## 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:

- Quasi-parabolic Higgs bundles and null hyperpolygon spaces (joint with A. Mandini), preprint arXiv:1907.01937 [math.AG] (2019).
- 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.