Oriol Serra

 

 

 

Departament de Matemàtiques

 

Room C3-113, Campus Nord

 

Universitat Politècnica de Catalunya

Tel.     +34 934 015 996

Jordi Girona, 1   

FAX    +34 934 015 981 

E-08034 Barcelona, Spain

e-mail:  oriol.serra at upc.edu

 

Current Activities

Research

Teaching

 

 

Short CV

 

 

 

 

 

 


Current Activities

 

I am currently serving as  chair of the Departament de Matemàtiques, director of OSRM, responsible of the research group Combgraph, member of the Scientific Committee of the Barcelona Graduate School in Mathematics, 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 involved in the following activities in the last five years

 

European Conference on Combinatorics, Graph Theory and Applications, August 2017, Vienna

Interactions with Combinatorics, June 2017, University of Birmingham

Random Discrete Structures and Beyond, Barcelona, June 2017

Interactions of harmonic analysis, combinatorics and number theory, Barcelona May 2017

Bordeaux Graph Workshop, Bordeaux, November 2016

CSASC 2016, Barcelona, September 2016

International Workshop on Optimal Network Topologies, Tingshua Sanya, July 2016

Gregory Freiman celebration, Tel Aviv, July 2016

Discrete Mathematical Days, Barcelona, July 2016

Additive Combinatorics in Bordeaux, Bordeaux, April 2016

_A conference celebrating 65th birthday of R. Balasubramanian_, Chennai, December 2015

Cargèse fall school on random graphs, Cargèse (Corsica), September 2015

Additive Combinatorics in Marseille 2015, CIRM, September 2015

EuroComb 2015, Bergen, September 2015

Workshop on Algebraic Combinatorics, Tilburg, June 2015

Congreso de la RSME, Granada, February 2015

Graph labelings, graph decompositions and Hamiltonian cycles, CIMPA Rschool, Vientianne, December 2014

Bordeaux Graph Workshop 2014, Bordeaux November 2014

Barcelona Mathematical Days, Barcelona, November 2014

Jornadas de Matemática Discreta y Algorítmica, JMDA2014, Tarragona, July 2014

Second Joint International Meeting of the  Israel Mathematical Union and the American Mathematical Society, Tel Aviv, June 2014

Workshop on Diophantine Problems, Graz, May 2014

Unlikely Intersections, CIRM February 2014

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

 

 

 

 

 

 

 

 

 

 

 

 

 


Research

 

Research interests

 

Additive Combinatorics

Extremal Graph Theory

Discrete Isoperimetric problems

 

 

Recent  preprints and papers

 

 

 

Gregory A. Freiman and Oriol Serra, On Doubling and Volume: Chains, submited

 

The well--known Freiman-Ruzsa Theorem provides a structural description of a set of integers with small doubling as a dense subset of a d--dimensional arithmetic progression.  The estimation of the density and dimension involved in the statement has been the object of intense research. Freiman conjectured in 2008 an exact formula for the largest volume of such a set. In this paper we prove the conjecture for a general class of sets called chains.

 

 

Víctor Diego, Oriol Serra, Lluís Vena, On a problem of Shapozenko on Johnson graphs, submitted

 

The problem refers to the characterization of sets with smallest vertex boundary for given cardinality in the Johnson graphs J(n,m). In the paper a solution for fixed cardinality and large n is shown to be the initial segment of the colex order, perhaps as expected. However an unexpected exception to this fact is also reported. 

 

 

Juanjo Rué, Oriol Serra, Lluís VenaCounting configuration-free sets in groups , submitted

 

By combining the hypergraph container method and the removal lemma for homomorphisms, counting results for the number of configurations in subsets of abelian groups are obtained. Sparse analogs for random subsets are also obtained, by obtaining threshold probabilities for the existence of configurations in random sets. These extend the sparse versions of  Szemerédi theorem obtained by Conlon and Gowers, by Schacht, by Balog, Morris and Samotij and by Saxton and Thomason.

 

 

 

Christine Bachoc, Oriol Serra, Gilles Zémor, Revisiting Kneser’s theorem for field extensions, to appear in  Combinatorica (2017) 

A Theorem of Hou, Leung and Xiang generalised Kneser's addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou's conjecture. This result is a consequence of a strengthening of Hou et al.'s theorem that is a transposition to extension fields of an addition theorem of Balandraud.

 

  

Christine Bachoc, Oriol Serra, Gilles Zémor, An analogue of Vosper's Theorem for Extension Fields, to appear in Math. Proc. Camb. Phil. Soc. (2017)

 

Linear extensions of classical problems in additive combinatorics have been recently obtained in the literature. Inverse theorems, where one aims at providing the structure of sets with small sumset, where not discussed in this setting. The simplest one, Vosper theorem, is proved in this paper by using the approach of the isoperimetric method. What makes the paper particularly interesting is the connection with MSD codes in spaces of bilinear forms and the use of the Delsarte linear programing method.

 

 

Florent Foucaud, Guillem Perarnau, Oriol Serra, Random subgraphs make identification affordable, Journal of Combinatorics 8(1) (2017) 55-77

 

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.

