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):
Homework 3 (due Apr 30):
Problems 7.3, 7.4, 7.5(c), 8.1, 8.2, 8.3, 8.12(e)
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).