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

Number Theory / Representation Theory Seminar

Teaching

• MAT 1110 (Linear Algebraic Groups)
  Homework 1 (due Feb 25): Springer 2.1.5(3,5), 2.2.2(4), 2.3.4(2,3), 2.4.10(3), 3.2.10(2,3,4,5)
  Homework 2 (due Apr 5): Springer 4.4.11(1,3,4), 4.4.15(6), 5.3.5(2), 5.5.9(1,3), 5.5.11(2), additional problems
      (for 4.4.11(4) try to generalise to all diagonalisable groups)
  Homework 3 (due Apr 30): Springer 6.2.11(4), 6.3.7(2,3,4,5), 6.4.15(1,2,4), 7.2.5(3), 7.4.7(2,3,4)
      please do at least three of these problems

Research

• Ordinary representations of G(Q_p) and fundamental algebraic representations (with Christophe Breuil), 78 pages

• Weight cycling and Serre-type conjectures for unitary groups (with Matthew Emerton and Toby Gee), 66 pages.
  Duke Mathematical Journal, to appear.

• 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 GSp₄ (with Jacques Tilouine), 36 pages.
  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.)

• The weight in a Serre-type conjecture for tame n-dimensional Galois representations. Ph.D. thesis, 2006. With some typos corrected.
  (More emphasis on GL₃ and GL₄ compared to the paper of the same title above.)

Other Notes

• 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)

Fields Thematic Program on Galois Representations (January-June 2012)

Northwestern Number Theory Seminar (2008-2010)