Research

Algebra and Lie research groups | Network of Ontario Lie Theorists | Seminars | Algebra seminar | Lie seminar |

Upcoming Activity

Perspectives in representation theory |

Teaching

MAT 2742 | MAT 1302 | Sessional Dates |

Slides/Notes

Below are the slides for talks I have given in the past. Since I often give some version of the same talk several times with slightly different names, the title of the slides below may not precisely match the title of a talk to which they correspond.

• Classification of irreducible quasifinite modules over map Virasoro algebras (2011)
• The representation theory of equivariant map algebras (2011)
• La théorie des représentations des algèbres de fonctions équivariantes (2011)
• Hecke algebras and a categorification of the Heisenberg algebra (2010)
• Quiver grassmannians, quiver varieties and the preprojective algebra (2009)
• Lectures on geometric realizations of crystals (2009), Lecture notes from the University of Ottawa Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras.
• Irreducible finite-dimensional representations of equivariant map algebras (2009)
  
  
  • audio for talk given at the Southern Ontario Groups and Geometry Workshop
  • video for talk given at the International Workshop on Combinatorial and Geometric Approach to Representation Theory
• Moduli spaces of sheaves and the boson-fermion correspondence (2008)
• Quivers and the Euclidean algebra (2008)
• Crystals, quiver varieties and coboundary categories for Kac-Moody algebras (2008)
• Geometric representation theory - Slides for a "New Professor Lecture" given at the University of Ottawa, aimed at a general science audience (2007)
• Quiver varieties and geometric representation theory (2006)
• A geometric boson-fermion correspondence (2005)
• Quiver varieties and branching rules (2005)
• Quiver varieties and Demazure modules (2005)
• Cohomology of flag varieties (audio) - Notes and audio for an expository talk given at the Fields Institute Workshop on Schubert Varieties and Schubert Calculus, June 2005
• Geometric representation theory on flag varieties (audio) - Notes and audio for an expository talk given at the Fields Institute Workshop on Schubert Varieties and Schubert Calculus, June 2005

• A brief overview of quiver varieties and representation theory

Talks

Below is a complete list of talks I have given in the past. For a list of upcoming talks, see here.

