Goldsmith Building, 525
DegreesUniversity of Paris XI, Ph.D.
University of Paris XI, Ed.M.
Ecole Normale Superieure, M.A.
Ecole Normale Superieure, B.A.
ExpertiseNumber Theory, Algebra, Algebraic Geometry
ProfileMy 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).
|MATH||22b||Linear Algebra and Intermediate Calculus, Part II|
|MATH||30b||Introduction to Algebra, Part II|
|MATH||201a||Topics in Algebra|
|MATH||202b||Algebraic Geometry II|
Awards and Honors
American Mathematical Society Centennial Fellowship (2010 - 2011)
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.