LGRT 1523

Professor Weston studies the interplay between L-functions and certain arithmetic objects known as Selmer groups. Selmer groups are generalizations of ideal class groups and the group of rational points on an elliptic curve which distill the information contained in p-adic representations of the absolute Galois group. He has used such relations to enlarge dramatically the number of cases in which one can precisely compute universal deformation rings as in the work of Wiles. Jointly with Robert Pollack of Boston University, he also studies the behavior of L-functions and Selmer groups of modular forms in certain p-adic analytic families. In many cases they are able to show that one can use values of the L-functions (which are relatively computable) to compute Selmer groups (which are a priori very difficult to compute).


Ph.D. Harvard University, 2000

S.M. Harvard University, 1997

S.B. Massachusetts Institute of Technology, 1996


Number Theory

Selected Publications

  • R. Pollack, T. Weston, On anticyclotomic μ-invariants of modular forms, Composito Mathematica 147 (2011), 1353-1381.
  • R. Pollack, T. Weston, Mazur-Tate elements of nonordinary modular forms, Duke Mathematical Journal 156 (2011), 349-385.
  • M. Emerton, R. Pollack, T. Weston, Variation of Iwasawa invariants in Hida families, Inventiones Mathematicae 163 (2006), 523-580.
  • T. Weston, Iwasawa invariants of Galois deformations, Manuscripta Mathematica 118 (2005), 161-180.
  • T. Weston, Unobstructed modular deformation problems, American Journal of Mathematics 126 (2004), 1237-1252.