Research

I work with generalized complex structures and related objects. I'm interested in both topological questions about those and their relation to string theory.  I have been working with Marco Gualtieri on many aspects of this area and have also collaborated with Henrique Bursztyn.


I am also interested in symplectic topology and have collaborated with Marisa Fernandez and Vicente Munoz in this area.


Below is a list of my written work with links to versions of the papers. You can also find most of my publications on the ArXiv or on Google scholar.


Research papers:


  1. •Fibrations in semi-toric and generalized complex geometry

  2. Cavalcanti, G. R., Witte, A. and Klaasse, R. L. ArXiv 2012.13282, 2020.


  1. •Self-crossing stable generalized complex structures

  2. Cavalcanti, G. R., Witte, A. and Klaasse, R. L. ArXiv 2004.07559, 2020.


  1. •A neighbourhood theorem for submanifolds in generalized complex geometry

  2. Bailey, M., Cavalcanti, G. R. and Leer-Duran, J. ArXiv 1906.12069, 2019.



    2. • Hodge theory of SKT manifolds.

    3. Cavalcanti, G. R.

    4. Adv. Math., 2020.


    1. •Fibrations and log-symplectic structures

    2. Cavalcanti, G. R. and Klaasse, R. L. J. Symp. Geom. 17, 603--638, 2019.


    1. •Classification of boundary Lefschetz fibrations over the disc

    2. Behrens, S., Cavalcanti, G. R. and Klaasse, R. L. ArXiv 1706.09207. Geometry and Physics. A Festschrift in honor of Nigel Hitchin. OUP 2018.


    1. •Fibrations and stable generalized complex structures

    2. Cavalcanti, G. R. and Klaasse, R. L. Proc. Lond. Math. Soc. 116, 1242-1280, 2018.


    1. •Type one generalized Calabi–Yaus

    2. Bailey, M., Cavalcanti, G. R. and Gualtieri, M. J. Geom. Phys 120, 89--95, 2017.


    1. •Blow-ups in generalized complex geometry

    2. Bailey, M., Cavalcanti, G. R. and Leer-Duran, J. Trans. Amer. Math. Soc. 371 (2019), no. 3, 2109–2131.



    2. •Stable generalized complex structures.

    3. Cavalcanti, G. R. and Gualtieri, M. ArXiv 1503.06357.  Proc. Lond. Math. Soc. (3) 116 (2018), no. 5, 1075–1111.


    1. •A remark on the number of components of the space of generalized complex structures.

    2. Cavalcanti, G. R.

    3. ArXiv 1310.4870.


    1. •Examples and counter-examples of log-symplectic manifolds.

    2. Cavalcanti, G. R.

    3. J. Topol. 10, 1-- 21, 2017.


    1. •Reduced holonomy and Hodge theory.

    2. Cavalcanti, G. R.

    3. ArXiv 1208.3558 — withdrawn: this paper was incorporated in the paper “Hodge theory of SKT manifolds”.


    1. • Generalized Kaehler geometry of instanton moduli space.

    2. Bursztyn, H., Cavalcanti, G. R. and Gualtieri, M.

    3. Comm. Math. Phys 333, 831-- 860, 2015.



    1. • Goto’s generalized Kaehler stability theorem.

    2. Cavalcanti, G. R.

    3. Poisson Geometry in Mathematics and Physics, July 2012, Utrecht. Indag. Math. 25, no 5, 948–956, 2014.


    1. • Blowing up generalized Kahler 4-manifolds.

    2. Cavalcanti, G. R. and Gualtieri, M.

    3. Poisson Geometry in Mathematics and Physics, July 2010, Rio de Janeiro. Brazil. Bull. Braz. Math. Soc. (N.S.) 42 (2011), no. 4, 507–536.


    1. • Generalized complex geometry and T-duality.

    2. Cavalcanti, G. R. and Gualtieri, M.

    3. A celebration of the mathematical legacy of Raoul Bott, 341–365, CRM Proc. Lecture Notes, 50, Amer. Math. Soc., Providence, RI, 2010.


    1. • Blow-up of generalized complex 4-manifolds.

    2. Cavalcanti, G. and Gualtieri, M.

    3. J. Topol. 2, 840--864, 2009.


    1. • Generalized Kaehler and hyper-Kaehler quotients.

    2. Bursztyn, H., Cavalcanti, G. and Gualtieri, M.

    3. Contemporary Mathematics 450. Poisson Geometry in Mathematics and Physics, June 2006, Tokyo , Japan. ArXiv:math/0702104.


    1. • Symplectic resolutions, Lefschetz property and formality.

    2. Cavalcanti, G., Fernandez, M. and Munoz, V.

    3. Adv. Math., 218, 576--599, 2008.


    1. • On non-formality of a simply-connected symplectic 8-manifold.

    2. Cavalcanti, G. R., Fernandez, M. and Munoz, V.

    3. Proceedings of the XVI International Fall Workshop on Geometry and Physics, Lisboa, Portugal. ArXiv 0801.4248.


    1. • Computations of generalized Dolbeault cohomology.

    2. Cavalcanti, G. R.

    3. Proceedings of the workshop Geometry and Physics: Special metrics and supersymmetry. May 2008, Bilbao, Spain.


    1. • Introduction to generalized complex geometry.

    2. Cavalcanti, G. R.

    3. Publicações Matemáticas do IMPA. 26o Colóquio Brasileiro de Matemática. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2007


    1. • Reduction of Courant algebroids and generalized complex  structures.

    2. Bursztyn, H., Cavalcanti, G. R. and Gualtieri, M.

    3. Adv. Math. 211 (2) 726--765, 2007.


    1. • A surgery for generalized complex structures on 4-manifolds.

    2. Cavalcanti, G. R. and Gualtieri, M.

    3. J. Differential Geom., 76, 35--43, 2007.


    1. • Formality in generalized Kahler geometry.

    2. Cavalcanti, G. R.

    3. Topology Appl. 154, 1119--1125, 2007.


    1. • The Lefschetz property, formality and blowing up in symplectic geometry.

    2. Cavalcanti, G. R.

    3. Trans. Amer. Math. Soc. 359, 333--348, 2007.


    1. • Reduction of metric structures on Courant algebroids.

    2. Cavalcanti, G. R.

    3. J. Symp. Geom. 4 (3), 317--343, 2006.


    1. • The decomposition of forms and cohomology of generalized complex manifolds.

    2. Cavalcanti, G. R.

    3. J. Geom. Phys. 57, 121--132, 2006.


    1. • Formality of k-connected spaces in 4k+3- and 4k+4-dimensions.

    2. Cavalcanti, G. R.

    3. Math. Proc. Camb. Phil. Soc. 141, 101--112, 2006.


    1. • Generalized complex structures on nilmanifolds.

    2. Cavalcanti, G. R. and Gualtieri, M.

    3. J. Symp. Geom,  2, 393--410, 2004.


    1. • New aspects of the ddc-lemma.

    2. Cavalcanti, G. R.

    3. Oxford D. Phil. thesis. October 2004.