Florian Herzig

Associate Professor University of Toronto, Department of Mathematics

  • Toronto ON

Professor Herzig specializes in number theory

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University of Toronto, Department of Mathematics

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Research

Research Interests

Number Theory
Galois Representations
Mod p and p-adic Langlands program
Serre's Conjecture
Automorphic Forms
p-adic Hodge Theory

Accomplishments

Ribenboim Prize

2014

Province of Ontario Early Researcher Award

2014 - 2019

$100,000

Alfred P. Sloan Research Fellowship

2012 - 2016

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Education

Harvard University

Ph.D.

Mathematics

2006

Cambridge University

Mathematics

Certificate of Advanced Study

2001

Cambridge University

B.A.

Mathematics

2000

Articles

General Serre weight conjectures

arXiv Preprint

2015

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 ...

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Potentially crystalline lifts of certain prescribed types

arXiv Preprint

2015

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.

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Ordinary representations of G(ℚp) and fundamental algebraic representations

Duke Mathematical Journal

2015

Let G be a split connected reductive algebraic group over ℚp such that both G and its dual group Gˆ have connected centers...

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