Florian Herzig
Department of Mathematics
University of Toronto
40 St. George Street, #6290
Toronto, ON M5S 2E4
Office: Bahen Centre 6244
E-mail: my last name at math dot toronto dot edu
Curriculum vitae
Fall 2024
Research
Preprints
Publications
PDF files may differ slightly from published versions.
Conjectures and results on modular representations of GLn (K ) for a p -adic field K (with Christophe Breuil , Yongquan Hu , Stefano Morra , and Benjamin Schraen ), 193 pages.
Talk notes: Essen Spring School 2021 .
Memoirs of the American Mathematical Society, to appear.
On the irreducibility of p-adic Banach principal series of p-adic GL3 (with Noriyuki Abe ).
Vietnam Journal of Mathematics 52 (2024), no. 2, 451-478 (special issue dedicated to Pham Huu Tiep's 60th birthday).
Gelfand-Kirillov
dimension and mod p cohomology for GL2 (with Christophe Breuil , Yongquan Hu , Stefano Morra , and Benjamin Schraen ); Talk notes: Essen Spring School 2021 .
Inventiones Mathematicae 234 (2023), no. 1, 1-128.
Inverse Satake isomorphism and change of weight (with
Noriyuki Abe and Marie-France Vignéras ).
Representation Theory 26 (2022), 264-324.
On the existence of admissible supersingular representations of p-adic reductive groups (with Karol Koziol and Marie-France Vignéras and an appendix by Sug Woo Shin ).
Forum of Mathematics Sigma 8 (2020), e2, 73 pp.
Towards the finite slope part for GLn
(with Christophe Breuil ).
International Mathematics Research Notices 2020, no. 24, 10495-10552.
General Serre weight conjectures (with Toby Gee and
David Savitt ).
Journal of the European Mathematical Society 20 (2018), no. 12, 2859-2949.
On mod p local-global compatibility for GL3 in the ordinary case (with Daniel Le and Stefano Morra ).
Compositio Mathematica 153 (2017), no. 11, 2215-2286.
Potentially crystalline lifts of certain prescribed types (with Toby Gee , Tong Liu , and David Savitt ).
Documenta Mathematica 22 (2017), 397-422.
A classification of irreducible admissible mod p representations of p-adic reductive groups (with
Noriyuki Abe , Guy Henniart, and Marie-France Vignéras ).
Journal of the American Mathematical Society 30 (2017), no. 2, 495-559.
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 19 (2017), no. 4, 1231-1291.
Ordinary representations of G (Q p ) and fundamental algebraic representations (with
Christophe Breuil ).
Duke Mathematical Journal 164 (2015), no. 7, 1271-1352.
Weight cycling and Serre-type conjectures for unitary groups (with Matthew Emerton and Toby Gee ).
Duke Mathematical Journal 162 (2013), no. 9, 1649-1722. (Erratum. )
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 GLn .
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 ).
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
Questions on mod p representations of reductive p -adic groups (with Noriyuki Abe , Guy Henniart, and Marie-France Vignéras ).
Compiled for the workshop Geometric methods in the mod p local Langlands correspondence held in June 2016 at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa.
Linear algebraic groups
Notes for my graduate course, Spring 2013 (typed by Joshua Seaton). Updated Spring 2017.
p -modular representations of p -adic groups
Notes for my minicourse at IMS Singapore, April 2013 (typed by Karol Koziol). These notes focus on GL2 (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 GLn (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 GLn (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).