I am currently recruiting graduate students, primarily, thought not exclusively, to work on projects related to automorphic representations and the Langlands Program.
Langlands Program
The Langlands Program is a research agenda that predicts deep connections between many areas of mathematics that might seem, on first glance, to be unrelated: number theory, representation theory, algebraic geometry and harmonic analysis to name a few. For this reason, the Langlands Program is sometimes described as the grand unified theory of mathematics. But in spite of its broad scope, the open problems in the Langlands Program are very specific and generally very precisely articulated. Although the Langlands Program is only fifty years old, amazing progress has already been made, especially in the last ten years, including a proof of the Fundamental Lemma and the local Langlands Correspondence for general linear, symplectic and special orthogonal groups, relying on the theory of endoscopy. Much work remains to be done, however, including a better understanding of the Langlands Correspondence for nonclassical groups and the principle of functoriality especially beyond endoscopy. Results from the Langlands Program have applications in number theory and physics.
My current research in the Langlands Program focuses on three projects: the Voganish Project; automorphic representations of GSpin attached to Abelian varieties; and geometrization of various parts of the Langlands Correspondence. Information about these projects and my small army of collaborators may be found at automorphic.ca.
I seek students with a solid background in algebra, an interest in algebraic geometry and representation theory, and an open mind. If this sounds like you, visit the Automorphic Representations Research Group and then write to me from this page at the Faculty of Graduate Studies.
Doctoral students: Geoff Vooys, Majid Shahabi (2018), Jason Nicholson (2015), Aaron Christie (2012)
Masters students: Adam Gerlings (2015), MarieAndrée Langlois (2014), Milad Sabeti (2012), Ryan Stratford (2008), Aaron Christie (2006), Tracy Walker (2005), Brendan Ossen (2003).
Undergraduate students: Nicole Kitt (2018), Samuel Reid (2013), Tristan Jugdev (2010), Adrian Keet (2010), Colin Grabowski (2006), Tom Kuwahara (2006), Paul Dickinson (2003), Patrick Walls (2003), Vladimir Papish (2002).
Quing Zhang, PIMS PDF, September 2018  July 2020
Bin Xu, PIMS PDF, September 2015  July 2017. Now at Tsingua University.
Ahmed Moussaoui, PIMS PDF, September 2015  July 2017. Now at the University of Versailles
Andrew Fiori, PIMS PDF with Michael Jacobson, September 2015  July 2017. Now at the University of Lethbridge.
David Roe, PIMS PDF with Matthew Greenberg, September 2011  July 2014. Now at MIT.
Masoud Kamgarpour, September 2010  July 2011. Now at University of Queensland.
Lassina Dembéle, PIMS PDF, September 2005  August 2007. Now at Dartmouth University.
Pramod Achar (Louisiana State University), Jeffrey Achter (Colorado State U.), AnneMarie Aubert (CNRS, Paris), Raf Cluckers (Leuven), Lassina Dembele (Warwick), Andrew Fiori (U. Lethbridge), Julia Gordon (U. British Columbia), Thomas Hales (U. Pitt.), Masoud Kamgarpour (U. Queensland), Ahmed Moussaoui (Verseilles), James Mracek (U. Toronto), Monica Nevins (U. Ottawa), David Roe (UPitt), Hadi Salmasian (U. Ottawa), Loren Spice (Texas Christian U.)., Bin Xu (Tsinghua)
Harmonic Analysis and the Trace Formula, Mathematisches Forshungsinstitut Oberwolfach (MFO), Arthur packets and AdamsBarbashVogan packets for padic groups (joint presentation with Bin Xu, joint research with Andrew Fiori, James Mracek and Ahmed Moussaoui), 2127 May 2017
Canadian Mathematical Society, Representation Theory Session and Computational Number Theory Session, June 2016
Explicit methods for modularity of K3 surfaces and higherrank motives, Institute for Computational and Experimental Research in Mathematics (ICERM), 1923 October 2015.
Representation Theory and Analysis on Lie Groups over Local Fields, University of Ottawa, 7010 May, 2015.
Alberta Number Theory Days VII, Banff International Research Station (BIRS), 24 June 2015.
Motivic Integration, Orbital integrals and Zeta functions, Banff International Research Station (BIRS), 30 November  5 December, 2014.
The Future of Trace Formulas, Banff International Research Station (BIRS), 14 June 2014.
Alberta Number Theory Days VI, Banff International Research Station (BIRS), 1920 April 2014.
Pacific Rim International Mathematical Association (PRIMA), Shanghai, Second Congress, 2428 June, 2013.
American Institute of Mathematics, Algorithms for lattices and algebraic automorphic forms, Palo Alto, 610 May, 2013.
Conférence en l'honneur de Gérard Laumon, Université ParisSud, 2529 juin, 2012.
Poste Rouge au CNRS, Institut de Mathématiques de Jussieu, Paris, MayJuly 2012.
Geometrization of Admissible Characters (5Day Resarch in Groups), Banff International Research Station (BIRS), 511 May, 2012.
Sage Days 36, padic Computation, University of California, San Diego, 1923 February 2011
Tata Institute for Fundamental Research (TIFR), India, International Colloquium on Automorphic Forms, 311 January 2012.
Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany, 2week Research in Pairs, 317 July 2011.
Banff International Research Station (BIRS), Canada, 5Day Workshop on Lpackets, 26 June  1 July, 2011.
Calgary Site Director, Pacific Instititue for the Mathematical Sciences, 20082015
W2021  MATH 627  Algebraic Geometry  
