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Clifton Cunningham
Mathematical Sciences 458
ccunning@ucalgary.ca
http://automorphic.ca/
Number Theory:
Langlands Programme
Topology and Algebraic Geometry:
Algebraic and Arithmetic Geometry
Graduate Supervision Opportunities
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 non-classical 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), Marie-Andrée 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.), Anne-Marie 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)
Erdös Number
My Erdös Number is 4: Clifton Cunningham - Anne-Marie Aubert - Roger Howe - László Lovász - Paul Erdös
Meetings and Visiting Positions
Harmonic Analysis and the Trace Formula, Mathematisches Forshungsinstitut Oberwolfach (MFO), Arthur packets and Adams-Barbash-Vogan packets for p-adic groups (joint presentation with Bin Xu, joint research with Andrew Fiori, James Mracek and Ahmed Moussaoui), 21-27 May 2017
Canadian Mathematical Society, Representation Theory Session and Computational Number Theory Session, June 2016
Explicit methods for modularity of K3 surfaces and higher-rank motives, Institute for Computational and Experimental Research in Mathematics (ICERM), 19-23 October 2015.
Representation Theory and Analysis on Lie Groups over Local Fields, University of Ottawa, 70--10 May, 2015.
Alberta Number Theory Days VII, Banff International Research Station (BIRS), 2--4 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), 1--4 June 2014.
Alberta Number Theory Days VI, Banff International Research Station (BIRS), 19--20 April 2014.
Pacific Rim International Mathematical Association (PRIMA), Shanghai, Second Congress, 24--28 June, 2013.
American Institute of Mathematics, Algorithms for lattices and algebraic automorphic forms, Palo Alto, 6--10 May, 2013.
Conférence en l'honneur de Gérard Laumon, Université Paris-Sud, 25--29 juin, 2012.
Poste Rouge au CNRS, Institut de Mathématiques de Jussieu, Paris, May--July 2012.
Geometrization of Admissible Characters (5-Day Resarch in Groups), Banff International Research Station (BIRS), 5--11 May, 2012.
Sage Days 36, p-adic Computation, University of California, San Diego, 19--23 February 2011
Tata Institute for Fundamental Research (TIFR), India, International Colloquium on Automorphic Forms, 3--11 January 2012.
Mathematisches Forschungsinstitut Oberwolfach (MFO), Germany, 2-week Research in Pairs, 3--17 July 2011.
Banff International Research Station (BIRS), Canada, 5-Day Workshop on L-packets, 26 June -- 1 July, 2011.
Calgary Site Director, Pacific Instititue for the Mathematical Sciences, 2008-2015
Not currently teaching any courses.
Cunningham, Clifton and Nevins, Monica. Ottawa Lectures on Admissible Representations of p-adic Groups Fields Institute Monograph Series, 2009. 207 pages. Print.
Books and Monographs - Peer Reviewed
Cunningham, Clifton, Moussaoui, Ahmed, Mracek, James, Fiori, Andrew and Xu, Bin. Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples Memoirs of the American Mathematical Society, 2021. Print.
Aubert, A. and Cunningham, Clifton. An introduction to sheaves on adic spaces for {$p$}-adic group representation theory 46. 2002.
Cunningham, Clifton. Characters of depth-zero supercuspidal representations 1999.
Journal Articles - Peer Reviewed
Cunningham, Clifton and Roe, David. "From the function-sheaf dictionary to quasicharacters of p-adic tori". Journal of the Institute of Mathematics of Jussieu 17.1 (2018): 1--37. Print.
Cunningham, Clifton and Achter, Jeffrey. "A note on L-packets and abelian varieties over local fields". Pacific Journal of Mathematics 273.2 (2015): 395--412. Print.
Cunningham, Clifton and Kamgarpour, Masoud. "Geometrization of continuous characters of $\mathbb{Z}_p^\times$". Pacific Journal of Mathematics 261.1 (2013): 95-99. Print.
Cunningham, Clifton, Gordon, Julia and Spice, Loren. "On the computability of some positive-depth characters near the identity". Representation Theory 15. (2011): 531--567. Print.
Cunningham, Clifton and Achar, Pramod. "Toward a Mackey formula for compact restriction of character sheaves". Contemporary Mathematics 543. (2010): 1--18. Print.
Cunningham, Clifton and Dembélé, Lassina. "Computation of genus 2 Hilbert-Siegel modular forms over Q(sqrt{5}) via the Jacquet-Langlands Correspondence". Experimental Mathematics 18.3 (2009): 337--345. Print.
Cunningham, Clifton and Gordon, Julia. "Motivic proof of a character formula for SL(2)". Experimental Mathematics 18.1 (2009): 11--44. Print.
Cunningham, Clifton. "Report from the Ambassador to Cida-2". College Mathematics Journal 39.5 (2008): 337--345. Print.
Cunningham, Clifton and Hales, Thomas. "Good Orbital Integrals". Representation Theory 8. (2004): 414--457. Print.
Cunningham, Clifton and Achter, Jeffrey. "Isogeny classes of Hilbert-Blumenthal abelian varieties over finite fields". Journal of Number Theory 92.2 (2002): 272--303. Print.
Cunningham, Clifton. "Characters of depth-zero, supercuspidal representations of the rank-2 symplectic group". Canadian Journal of Mathematics 52.2 (2000): 306--331. Print.
Cunningham, Clifton. From perverse sheaves to Shalika germs: the characters of depth-zero supercuspidal representations of Sp(4) 1997.
Cunningham, Clifton and Roe, David. "Commutative character sheaves and geometric types for supercuspidal representations". Arxiv, (2017). Print.
Cunningham, Clifton and Dembélé, Lassina. "Lifts of Hilbert modular forms and application to a Conjecture of Gross". Arxiv, (2017). Print.
Technical Papers / Research Reports
Cunningham, Clifton, Achar, Pramod, Kamgarpour, Massoud, Roe, David and Salmasian, Hadi. Geometrization of Smooth Characters (Banff International Research Station, Research in Pairs) 2011.
Cunningham, Clifton and Achar, Pramod. Geometrization of Smooth Characters (Mathematisches Forschungsinstitut Oberwolfach) 2011.
Cunningham, Clifton, Moeglin, Colette and Vinayak, Vatsal. L-packets (Banff International Research Station, 5-day workshop) 2011.
clifton-cunningham-cv.pdf
University of Toronto, 1997