Oriol Serra





Room C3113, Campus Nord 


Tel. +34 934
015 996 

Jordi Girona, 1 
FAX +34 934 015 981 

E08034 Barcelona, Spain 
email: oriol.serra at upc.edu 
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
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
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 wellknown FreimanRuzsa Theorem provides a
structural description of a set of integers with small doubling as a dense
subset of a ddimensional 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 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, 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 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.
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)
5577
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 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.
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 are provided. The result for p=c/n, c>1, is derived from the
computation of treewidth and provides a more direct proof of a conjecture by
Gao on the linearity of treewidth 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 treedepth.
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 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.
The structure of 3colorings 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 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.
The Bonenesen inequality is an strenghtenning of the
BrunnMinkowski 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