• Classification of irreducible quasifinite modules over map Virasoro algebras, CMS Winter Meeting, Special session on representations of algebras, Toronto, December 10–12, 2011.
• Equivariant map algebras: irreducible representations and block decompositions, Geometric representation theory seminar, University of Toronto, Oct 28, 2011.
• A graphical categorification of the Heisenberg algebra, Keynote Lecture, Category theory Octoberfest '11, University of Ottawa, Oct 22, 2011.
• A gentle introduction to categorification, Basic notions seminar, University of Oregon, Oct 7, 2011.
• A gentle introduction to categorification, Colloquium, University of Western Ontario, Sep 16, 2011.
• An introduction to categorification and Hecke algebras and Heisenberg categorification, Séminaire d'algèbre et géométrie, Laboratoire de Mathématiques Nicolas Oresme, Caen, France
• Hecke algebras and a categorification of the Heisenberg algebra, Topological quantum field theory seminar, Departamento de Mathemática, Instituto Superior Técnico, Lisbon, Portugal, Jun 8, 2011.
• La théorie des représentations des algèbres de fonctions équivariantes, Séminaire d'algèbre, Institut Camille Jordan, Lyon, France, May 26, 2011.
• Representation theory of equivariant map algebras, International Conference on Infinite Dimensional Lie Theory and its Applications, IPM (Institute for Research in Applied Sciences), School of Mathematics, Tehran, Iran, May 16, 2011.
• Representation theory of equivariant map algebras, Workshop on the Interaction of Representation Theory with Geometry and Combinatorics (HIM Trimester Program on the Interaction of Representation Theory with Geometry and Combinatorics), Mar 28, 2011.
• La théorie des représentations des algèbres de fonctions équivariantes, Séminaire sur les Algèbres Enveloppantes et Théorie des Représentations, Institut de Mathématiques de Jussieu, Paris, France, Feb 25, 2011.
• Hecke algebras and Heisenberg categorification, Trimester seminar, Trimester Program on the Interaction of Representation Theory with Geometry and Combinatorics, Hausdorff Research Institute for Mathematics, Bonn, Germany, Jan 27, 2011.
• Hecke algebras and a categorification of the Heisenberg algebra, Taipei conference on representation theory, Institute of Mathematics, Academia Sinica, Taipei, Taiwan, Dec 20, 2010.
• Hecke algebras and a categorification of the Heisenberg algebra, Algebra Seminar, University of Ottawa, Nov 23, 2010.
• Hecke algebras and a categorification of the Heisenberg algebra, CUNY Representation Theory Seminar, CUNY Graduate Center, Nov 19, 2010.
• Hecke algebras and a categorification of the Heisenberg algebra, LaCIM Seminar, Université de Québec à Montréal, Nov 12, 2010.
• Equivariant map algebras: Extensions and block decompositions, Lie Seminar, University of Ottawa, Nov 4, 2010.
• Hecke algebras and a categorification of the Heisenberg algebra, Algebraic and Combinatorial Approaches to Representation Theory (ICM Satellite Conference), Indian Institute of Science, Bangalore, India, Aug 12, 2010.
• Quiver grassmannians, quiver varieties and the preprojective algebra, University of Melbourne, May 32, 2010.
• Categorification for the vacationing mathematician, Colloquium, University of New South Wales, May 18, 2010.
• Equivariant map algebras and their representation theory, Algebra Seminar, University of Sydney, May 12, 2010.
• Equivariant map algebras, Workshop on Lie Theory and its Applications (1st NOLT Workshop), Carleton University, Feb 27, 2010.
• Equivariant map algebras, Algebraic geometry seminar, Columbia University, Feb 19, 2010.
• Equivariant map algebras, Joint Mathematics Meetings, San Francisco, CA, Special Session on Representation Theory and Nonassociative Algebras, Jan 2010.
• Quiver grassmannians, quiver varieties and the preprojective algebra, CMS Winter Meeting, Windsor, ON, Special Session on Lie Algebras and Representation Theory, Dec 2009.
• Categorification for the vacationing mathematician, Colloquium, University of Ottawa, Nov 27, 2009.
• Quiver grassmannians, quiver varieties and the preprojective algebra, Algebra Seminar, University of Ottawa, Nov 18, 2009.
• Quiver grassmannians, quiver varieties and the preprojective algebra, AMS 2009 Fall Western Section Meeting, Riverside, CA, Special Session on Representation Theory, Nov 2009.
