Departament de Matemàtica Aplicada IV
Universitat Politècnica de Catalunya
Escola d'Enginyeria de Telecomunicacio i Aerospacial de Castelldefels
Campus de Baix Llobregat
Avinguda del Canal Olimpic, 15
Tel: +34.93.413.41.03 / Fax: +34.93.401.59.81
An HTML version of my Curriculum
Vitae is available. It is possible to view articles from the
list of publications.
My research interests include incidence geometries, codes, semifields and graphs and generally involve applying linear algebra methods to these combinatorial objects.
The following pdf files are edited from recent talks on
the maximum wieght of a linear code (pdf),
an alternative way to generalise the pentagon (pdf),
complete bipartite Turan numbers (pdf),
the MDS conjecture for linear codes (pdf),
Jaeger's conjecture on nowhere zero points for linear maps (pdf), and
functions over prime fields that do not determine all directions (pdf).
A proof of the MDS conjecture over prime fields (that linear maximum distance separable codes of dimension at most p have length at most p+1, where p is the number of elements in the field) is contained in this article.
Here is a video of me trying to convince the participants of a BIRS (Banff International Research Station) workshop that it is a generalisation of Segre's ''arc is a conic'' theorem, the original proof of which is available here. Alternatively, here is another video of a similar talk, but with a more coding theory bias, from the 3rd International Castle Meeting on Coding Theory and Applications, held in Cardona in September 2011.
I have compiled a table of the maximum lengths of three-dimensional linear codes, where the difference between the length and minimum distance is fixed. There is also a short background on codes and (n,r) arcs and a question relating to the attainability of the Griesmer bound.
I am on the editorial board of
Designs, Codes and Cryptography,
Finite Fields and their Applications and
Journal of Geometry.
A quote from Lockhart's Lament "The mathematics curriculum doesn't need to be reformed, it needs to be scrapped". Read it to find out what it should be replaced by.
There are notes available for the courses
An introduction to finite geometry in
format (65 pages),
co-authored with Zsuzsa Weiner.
This is the third edition updated September 2011.
Lacunary polynomials over finite fields in
format (12 pages).
Stuff to do in Barcelona
Lunch at Mamá café
Piano classes with Victoria (currently in Madrid)
Tango classes with Martin and Andrea.
Updated 14 December 2012