Associate Professor | University of Toronto, Department of Mathematics
Toronto, ON, CA
Professor Herzig specializes in number theory
Industry Applications (2)
Research Interests (6)
Ribenboim Prize (professional)
Province of Ontario Early Researcher Award (professional)
2014 - 2019
Alfred P. Sloan Research Fellowship (professional)
2012 - 2016
Connaught New Researcher Award (professional)
2012 - 2014
NSERC Discovery Grant (professional)
2012 - 2017
Harvard University: Ph.D., Mathematics 2006
Cambridge University: Mathematics, Certificate of Advanced Study 2001
Cambridge University: B.A., Mathematics 2000
We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL (n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Q_p, and we also generalise the second author's previous conjecture for GL (n)/Q to this setting, and show that the two ...
We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representation of the absolute Galois group of K, where K/Q_p is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, making use of automorphy lifting theorems.
Duke Mathematical Journal
Let G be a split connected reductive algebraic group over ℚp such that both G and its dual group Gˆ have connected centers...
Algebra and Number Theory
The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor–Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown by Guralnick, Herzig, Taylor, and Thorne that if the dimension is small compared to the characteristic, then all absolutely irreducible representations are adequate. Here we ...
Modular Representation Theory of Finite and p-Adic Groups
These notes are an introduction to the p-modular (or "mod-p") representation theory of p-adic reductive groups. We will focus on the group Gl2(Qp), but we try to provide statements that generalize to an arbitrary p-adic reductive group G (for example, GLn(Qp))...