Research
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:
Cavalcanti, G. R., Witte, A. and Klaasse, R. L. ArXiv 2012.13282, 2020.
Cavalcanti, G. R., Witte, A. and Klaasse, R. L. ArXiv 2004.07559, 2020.
•A neighbourhood theorem for submanifolds in generalized complex geometry
Bailey, M., Cavalcanti, G. R. and Leer-Duran, J. ArXiv 1906.12069, 2019.
Cavalcanti, G. R.
Adv. Math., 2020.
Cavalcanti, G. R. and Klaasse, R. L. J. Symp. Geom. 17, 603--638, 2019.
•Classification of boundary Lefschetz fibrations over the disc
Behrens, S., Cavalcanti, G. R. and Klaasse, R. L. ArXiv 1706.09207. Geometry and Physics. A Festschrift in honor of Nigel Hitchin. OUP 2018.
Cavalcanti, G. R. and Klaasse, R. L. Proc. Lond. Math. Soc. 116, 1242-1280, 2018.
Bailey, M., Cavalcanti, G. R. and Gualtieri, M. J. Geom. Phys 120, 89--95, 2017.
Bailey, M., Cavalcanti, G. R. and Leer-Duran, J. Trans. Amer. Math. Soc. 371 (2019), no. 3, 2109–2131.
Cavalcanti, G. R. and Gualtieri, M. ArXiv 1503.06357. Proc. Lond. Math. Soc. (3) 116 (2018), no. 5, 1075–1111.
•A remark on the number of components of the space of generalized complex structures.
Cavalcanti, G. R.
ArXiv 1310.4870.
Cavalcanti, G. R.
J. Topol. 10, 1-- 21, 2017.
Cavalcanti, G. R.
ArXiv 1208.3558 — withdrawn: this paper was incorporated in the paper “Hodge theory of SKT manifolds”.
Bursztyn, H., Cavalcanti, G. R. and Gualtieri, M.
Comm. Math. Phys 333, 831-- 860, 2015.
Cavalcanti, G. R.
Poisson Geometry in Mathematics and Physics, July 2012, Utrecht. Indag. Math. 25, no 5, 948–956, 2014.
Cavalcanti, G. R. and Gualtieri, M.
Poisson Geometry in Mathematics and Physics, July 2010, Rio de Janeiro. Brazil. Bull. Braz. Math. Soc. (N.S.) 42 (2011), no. 4, 507–536.
Cavalcanti, G. R. and Gualtieri, M.
A celebration of the mathematical legacy of Raoul Bott, 341–365, CRM Proc. Lecture Notes, 50, Amer. Math. Soc., Providence, RI, 2010.
Cavalcanti, G. and Gualtieri, M.
J. Topol. 2, 840--864, 2009.
Bursztyn, H., Cavalcanti, G. and Gualtieri, M.
Contemporary Mathematics 450. Poisson Geometry in Mathematics and Physics, June 2006, Tokyo , Japan. ArXiv:math/0702104.
Cavalcanti, G., Fernandez, M. and Munoz, V.
Adv. Math., 218, 576--599, 2008.
• On non-formality of a simply-connected symplectic 8-manifold.
Cavalcanti, G. R., Fernandez, M. and Munoz, V.
Proceedings of the XVI International Fall Workshop on Geometry and Physics, Lisboa, Portugal. ArXiv 0801.4248.
Cavalcanti, G. R.
Proceedings of the workshop Geometry and Physics: Special metrics and supersymmetry. May 2008, Bilbao, Spain.
Cavalcanti, G. R.
Publicações Matemáticas do IMPA. 26o Colóquio Brasileiro de Matemática. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2007
• Reduction of Courant algebroids and generalized complex structures.
Bursztyn, H., Cavalcanti, G. R. and Gualtieri, M.
Adv. Math. 211 (2) 726--765, 2007.
• A surgery for generalized complex structures on 4-manifolds.
Cavalcanti, G. R. and Gualtieri, M.
J. Differential Geom., 76, 35--43, 2007.
Cavalcanti, G. R.
Topology Appl. 154, 1119--1125, 2007.
• The Lefschetz property, formality and blowing up in symplectic geometry.
Cavalcanti, G. R.
Trans. Amer. Math. Soc. 359, 333--348, 2007.
Cavalcanti, G. R.
J. Symp. Geom. 4 (3), 317--343, 2006.
• The decomposition of forms and cohomology of generalized complex manifolds.
Cavalcanti, G. R.
J. Geom. Phys. 57, 121--132, 2006.
• Formality of k-connected spaces in 4k+3- and 4k+4-dimensions.
Cavalcanti, G. R.
Math. Proc. Camb. Phil. Soc. 141, 101--112, 2006.
Cavalcanti, G. R. and Gualtieri, M.
J. Symp. Geom, 2, 393--410, 2004.
Cavalcanti, G. R.
Oxford D. Phil. thesis. October 2004.