 

 

 

Guillem Perarnau, Oriol Serra, Correlation among runners and some results on the Lonely Runner Conjecture, Electronic Journal of Combinatorics, 23(1) (2016) Paper #P1.50 (22pp)

 

This paper provides an improvement on the trivial bound for the Lonely Runner Problem by using an approach based on Hunter’s theorem on the Bonferroni inequalities. It also contains an improved bound (already known) for the case of n runners when 2n-3 is a prime and a nice setting on dynamic circular graphs suggested by J. Grytzuk. A recent post by Terry Tao comments on the problem.

 

 

Karoly Boroczky, Francisco Santos, Oriol Serra, On sumsets and convex hull, Discrete Comput. Geom.52 (2014), no. 4, 705–729.

 

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.

 

 

 

O. Serra and L. Vena, On the number of monochromatic solutions of integer linear systems on Abelian groups,    European J. Combin. 35 (2014), 459–473.

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.

 

 

G. Perarnau, O. Serra, On the treedepth of random graphsDiscrete Appl. Math. 168 (2014), 119–126. 

 

Asymptotic almost sure values of the treedepth of random graphs are provided. The result for p=c/n, c>1, is derived from the computation of tree-width and provides a more direct proof of a conjecture by Gao on the linearity of tree-width recently proved by Lee, Lee and Oum. We also show that, for c=1, every width parameter is a.a.s. constant, and that random regular graphs have linear tree-depth. 

 

Montejano and O. Serra, Counting patterns in colored orthogonal arrays,   Discrete Math. 317 (2014), 44–52.

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.

 

 

O. Serra, G. Zémor, A Structure Theorem for Small Sumsets in Nonabelian Groups,    European J. Combin. 34 (2013), no. 8, 1436–1453.

 

If a set in a S nonabelian 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.

 

 

W. Dicks and O.  Serra,  The Dicks-Ivanov problem and the Hamidoune problem. European J. Combin. 34 (2013), no. 8, 1326–1330.

 

This is a note on a problem of Hamidoune related to a theorem by Pollard on estimations of sets in a product which admit more than two representations. On a special volume devoted to Hamidoune.

 

 

G. Perarnau, O. Serra, Rainbow Matchings: Existence and Counting,  Combin. Probab. Comput. 22 (2013), no. 5, 783–799.

 

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. A. Freiman, D. Grynkiewicz, O. Serra, Y. V. Stanchescu, Inverse Additive Problems for Minkowski Sumsets II,  J. Geom. Anal. 23 (2013), no. 1, 395–414.

 

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,  Collectanea Mathematica, 63 (2012),   Issue 3,  261-286.

 

A discrete version in dimension two of the Bonessen strengthening of the Brunn—Minkowski inequality.

 

 

D. Král, O. Serra and L. Vena, On the Removal Lemma for Linear Systems over Abelian Groups ,   European J. Combin. 34 (2013), no. 2, 248–259.

 

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 , Electron. J. Combin. 19 (2012), no. 1, Paper 45, 20 pp.  

 

The structure of 3-colorings of abelian groups which have no rainbow AP(3) is given. 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. Math. 187 (2012), 193–207.

   

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.

 

 

K.J. Böröczky and O.Serra,  Remarks on the equality case of the Bonnesen inequality. Arch. Math. (Basel) 99 (2012), no. 2, 189–199. 

 

The Bonenesen inequality is an strenghtenning of the Brunn-Minkowski inequality for which the equality case is characterized for the version of projections. Here the Schwarz rounding method is used.

 

 

 

 

 

 

 

 

 

 

 

 


Teaching

 

Spring 2017, Combinatorics, Master of Applied Mathematics and Mathematical Engineering, FME

Spring 2017, Real Analysis, Grau de matemàtiques, FME

 

Fall 2016, Combinatorics and Graph Theory, Grau de Matemàtiques, FME

Fall 2016, Probability and Stochastic  Processes, Master in Statistics and Operation Research, FME

Fall 2016, Graph Theory, Master of Applied Mathematics and Mathematical Engineering, FME

Fall 2016, Probability Theory, Grau de Matemàtiques, FME

 

 

Spring 2016, Combinatorics, Master of Applied Mathematics and Mathematical Engineering, FME

 

Fall 2015, Combinatorics and Graph Theory, Grau de Matemàtiques, FME

Fall 2015, Probability and Stochastic  Processes, Master in Statistics and Operation Research, FME

Fall 2015, Graph Theory, Master of Applied Mathematics and Mathematical Engineering, FME

Fall 2015, Probability Theory, Grau de Matemàtiques, FME

Spring 2015, Combinatorics, Master of Applied Mathematics and Mathematical Engineering, FME

 

Fall 2014 , Probability Theory, Grau de Matemàtiques, FME

Fall 2014, Probability and Stochastic  Processes, Master in Statistics and Operation Research, FME

Fall 2014, Graph Theory, Master of Applied Mathematics and Mathematical Engineering, FME

 

Spring 2014, Combinatorics, Master of Applied Mathematics and Mathematical Engineering, FME

 

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