Oriol Serra 


 


Address:

 Tel.     34-93 401 5996

Departament de Matemàtica Aplicada 4       

FAX:  34-93 401 5981

Mòdul C3, Campus Nord

e-mail:  oriol.serra at upc.edu

Universitat Politècnica de Catalunya

 

Jordi Girona, 1   

 

E-08034 Barcelona, Spain

 


                
Current Activities

Research

Teaching

 

Short CV


Current Activities

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

EuroComb 2013, September2013

CSASC 2013, June 2013

IWONT 2012, July 2012

Additive Combinatorics in Paris, July 2012

JMDA 2012

Perspectives in Discrete Mathematics, ESF-EMS-ERCOM Conference June 2012

Advanced Course: Combinatorial Convexity, by Imre Leader, May 2012

RSME-SMM Joint Meeting, Jan 2012

CSASC 2011, September 2011

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

Advanced Course: Polymatroids etc, by Jack Edmonds, Jan 11-21 2010

 


Research

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 d-dimensional 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 |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,   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 edge-coloring 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, 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,   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 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,   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.

 


Teaching

 

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