Areas of interest

• Algebraic Combinatorics.
• Enumerative Combinatorics.
• Geometric Combinatorics.
• Symplectic Geometry.

Monographs

• Existence of periodic solutions of a particular hamiltonian equation (in Spanish), M.Sc. Thesis, Pontificia Universidad Católica del Perú, June 1997. Advisor: Alfredo Poirier.
• The Theory of the Poincare Index, Diploma Thesis, International Centre for Theoretical Physics at Trieste, Italy, September 1998. Advisor: Giovanni Vidossich.
• Weighted polytope decompositions and applications, Ph.D. Thesis, University of California at Santa Cruz, United States of America, December 2004. Advisor: Jonathan Weitsman.

Peer-reviewed papers

1. J. Agapito and L. Godinho, Cone decompositions of non-simple polytopes, Accepted for publication at J. Symplectic Geom., June (2015), 24pp.
2. J. Agapito, Â. Mestre, P. Petrullo and Maria M. Torres, On one-parameter Catalan arrays, J. Integer Seq. 18 (2015), Article 15.5.1, 13pp.
3. J. Agapito, On symmetric polynomials with only real zeros and nonnegative \(\gamma\)-vectors, Linear Algebra Appl. 451 (2014), 260--289.
4. J. Agapito, Â. Mestre, P. Petrullo and Maria M. Torres, A symbolic treatment of Riordan arrays, Linear Algebra Appl. 439 (2013), no. 7, 1700--1715.
5. J. Agapito Ruiz, Riordan arrays from an umbral symbolic viewpoint, Bol. Soc. Port. Mat. 2012, Special Issue, 5--8.
6. J. Agapito and L. Godinho, Intersection numbers of polygon spaces, Trans. Amer. Math. Soc. 361 (2009), no. 9, 4969--4997.
7. J. Agapito and L. Godinho, New polytope decompositions and Euler-Maclaurin formulas for simple integral polytopes, Adv. Math. 214 (2007), no. 1, 379--416.
8. J. Agapito, Weighted Brianchon-Gram decomposition, Canad. Math. Bull. 49 (2006), no. 2, 161--169.
9. J. Agapito and J. Weitsman, The weighted Euler-Maclaurin formula for a simple integral polytope, Asian J. Math. 9 (2005), no. 2, 199--211.
10. J. Agapito, A weighted version of quantization commutes with reduction for a toric manifold. Integer points in polyhedra--geometry, number theory, algebra, optimization, 1--14, Contemp. Math., 374, Amer. Math. Soc., Providence, RI, 2005.

Non-refereed papers

• J. Agapito, Contagem dos pontos inteiros de um polítopo. An expository paper (in Portuguese). Published in an internal magazine of Universidade Lusófona de Humanidades e Tecnologias, Lisboa (2009).