no.1 (2014), 131-155.
G. Harcos and N. T., On the sup-norm of Maass cusp forms of large level. III, Math. Ann., 356 no.1 (2013), 209-216.
J. Tsimerman and N. T., Non-split Sums of Coefficients of GL(2)-Automorphic Forms, Israel. J. of Math., 195 no.2 (2013), 677-723.
A. Ichino and N. T., On the Voronoi formula for GL(n), Amer. J. of Math., 135 no.1 (2013), 65-101.
N. T., A non-split sum of coefficients of modular forms, Duke Math. J., 157 no.1 (2011), 109–165.
N. T., Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert, Compos. Math., 147 no.4 (2011), 1059-1084.