Florian Herzig
Department of Mathematics
University of Toronto
40 St. George Street, #6290
Toronto, ON M5S 2E4
Office: Bahen Centre 6186
E-mail: my last name at math dot toronto dot edu
Curriculum vitae
MAT 1210 (Arithmetic of Elliptic Curves);
Main reference: Silverman's book
Homework 1 (due Feb 25):
Problems 1.10, 2.3, 2.4, 3.3(d) + show this is an elliptic curve + find a Weierstrass equation (hint: recall how we found Weierstrass coordinates for a general elliptic curves), 3.5, 3.8
Consider E: y^2 = x^3 - 43x + 166 over the rationals and P = (3,8). Show by hand that P has finite order. (Hint: it may be more
efficient to compute some 2^i P first.)
Homework 2 (due Mar 27):
Research
Preprints
Publications
PDF files may differ slightly from published versions.
Adequate groups of low degree (with
Robert Guralnick and Pham Huu Tiep ).
Algebra & Number Theory 9 (2015), no. 1, 77-147.
Adequate groups and indecomposable modules (with
Robert Guralnick and Pham Huu Tiep ).
Journal of the European Mathematical Society, to appear.
Ordinary representations of G (Q _{p} ) and fundamental algebraic representations (with
Christophe Breuil ).
Duke Mathematical Journal, to appear.
Weight cycling and Serre-type conjectures for unitary groups (with Matthew Emerton and Toby Gee ).
Duke Mathematical Journal 162 (2013), no. 9, 1649-1722.
Adequate subgroups
(with Robert Guralnick ,
Richard Taylor , and
Jack Thorne ).
Appendix to On the automorphy of l-adic Galois representations with small residual image by Jack Thorne.
Journal de l'Institut de Mathématiques de Jussieu 11 (2012), no. 4, 907-920.
The classification of irreducible admissible mod p representations of a p-adic GL_{n} .
Inventiones Mathematicae 186 (2011), no. 2, 373-434.
A Satake isomorphism in characteristic p.
Compositio Mathematica 147 (2011), no. 1, 263-283.
Conjecture de type de Serre et formes compagnons pour GSp_{4} (with Jacques Tilouine ).
Journal für die reine und angewandte Mathematik (Crelle) 676 (2013), 1-32.
The weight in a Serre-type conjecture for tame n-dimensional Galois representations.
Duke Mathematical Journal 149 (2009), no. 1, 37-116. (Typos. )
Thesis
Other Notes
Linear algebraic groups
Notes for my graduate course, Spring 2013 (typed by Joshua Seaton).
p -modular representations of p -adic groups
Notes for my minicourse at IMS Singapore, April 2013 (typed by Karol Koziol). These notes focus on GL_{2} (Q _{p} ).
Appeared in IMS Lecture Notes Series, vol. 30 (2015) .
The mod p representation theory of p -adic groups Notes for my graduate course at Fields Institute, spring 2012 (typed by Christian Johansson).
Classification of irreducible mod p representations of a p-adic GL_{n} (scanned).
Notes for mini-course at the Galois Trimester , Paris (Jan 4-Mar 27, 2010).
Serre-type conjecture for tame n-dimensional mod p Galois representations (scanned).
Serre-type conjectures, mod p cohomology, and representation theory of GL_{n} (Q _{p} ) (scanned).
Notes for half of a mini-course with Matthew Emerton at the summer school
Représentations p -adiques des groupes p -adiques , Paris (July 7-12, 2008).
Smooth representations of p-adic reductive groups.
Notes for the Instructional Conference on Representation Theory and Arithmetic , Northwestern (May 5-9, 2008).