My research is focused on algebraic geometry, particularly geometry and topology of moduli spaces and character varieties, and stability-related questions. I also have developed interests towards data analysis and mathematical education, as well as produced several research and teaching-related books.

Publications

Articles in Pure Mathematics

(12) Á. González-Prieto and A. Zamora, Root data in character varieties, arXiv:2408.03111 (2024).

(11) T. Gómez, A. Fernández Herrero and A. Zamora, A guide to moduli theory beyond GIT. Contemporary Mathematics AMS 803, Moduli Spaces and Vector Bundles—New Trends (P. Gothen, M. Melo, M. Teixidor i Bigas, Eds.), pp. 223-256 (2024) doi: 10.1090/conm/803/16100 arXiv:2302.01871.

(10) T. Gómez, A. Fernández Herrero and A. Zamora, The moduli stack of principal rho-sheaves and Gieseker-Harder-Narasimhan filtrations. Math. Z. 307, 51 (2024), doi: 10.1007/s00209-024-03497-6. (arXiv:2107.03918)

(9) C. Florentino, A. Nozad and A. Zamora, Generating series for the E-polynomials of GLn-character varieties, Math. Nachr., 296, 243-266 (2023), doi: 10.1002/mana.202000416. (arXiv:1902.06837)

(8) C. Florentino, A. Nozad, J. Silva and A. Zamora, On Hodge polynomials of singular character varieties, Current Trends in Analysis, its Applications and Computation. Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019. Trends in Mathematics, Birkhäuser, Cham. 99-110 (2022). (arXiv:2006.14520)

(7) C. Florentino, A. Nozad and A. Zamora, Serre polynomials of SLn- and PGLn-character varieties of free groups, J. of Geom. Phys. 161 (2021) 104008, doi: 10.1016/j.geomphys.2020.104008. (arxiv:1912.05852)

(6) R. Terpereau and A. Zamora, Stability conditions and related filtrations for (G,h)-constellations, Int. J. of Math., 28, Issue 14, 1750098 (2017) [34 pages] doi: 10.1142/S0129167X17500987. (arXiv:1506.08706)

(5) I. Biswas and A. Zamora, On the Gieseker Harder-Narasimhan filtration for principal bundles, Bull. Sci. math 140, Issue 4, 58-69 (2016). (arXiv:1411.2884)

(4) T. Gómez, I. Sols and A. Zamora, The Harder-Narasimhan filtration as the image of the Kempf filtration, El legado matemático de Juan Bautista Sancho Guimerá, López A. Ruipérez D. (Eds.), Salamanca: Ed. Universidad de Salamanca, 205-232 (2016) doi:10.2307/j.ctt1hch7vj.13.

(3) A. Zamora, Harder-Narasimhan filtration for rank 2 tensors and stable coverings, Proc. Indian Acad. Sci. (Math. Sci.) 126, Issue 3, 305-327, (2016). (arXiv:1306.5651)

(2) T. Gómez, I. Sols and A. Zamora, A GIT characterization of the Harder-Narasimhan filtration, Rev. Mat. Complut. 28, Issue 1, 169-190 (2015). (arXiv:1210.5475)

(1) A. Zamora, On the Harder-Narasimhan filtration of finite dimensional representations of quivers, Geom. Dedicata 170, Issue 1, 185-194 (2014). (arXiv:1112.1886)

Research Books

(2) A. Zamora Saiz and R. Zúñiga-Rojas, Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration, SpringerBriefs, Springer Nature (2021). (link)

(1) A. Zamora Saiz, C. Quesada González, L. Hurtado Gil and D. Mondéjar Ruiz, An introduction to data analysis with R, Springer Nature, collection Use R! (2020). (link)

Teaching Books

(4) A. Zamora Saiz and H. Barge Yáñez, Geometría Afín y Proyectiva, Sanz y Torres (2022). (link) (Erratum).

(3) J. Sánchez and A. Zamora Saiz, Matemática Discreta I a través de problemas, Fundación General de la Universidad Politécnica de Madrid (2021).

(2) H. Barge Yáñez and A. Zamora Saiz, Topología, Sanz y Torres (2021). (link) (Erratum)

(1) M. Córdoba Bueno and A. Zamora Saiz, Fundaments of statistical inference, 2nd Edition, Ed. Dykinson (2018).

Articles in Mathematical Education

(2) D. de la Fuente Benito, J. A. Sánchez Pelegrín, A. Zamora Saiz, Enseñando Relatividad Especial gráficamente, Pensamiento Matemático, Historias de Matemáticas, Volumen X, Número 1, pp. 073-082, (2020).

(1) J. A. Sánchez Pelegrín, D. de la Fuente Benito, A. Zamora Saiz, Optimización en secundaria: el problema de Herón, Números, Volumen 104, pp. 75-82, (2020).

Articles in Data Analysis

(1) A. Rabadán, A. Zamora, M. Díaz, R. Bernabéu, Consumer preferences associated with the protected geographical indication label in the marketing of lamb meat, Small Ruminant Research 202 106454 (2021).