• Equivariant map algebras, Southern Ontario Groups and Geometry (SOGG) Workshop, Fields Institute, Toronto, Oct 2009.
• Equivariant map algebras, International workshop on combinatorial and geometric approach to representation theory, Seoul National University, Seoul, Korea, Sep 2009.
• Moduli spaces of sheaves and the boson-fermion correspondence, International Workshop on Quantized Algebra and Physics, Chern Institute of Mathematics, Nankai University, Tianjin, China, Jul 2009.
• Irreducible finite-dimensional representations of equivariant map algebras, International Workshop on Algebraic Groups, Quantum Groups, and Related Topics, Peking University, Beijing, China, July 2009.
• Moduli spaces of sheaves and the boson-fermion correspondence, Geometry seminar, Boston University, Boston, MA, Apr 22, 2009.
• Quiver grassmannians, AMS 2009 Spring Central Sectional Meeting, Urbana, IL, Special Session on Algebra, Geometry and Combinatorics, Mar 28, 2009.
• Moduli spaces of sheaves and the boson-fermion correspondence, Geometric representation theory seminar, University of Toronto, Mar 20, 2009.
• Bosons, fermions and geometry, Colloquium, Queen's University, Nov 21, 2008.
• Moduli spaces of sheaves and the boson-fermion correspondence, Algebra Seminar, University of Ottawa, Nov 4, 2008.
• Moduli spaces of sheaves and the boson-fermion correspondence, Special Session on Representation Theory, Global KMS International Conference, Jeju, Korea, Oct 23, 2008.
• Crystals, Quiver varieties and coboundary categories for Kac-Moody algebras, Mini-symposium on Representation Theory, Jeju, Korea, Oct 22, 2008.
• Moduli spaces of sheaves and the boson-fermion correspondence, New York Algebra Colloquium, CUNY Graduate Center, Oct 3, 2008.
• Quivers and the Euclidean group, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), Valparaiso-Viña del Mar, Chile, Jun 24, 2008.
• Crystals, Quiver Varieties and Coboundary Categories for Kac-Moody Algebras, Seminar, Universidad Nacional de Córdoba, Jun 20, 2008.
• Moduli spaces of sheaves and the boson-fermion correspondence, Workshop USP-UNICAMP on Representation Theory, Algebraic Geometry and Mathematical Physics, Universidade de São Paulo / UNICAMP, Jun 11, 2008.
• Quivers and the Euclidean group, AMS-SBM (Sociedade Brasileira de Matemática) First Joint Meeting, Special Session "Lie Algebras and Their Applications", IMPA, Rio de Janeiro, Brazil, Jun 5, 2008.
• Moduli spaces of sheaves and the boson-fermion correspondence, Conference "Lie Theory and Geometry: The Mathematical Legacy of Bertram Kostant", UBC, May 22, 2008.
• Quivers and cacti, Combinatorics and Geometry Seminar, Stanford University, Mar 19, 2008.
• Crystals, quiver varieties and coboundary categories for Kac-Moody algebras, BIRS Workshop – Quantum affine Lie algebras, extended affine Lie algebras, and applications, Mar 4, 2008.
• Quivers and the Euclidean Group, Algebra Seminar, University of Ottawa, Dec 4, 2007.
• A geometric construction of a crystal graph commutor, Conference "Algebras, Representations and Applications", Lie and Jordan Algebras, their Representations and Applications III in Honour of Prof. Ivan Shestakov's 60th Birthday, Maresias, Brazil, Aug 28, 2007.
• A geometric construction of a crystal graph commutor, The 4th International Conference on Representation Theory, Lhasa, Tibet, China, Jul 18, 2007.
• A geometric construction of a crystal graph commutor, Workshop on Lie Theory, University of Science and Technology of China, Hefei, China, Jul 9, 2007.
• Quiver varieties and geometric representation theory, Colloquium, Academia Sinica, Taipei, Taiwan, Jul 2, 2007.
• A geometric realization of a crystal commutor, AMS 2007 Spring Southeastern Sectional Meeting, Davidson, NC, Special Session on Geometric and Combinatorial Methods in Representation Theory, Mar 3, 2006.
• Quiver varieties and geometric representation theory, Seminar, UMass Boston, Mar 1, 2006.
• Quiver varieties and geometric representation theory, Colloquium, Concordia University, Feb 27, 2006.
• Quiver varieties and geometric representation theory, Colloquium, UC Riverside, Feb 23, 2006.
• Quiver varieties and geometric representation theory, Colloquium, Texas A&M, Feb 14, 2006.
• Quiver varieties and geometric representation theory, Colloquium, University of Pittsburgh, Feb 10, 2006.
