Joel Bellaiche

Professor of Mathematics

Departments/Programs

Mathematics

Degrees

University of Paris XI, Ph.D.
University of Paris XI, Ed.M.
Ecole Normale Superieure, M.A.
Ecole Normale Superieure, B.A.

Expertise

Number Theory, Algebra, Algebraic Geometry

Profile

My main research interest lies in number theory, both algebraic and, more recently, analytic. I am also interested in the closely related fields of group theory, representation theory, and algebraic geometry.
A large part of my work has involved the topic of Galois representations, which provides a unifying language to study many classical and new questions in number theory. Since Galois representations are often difficult to construct, and even more, to study, I develop and use tools belonging to the so-called Langlands program, a large field of current research aiming at understanding deep relations between Galois representations and some more analytic objects called automorphic representations (of which on of the most famous avatar are the modular forms).

Courses Taught

MATH	131a	Algebra I
MATH	141b	Complex Analysis
MATH	200a	Second-Year Seminar
MATH	201a	Topics in Algebra
MATH	202a	Algebraic Geometry I
MATH	203a	Number Theory
MATH	203b	Topics in Number Theory
MATH	250a	Complex Algebraic Geometry I

Awards and Honors

American Mathematical Society Centennial Fellowship (2010 - 2011)

Scholarship

Bellaiche, Joel. The Eigenbook. Eigenvarieties, p-adic families of Galois representations, p-adic L-functions. first ed. Springer-Birkhauser, 2021. (forthcoming)

Bellaiche, Joel. "Image of pseudo-representations and coefficients of modular forms modulo p." Advances in Math. 353. 1 (2020): 647-721.

Bellaïche, Joël; Green, Ben; Soundararajan, Kannan. "Nonzero coefficients of half-integral weight modular forms mod ℓ.." Res. Math. Sci. 5 (2018), n no 1. Paper No. 6, 10 pp. 11F37 (special issue in honor of Don Zagier) (2018): 10pp.

Bellaiche, Joel and Nicolas, Jean-Louis. "Parité des coefficients de formes modulaires." Ramanujan Journal 40 (2016). 1 (2017): 1-44.

Bellaiche, Joel. "A Remark on the Error Term in Chebotarev's Density Theorem." Math. Research Letters 23 (2017). 1 (2017): 10 pages.

Bellaiche, Joel & Dasgupta, Samit. "the p-adic L function of critical Eisenstein series." Composite Mathematicae 151 (2015). 6 (2016): 999-1040.

Bellaiche, Joel & Dimitrov, Mladen. "On the eigencurve at classical weight 1 points.." Duke Mathematical Journal 165. 2 (2016): 245-266.

Bellaiche, Joel. "Théorème de Chebotarev et complexité de Littlewood.." Annales Scientifiques de L'École Normale Supérieure 49 (2016). 3 (2016): 579--632.

Bellaiche, Joel & Soundararajan, Kannan. "The number of nonzero coefficients of modular forms (mod p)." Algebra and Number Theory 9. 8 (2015): 1825-1856.

Bellaiche, Joel. "Unitary Eigenvarieties at Isobaric Points.." Canad. J. Math. 67. 2 (2015): 315-32

Bellaiche, Joel; Khare, Chandrashekhar. "Level 1 Hecke algebras of modular forms modulo p." Compositio Mathematicae 151. 3 (2015): 397-415.

Bellaiche, Joel and Chenevier, Gaetan. "Sous-groupes de Gl(2) et arbres." Journal of Algebra Reference: YJABR14652. 1 (2014): 10.1016/j.jalgebra.2014.02.005.

Bellaiche, Joel. "Critical p-adic L-function." Inventiones Math 189. 1 (2012): 1-60.

Bellaiche, Joel. "Pseudodeformations." Mathematsche Zeitchrift 270. 3-4 (2012): 1163-1180.

Bellaiche, Joel. "Ranks of Selmer groups in an analytic family." Trans. Amer. Math. Soc. 364. 9 (2012): 4735–4761.

Bellaiche, Joel. "Une représentation galoisienne universelle attachée aux formes modulaires modulo 2." Comptes-rendus de l'academie des sciences 2012. 9-10 (2012): 443-449.

Bellaiche, Joel and Chenevier Gaëtan. "The sign of Galois representations attached to automorphic forms for unitary groups." Compositio Mathematicae 147. 5 (2011): 1337-1352.

Bellaiche, Joel. "New examples of p-adically rigid automorphic forms." Mathematical Research Letters 17 (2010). 4 (2010): 781–792.

Bellaiche, Joel. "On the path-dependence of economic growth." Journal of Mathematical Economics 46. (2010): 163-178.