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 Matemàtiques, director of OSRM,
responsible with Prof. J. Fàbrega of the research group Combgraf, Scientific Committee
member 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 also involved in the following activities
Discrete Mathematical Days, Barcelona,
July 2016
Additive Combinatorics in
Bordeaux, Bordeaux, April 2016
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
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
Research interests
Additive Combinatorics
Extremal Graph Theory
Discrete Isoperimetric
problems
Recent preprints and papers
Christine Bachoc, Oriol Serra, Gilles Zémor, Revisiting Kneser’s theorem
for field extensions, submitted.
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 nonseparable
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.
Juanjo Rué, Oriol Serra,
Lluís Vena, Counting
configurationfree 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, An analogue of Vosper's Theorem for
Extension Fields, submitted
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.
Guillem Perarnau, Oriol Serra, Correlation
among runners and some results on the Lonely Runner Conjecture, to appear in
Electronic Journal of Combinatorics (2016)
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 2n3 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
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, to appear in Journal of
Combinatorics (2016)
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, 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 graphs, Discrete Appl. Math. 168 (2014), 119–126.
Asymptotic
almost sure values of the treedepth of
random graphs.
A.
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 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.
W. Dicks and O.
Serra, The DicksIvanov 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
edgecoloring 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, 261286.
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, Rainbowfree 3coloring of abelian groups , Electron. J. Combin. 19 (2012), no. 1, Paper
45, 20 pp.
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. 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 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.
K.J. Böröczky and O.Serra, Remarks on the equality case of the
Bonnesen inequality. Arch. Math. (Basel) 99 (2012), no. 2, 189–199.
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