• Quiver varieties and geometric representation theory, Special Seminar, Northeastern University, Feb 7, 2006.
• Quiver varieties and geometric representation theory, Colloquium, UMass Amherst, Feb 1, 2006.
• Quiver varieties and geometric representation theory, Algebra, Geometry and Physics Seminar, Stony Brook, Jan 25, 2006.
• Quiver varieties and geometric representation theory, Colloquium, Michigan State University, Jan 23, 2006.
• Quiver varieties and geometric representation theory, Joint Colloquium, University of Ottawa, Jan 17, 2006.
• Quiver varieties and geometric representation theory, Colloquium, University of Regina, Jan 9, 2006.
• The Ubiquitous Quiver, Algebraic Geometry Seminar, University of Toronto, Dec 5, 2005.
• A geometric boson-fermion correspondence, AMS 2005 Eastern Sectional Meeting, Annandale-on-Hudson, NY, Special Session on Representations of Infinite-Dimensional Lie Algebras, Vertex Operator Algebras, and Related Topics, Oct 8, 2005.
• Localization and the boson-fermion correspondence, Symplectic Geometry Seminar, University of Toronto, Oct 3, 2005.
• Comparing Geometric and Combinatorial Constructions of Crystal Graphs, Seoul National University, Sep 2, 2005.
• Geometric Construction of Crystal Graphs Using Quiver Varieties, Seoul National University, Sep 2, 2005.
• Cohomology of flag varieties and Geometric representation theory on flag varieties, Workshop on Schubert Varieties and Schubert Calculus, Fields Institute, June 2005.
• Quiver Varieties and Branching Rules, Workshop on Representation Theory and Geometry, UC Berkeley, May 2005.
• Quiver Varieties and Branching Rules, Lie Algebras, Vertex Operator Algebras and Their Applications: A Conference in Honor of Robert L. Wilson and James Lepowksy, NC State, May 2005.
• Quiver Varieties and Demazure Modules, Lie Theory Workshop, University of Ottawa, Mar 5, 2005.
• Quiver Varieties and Demazure Modules, Representation Theory, Combinatorics & Geometry Seminar, UC Berkeley, Feb 15, 2005.
• Three Seminar Mini-Course on Quiver Varieties and Representation Theory, Seminar on Moduli Spaces and Stacks, University of Toronto, Jan 2005.
• Quiver Varieties and Representation Theory, Algebraic Geometry Seminar, University of British Columbia, Dec 9, 2004.
• Quiver Varieties and Demazure Modules, Algebraic Geometry Seminar, Queen's University, Nov 1, 2004.
• Quiver Varieties, Young Tableaux and Crystal Graphs, Geometry, Symmetry and Physics Seminar, Yale University, Feb 17, 2004.
• Quiver Varieties, Young Tableaux and Crystal Bases, Symplectic Geometry Seminar, University of Toronto, Jan 26, 2004.
• Quiver varieties and Young tableaux, Seminar des Graduiertenkollegs, University of Münster, Dec 11, 2003.
• Geometric and combinatorial realizations of crystal graphs, Representation Theory Seminar, University of Wuppertal, Dec 10, 2003.
• Geometric and combinatorial realizations of crystal graphs, Seminar Darstellungstheorie von Algebren/Quantengruppen, Universität Bielefeld, Nov 18, 2003.
• A geometric approach to integrable models in statistical mechanics, Gauge Theory Seminar, Max Planck Institute. Oct 10, 2003.
• A geometric construction of representations of Kac-Moody algebras using quiver varieties, Seminar on Algebra, Geometry and Physics, Max Planck Institute, Sep 23, 2003.
• A connection between quiver varieties and integrable models in statistical mechanics, Osaka University, Aug 6, 2003.
• A connection between quiver varieties and integrable models in statistical mechanics, Kyoto University, Jul 29, 2003.
• Geometric Construction of Crystal Bases, Representation Theory Seminar, Yale University, Apr 2003.
• Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics, AMS 2003 Spring Central Sectional Meeting, Bloomington, IN, Special Session on Representations of Infinite Dimensional Lie Algebras and Mathematical Physics, Apr 4, 2003.
• Bases of representations of type A affine Lie algebras via quiver varieties and statistical mechanics, Algebra, Geometry and Physics Seminar, SUNY Stony Brook, Feb 12, 2003.
• The tensor product of representations of sl₂ via quivers, Representation Theory Seminar, University of Massachusetts at Amherst, Apr 8, 2002.
• The tensor product of representations of sl₂ via quivers, Junior Algebra Seminar, Yale University, Nov 27, 2001.