Currently at UPC, I stay connected with UB (former position and PhD) and UAB (degree), through the Seminari de Teoria de Nombres (UB-UAB-UPC), where I have been in charge of coordination tasks during last years.
Main research has been about hyperbolic uniformizations of Shimura curves, related with quaternion algebras and quadratic forms. The PhD thesis, on that topic, received the prize Josep Teixidor de Matemàtiques 2000-2001, awarded by the Institut d’Estudis Catalans.
Current research is focused in applications on Coding theory, in relation with hyperbolic geometry and algebraic structures as quaternion orders, and quadratic forms.
- Shimura curves
- Quaternion algebras
- Fuchsian groups
- Hyperbolic geometry
- Applications to coding theory and cryptography
- Alsina, M., Bayer, P., Quaternion orders, quadratic forms and Shimura curves, CRM Monograph Series 22, xvi+196 pp, American Mathematical Society, Providence, RI, (2004).
- Alsina, M., Binary quadratic forms and Eichler orders, Journal de Théorie des Nombres de Bordeaux 17, 13-23 (2005).
- Blanco-Chacón, I., Remón, D., Hollanti, C., Alsina, M., Nonuniform Fuchsian codes for noisy channels, Journal of the Franklin Institute 351, 5076-5098 (2014).
- Blanco-Chacón, I., Hollanti, C., Alsina, M., Remón, D., Fuchsian codes with arbitrarily high code rates, Journal of Pure and Applied Algebra 220, 180-196 (2016).