Current projectsI am currently working on finding algorithms to decide if a given algebraic curve is parametrizable by radicals and to compute such a parametrization when it exists. I am doing this with support from the Austrian Science Fund by the project "Radical parametrizations of algebraic curves" (see the project's website).
My mathematical background
I studied Mathematics in the University Complutense of Madrid from 1994 to 1999. My favourite topics there were Topology and its Algebraic branch. My Ph. D. Thesis, which I finished in March 2004 under the supervision of Jaime Gutiérrez, studied aspects of the decomposition of rational functions and related computations in function fields.
Afterwards I worked with John McKay on computational aspects of Monstrous Moonshine. I have also collaborated with Tanush Shaska on hyperelliptic curves with certain automorphism groups. My current research is on the problem of parametrizing algebraic curves by radicals, mainly in collaboration with Josef Schicho and Rafael Sendra.
Events I organizedThe following are some mathematical events in whose organization I have participated to various degrees.
- Co-organiser of the 2010 and 2011 editions of the Linz Algebra Research Day (LARD), jointly with members of the Department of Algebra of the JKU. This is a by-yearly informal workshop for the algebraists of Linz and surroundings to meet and tell others what they are doing or are interested in. You can see the three webpages here: 2010, 2011, 2011 Christmas.
- Coordinator of the irregularly bi-weekly Symbolic Computation seminars at RICAM (Linz, Austria) from October 2007 to August 2012.
- Co-organiser of the Second Workshop on Mathematical Cryptology (WMC 2008). Santander (Spain), 23-25 October 2008.
- Co-organiser of the session “Algorithms for computation in number theory” in the 2006 International Congress of Mathematical Software (ICMS). Castro Urdiales (Spain), 1–3 September 2006.
- Member of the local organization of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC). Santander (Spain), 4–7 July 2004.