Publications and preprints:

 

 

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

​

​

Generalizing the Mukai Conjecture to the symplectic category and the Kostant game (with. A. C. Castro and M. Pabiniak), to appear in Pure and Applied Mathematics Quarterly. arXiv:2206.00456 [math.SG]

​

On topological properties of positive complexity one spaces (with D. Sepe), Transformations Groups, 27 (2022), 723 - 735.

​

Rigidity of elliptic genera: from number theory to geometry and back (with K. Bringmann, A.C. Castro and M. Schwagenscheidt), International Math. Res. Notices (2021), https://doi.org/10.1093/imrn/rnab172

​

Fano quiver moduli (with H. Franzen and M. Reineke), Canadian Mathematical Bulletin, 64 (2021), 984 - 1000.

​

An invitation to circle actions (with L. Godinho), Proceedings of the European Congress of Mathematics 7 (2018), DOI 10.4171/176-1/16

​

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

 66 pages.

​

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.

​

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.