Tel. 34-93 401 5996
FAX: 34-93 401 5981
Mòdul C3, Campus Nord
Jordi Girona, 1
E-08034 Barcelona, Spain
I am currently serving as chair of the Departament de Matemàtica Aplicada 4, director of OSRM, responsible with Prof. J. Fàbrega of the research group Combgraf, in the board of the Societat Catalana de Matemàtiques, member of the Council of EMS, Editor of the Butlletí de l'SCM and in the editorial board of Integers and Electronic Journal of Graph Theory and Applications
I am also involved in the following activities
CSASC2010, Praha, Jan 22-27, 2010
IWONT2010, Barcelona, 9--11 June 2010
8th French Combinatorial Conference, Paris, June 28 July 2, 2010
JMDA7, Castro Urdiales, 7-9 July 2010
Recent preprints and papers
O. Serra and L. Vena, On the number of monochromatic solutions of integer linear systems on Abelian groups, submitted to Europ. J. of Combin.
It is shown that the number of monochromatic solutions of a linear system which satisfies a column condition in a coloring of a sufficiently large abelian group with bounded exponent is a positive fraction f the total number of solutions.
O. Serra, G. Zémor, A Structure Theorem for Small Sumsets in Nonabelian Groups, submitted to Europ. J. Combin.
If a set in a S nonabelain group satisfies |ST|<|S|+|T| then S is either a geometric progression, a periodic set with at most |S|-1 holes or a large set. This extends (except for the last possibility) known results for the abelian case.
G. A. Freiman, D. Grynkiewicz, O. Serra, Y. V. Stanchescu, Inverse Additive Problems for Minkowski Sumsets II, J. Geom. Anal.
The case of equality in the Bonnesen extension of the Brunn—Minkowsky inequality for projections.
G. A. Freiman, D. Grynkiewicz, O. Serra, Y. V. Stanchescu, Inverse Additive Problems for Minkowski Sumsets I, to appear in Collec. Math.
A discrete version in dimension two of the Bonessen strengthening of the Brunn—Minkowski inequality.
G. Perarnau, O. Serra, Rainbow Matchings: Existence and Counting, submitted to Comb. Prob. And Comp.
Asymptotic bounds on the number of rainbow matchings in edge—colored complete bipartite graphs. It is shown that a random edge-coloring contains a rainbow matching with high probability.
G. Perarnau, O. Serra, On the treedepth of random graphs, submitted to Discrete Appl. Math
Asymptotic almost sure values of the treedepth of random graphs
A. Montejano and O. Serra, Counting patterns in colored orthogonal arrays, submitted to Discrete Math.
A combinatorial counting device for the number of solutions of equations in groups (or more generally in orthogonal arrays). One application is the number of rainbow Schur triples in an equitable coloring of cyclic groups.
D. Král, O. Serra and L. Vena, On the Removal Lemma for Linear Systems over Abelian Groups , submitted to Europ. J. Combin.
This extends to finite abelian groups a previous paper by the same authors saying that if a linear system has not many solutions in some given sets, then we can remove small number of elements to eliminate all these solutions.
A. Montejano and O. Serra, Rainbow--free 3-coloring of abelian groups , Electronic J. Combin.
We give the structure of 3-colorings of abelian groups which have no rainbow AP(3). This structure theorem proves
in particular a conjecture of Jungic et al. on the size of the smallest color class in such a coloring.
D. Král, O. Serra and L. Vena, A removal Lemma for systems of linear equations in finite fields, Israel J. of Math.
This extends a previous paper by the same authors saying that if a linear system has not many solutions in some given sets,
then we can remove small number of elements to eliminate all these solutions.
S. L. Bezrukov, M. Rius and O. Serra, A generalization of the local-global theorem for isoperimetric orders, submitted to Electronnic Journal of Combinatorics
I particularly like this paper, an opinion apparently not shared by some referees, which provides a powerul tool to construct
graphs with orderings such that the initial segments minimize the boundary of sets of its size.
Y.O. Hamidoune, O. Serra, A note on Pollard's Theorem, preprint
This nice little note on Pollard's theorem for abelian groups was originally motivated by its potential and significant extension to nonabelian
groups. It will not be published in a journal.
David G. Grynkiewicz and O. Serra, Properties of two dimensional sets with small sumset,
In the project of extending Kemperman Structure Theorem beyond the Cauchy-Davenport bound in general abelian groups one encounters two
dimensional sets. This paper uses compression techniques to handle this particular case.
Simeon Ball and O. Serra, Punctured Combinatorial Nullstellensatze, to appear in Combinatorica
Motivated by some applications to geometry this paper considers two extensions of Alon's Nullstellensatz, one related to the punctured case and
the second one dealing with multiplicity of roots.
J. Cilleruelo, Y.O. Hamidoune and O. Serra, Addition Theorems in Acyclic Semigroups, to appear in M. Nathanson Festschrift, Springer
An extension of the Cauchy Davenport inequality and Vosper's inverse theorem to families of sets is proved.
J. Cilleruelo, Y.O. Hamidoune and O. Serra, On sums of dilates, to appear in Combinatorics, Probability and Computing.
A characterization of sets of integers with small sum with its k-dilations is obtained.
O. Serra and G. Zémor, Cycle codes of graphs and MDS array codes, preprint
A nice construction of MDS array codes is given in connection with the 1-factorization conjecture of graphs. Simple erasure and error decoding
algorithms are provided.
O. Serra and G. Zémor, Large sets with small doubling modulo p are well covered by an arithmetic progression, to appear in Annales de l'Institut Fourier
The isoperimeric method of Hamidoune is used to prove the Bilu-Lev-Ruzsa conjecture of sets with small sum modulo p with a modest doubling
constant but with no unnecessary restrictions on the size of the sets.
Spring 2012, Graph Theory, Master of Applied Mathematics and Mathematical Engineering, FME
Fall 2011, Probability Theory, Grau de Matemàtiques, FME
Fall 2011, Combinatorics, Master of Applied Mathematics and Mathematical Engineering, FME
Fall 2011, Combinatoria, LLicenciatura de Matemàtiques, FME
Spring 2010 Algebraic and Topological Graph Theory, Master of Applied Mathematics, FME
Spring 2010 Algebraic Combinatorics, Master of Applied Mathematics, FME
Spring 2010, Calcul Vectorial, Enginyeria de Telecomunicació, ETSETB
Fall 2009 Combinatorics, Llicenciatura de Matemàtiques, FME
Fall2009 Calcul, Enginyeria de Telecomunicació, ESTETB