Oriol Serra
Address: 
Tel.
3493 401 5996 
FAX: 3493 401 5981 

Mòdul C3, Campus Nord 
email: oriol.serra at upc.edu 


Jordi Girona, 1 

E08034 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, Execuive Committee
member of the Barcelona Graduate School in
Mathematics, in the board of the Societat
Catalana de Matemàtiques, member of the Council of EMS,
and in the editorial board of Integers
and Electronic Journal of Graph
Theory and Applications
I am currently running the
Seminar
Combinatorics, Graph Theory and Applications
I am or have been also
involved in the following activities
Additive Combinatorics in Paris, July 2012
Perspectives in Discrete
Mathematics, ESFEMSERCOM Conference June 2012
Advanced
Course: Combinatorial Convexity, by Imre Leader, May 2012
RSMESMM Joint Meeting, Jan 2012
CSASC2010, Praha, Jan 2227, 2010
IWONT2010, Barcelona, 911 June 2010
8th French Combinatorial Conference, Paris, June 28 July 2, 2010
JMDA7, Castro Urdiales, 79 July 2010
Advanced Course: Polymatroids etc, by Jack Edmonds, Jan 1121 2010
Recent
preprints and papers
Karoly
Boroczky, Francisco
Santos, Oriol Serra,
On sumsets and convex hull,
submitted to Discrete and Comput. Geometry
The characterization of equality case of a recent inequlaity
by Mate Matolcsi and Imre Z. Ruzsa on cardinalities of sumsets in ddimensional
Euclidian space is obtained. It involves
characterization of totally stackable polytopes recently obtained by Benjamin Nill
and Arnau Padrol.
Florent
Foucaud, Guillem Perarnau, Oriol Serra, Random
subgraphs make identification affordable, submitted to J. Graph Theory
Identification codes in graphs with n vertices have minimum
size log n. It is shown that dense graphs always admit spanning subgraphs with
such optimal identification codes. This is a consequence of more general reslt which uses some particularly
chosen random subgraphs.
O.
Serra and L. Vena, On the number of
monochromatic solutions of integer linear systems on Abelian groups, 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, 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 S1 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, 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, Comb. Prob. And Comp.
Asymptotic bounds
on the number of rainbow matchings in edge—colored complete bipartite graphs.
It is shown that a random edgecoloring contains a rainbow matching with high
probability.
G.
Perarnau, O. Serra, On the treedepth
of random graphs, Discrete Appl.
Math
Asymptotic almost
sure values of the treedepth of random
graphs
A.
Montejano
and O. Serra, Counting patterns in
colored orthogonal arrays, 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 , 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, Rainbowfree 3coloring of abelian groups , Electronic J. Combin.
We give the structure of 3colorings 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 localglobal 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 CauchyDavenport 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, 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, 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, Combinatorics, Probability and Computing.
A characterization of sets of integers with small sum with its kdilations 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 1factorization 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, Annales de l'Institut Fourier
The isoperimeric method of Hamidoune is used to prove the BiluLevRuzsa conjecture of sets with small sum modulo p with a modest doubling
constant but with no unnecessary restrictions on the size of the sets.
Fall 2013, Probability
Theory, Grau de Matemàtiques, FME
Fall 2013, Graph
Theory, Master of Applied Mathematics and Mathematical Engineering, FME
Fall 2103, Random
Structures and teh Probabilistic Method, Barcelona Graduate School of
Mathematics
Spring 2013, Graph Theory, Master of Applied Mathematics and
Mathematical Engineering, FME
Fall 2012, Probability Theory, Grau de Matemàtiques, FME
Fall 2012, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
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