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University of Toronto

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- MAT 224 (Linear Algebra II)

*On mod p local-global compatibility for*GL_{3}*in the ordinary case*(with Daniel Le and Stefano Morra), 70 pages*General Serre weight conjectures*(with Toby Gee and David Savitt), 81 pages (new version: February 2016)*Potentially crystalline lifts of certain prescribed types*(with Toby Gee, Tong Liu, and David Savitt), 22 pages (new version: September 2015)

PDF files may differ slightly from published versions.

*A classification of irreducible admissible mod p representations of p-adic reductive groups*(with Noriyuki Abe, Guy Henniart, and Marie-France Vigneras), 63 pages.

Journal of the American Mathematical Society, accepted (pending revision).*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**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.*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.)

*The weight in a Serre-type conjecture for tame n-dimensional Galois representations.*Ph.D. thesis, 2006. With some typos corrected.

(More emphasis on GL_{3}and GL_{4}compared to the paper of the same title above.)

- 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(scanned)._{n}

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**) (scanned)._{p}

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).