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

- MAT 1101 (Algebra II), Winter 2024

*On the irreducibility of p-adic Banach principal series of p-adic reductive groups*(with Noriyuki Abe), 85 pages.*Multivariable $(\varphi,\mathcal O_K^\times)$-modules and local-global compatibility*(with Christophe Breuil, Yongquan Hu, Stefano Morra, and Benjamin Schraen), 94 pages.

Talk notes: Banff 2023

PDF files may differ slightly from published versions.

*Conjectures and results on modular representations of*GL_{n}(*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*GL_{3}(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*GL_{2}(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*GL_{n}(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*GL_{3}*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*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.)

- 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 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).