Marco Gualtieri



Assistant professor, University of Toronto

Research

My research areas are differential geometry and mathematical physics. More specifically, I work on generalized geometry, as initiated by Nigel Hitchin.
Most recently, I have been working on holomorphic aspects of Courant, Dirac, and Poisson geometry, as well as their interactions with generalized Kahler geometry. My collaborators are Gil R. Cavalcanti, Henrique Bursztyn, Vestislav Apostolov, and Tadashi Tokieda.

Here's a list of my available papers. There are several in the pipeline, so stay tuned:

  1. Generalized Kahler geometry, develops generalized Kahler structure and its connection to holomorphic Courant brackets.
  2. Blow-up of generalized complex 4-manifolds, with Gil Cavalcanti, develops blow-up and blow-down operations and shows that 3 CP^2 is generalized complex.
  3. Branes on Poisson varieties, using the theory of Poisson modules to construct examples of bi-Hermitian metrics on Poisson varieties.
  4. Generalized complex geometry, an article based on the thesis, significantly condensed (no generalized Kahler) and with several new ideas. Prepared while teaching the topics course below.
  5. Generalized complex geometry, my 2004 doctoral thesis. Develops the basic structure theory of generalized complex geometry as well as generalized Kaehler geometry
  6. Generalized complex structures on nilmanifolds, (J. Symp. Geom.) with Gil Cavalcanti. Some of the first nontrivial examples of generalized complex structures.
  7. Generalized geometry and the Hodge decomposition, proves a Hodge decomposition for generalized Kaehler structures.
  8. A surgery for generalized complex structures on 4-manifolds, (J. Diff. Geom.) with Gil Cavalcanti. Presents the first generalized complex 4-manifold which is neither symplectic nor complex.
  9. Reduction of Courant algebroids and generalized complex structures, with Henrique Bursztyn and Gil Cavalcanti. Develops a theory of reduction for Courant algebroids and related geometrical structures.
  10. Generalized Kaehler manifolds with split tangent bundle, with Vestislav Apostolov. Completes the classification of generalized Kaehler 4-manifolds.
  11. Golfer's Dilemma, (Am. J. Physics) with Tadashi Tokieda et al. Explains why the golf ball sometimes emerges from the hole.

Teaching