Publications and preprints:

 

 

(*The title links to the Arxiv articles, which may not be updated*)

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- "On topological properties of positive complexity one spaces" (with D. Sepe), to appear on Transformations Groups.

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- "An invitation to circle actions" (with L. Godinho), to appear in Proceedings of the European Congress of Mathematics 7.

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- "Faithful Semitoric systems" (with S. Hohloch, D. Sepe and M. Symington) (previously "Vertical almost toric systems"), SIGMA 14, No. 084,  (2018) 

   66 pages.

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- "12, 24 and beyond" (with L. Godinho and F. v. Heymann), Advances in Mathematics, 319 (2017), 472 - 521.

 

-  "Canonical bases for the equivariant cohomology and K-theory rings of symplectic toric manifolds" (with M. Pabiniak).  J. Symplectic Geometry 16,           No. 4 (2018), 1117 - 1165.

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-  "On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action", Communications

    in Contemporary Mathematics, 19, No. 04 (2017).

 

- " Fermat and the number of fixed points of periodic flows"  (with L. Godinho and Á. Pelayo), Communications in Number Theory and Physics, 9, No.       4  (2015), 643 - 687.

 

- " From compact semi-toric systems to Hamiltonian S^1 -spaces" (with S. Hohloch and D. Sepe), Discrete and Continuous Dynamical Systems -                     Series A,  35 (1), 247 – 281 (2015).

 

- " Polynomial Assignments" (with V. Guillemin and C. Zara), Indagationes Mathematicae, 25, No. 5 (2014), 992–1018.

 

- " New tools for classifying Hamiltonian circle actions with isolated fixed points" (with L. Godinho), Foundations of Computational Mathematics,

     14 (4), 791 – 860 (2014). DOI: 10.1007/s10208-014-9204-1. The accompanying software can be found here. 

 

- " Balanced fiber bundles and GKM theory" (with V. Guillemin and C. Zara), International Math. Res. Notices, 17 , 3886 – 3910 (2013).

 

- " Moduli spaces of toric manifolds" (with A. Pelayo, A.R. Pires and T.S. Ratiu), Geometriae Dedicata, 169 (1), 323–341 (2014).

      DOI: 10.1007/s10711-013-9858-x.

 

- " New Techniques for obtaining Schubert-type formulas for Hamiltonian manifolds" (with S. Tolman),  J. Symplectic Geometry, 11 (2), 179 – 230                  (2013). 

 

- " Equivariant K-theory of GKM bundles" (with V. Guillemin and C. Zara),  Annals of Global Analysis and Geometry, 43 (1), 31 – 45 (2013).

 

- " Cohomology of GKM fiber bundles" (with V. Guillemin and C. Zara),  J. Algebraic Combinatorics, 35 (1), 19 – 59 (2012). 

 

- " Towards classifying Hamiltonian torus actions with isolated fixed points" (with L. Godinho), Proceedings of the Sociedade Portuguesa de                         Matemática, May 2013. 

 

 

In preparation: 

 

- " From Hamiltonian S^1 spaces to compact semi-toric systems" (with S. Hohloch, M. Symington and D. Sepe). 

 

- " Surgeries of vertical almost-toric systems" (with S. Hohloch, M. Symington and D. Sepe). 

 

 

Thesis:

 

“ The topology of GKM spaces and GKM fibrations”, Ph.D. Thesis, MIT, June 2009.