Lecture Notes:

• An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity, with José Natário, Springer Universitext, 2014.
  

Software:

• Software based on the paper New tools for classifying Hamiltonian circle actions with isolated fixed points, (joint with S. Sabatini): software.

Research Publications:

• On a symplectic generalization of a Hirzebruch problem (joint with Nicholas Lindsay, Silvia Sabatini), preprint (2024), 63 pages.


• Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four (joint with G. T. Mwakyoma-Oliveira and D. Sepe), submitted (2024), 114 pages.


• Quasi-parabolic Higgs bundles and null hyperpolygon spaces (joint with A. Mandini), Trans. Amer. Math. Soc. 374 (2021), 7411-7447.


• An invitation to circle actions (joint with S. Sabatini), European Congress of Mathematics, 355-371, Eur. Math. Soc., Zürich, (2018).


• 12, 24 and beyond (joint with F. von Heymann and S. Sabatini), Adv. in Math. 319 (2017), 472-521.


• Cone decompositions of non-simple polytopes (joint with J. Agapito), Journal of Symplectic Geometry, 14 (2016), pp. 737-766.


• Fermat and the number of fixed points of periodic flows (joint with Á. Pelayo and S. Sabatini), Commun. Number Theory Phys., 9 (2015), 643-687.
  


• Symplectic form on hyperpolygon spaces (joint with I. Biswas, C. Florentino and A. Mandini), Geometriae Dedicata, 179 (2015), 187-195. DOI: 10.1007/s10711-015-0075-7.


• New tools for classifying Hamiltonian circle actions with isolated fixed points, (joint with S. Sabatini), Foundations of Computational Mathematics, 14 (2014), 791-860. DOI: 10.1007/s10208-014-9204-1.
  


• Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1 (joint with I. Biswas, C. Florentino and A. Mandini), Transform. Groups 18 (2013), 995-1018.


• Hyperpolygon spaces and moduli spaces of parabolic Higgs bundles (joint with A. Mandini), Adv. in Math. 244 (2013), 465-532.
  


• Addendum and erratum to "The fundamental group of S^1-manifolds" (joint with M. E. Sousa-Dias), Canad. J. Math. 65 (2013), 553-558.


• The fundamental group of S^1-manifolds (joint with M. E. Sousa-Dias), Canad. J. Math. 62 (2010), 1082-1098.


• Intersection numbers of polygon spaces (joint with J. Agapito), Trans. Amer. Math. Soc. 361 (2009), 4969-4997.
  


• Hearing the weights of weighted projective planes (joint with M. Abreu, E. Dryden and P. Freitas), Ann. Global Anal. Geom. 33 (2008), 373-395.
  


• New polytope decompositions and Euler-Maclaurin formulas for simple integral polytopes (joint with J. Agapito), Adv. in Math. 214 (2007), 379-416.
  


• Equivariant cohomology of S^1-actions on 4-manifolds, Canad. Math. Bull. 50 (2007), 365-376.
  


• Semifree symplectic circle actions on 4-orbifolds, Trans. Amer. Math. Soc. 358 no. 11 (2006), 4919-4933.
  


• On certain symplectic circle actions, J. Symplectic Geom. 3 no. 3 (2005), 357-383.


• Blowing up symplectic orbifolds, Ann. Global Anal. Geom. 20 (2001), 117-162.


• Circle Actions on Symplectic Manifolds, Ph.D. Thesis, SUNY at Stony Brook, 1999.