Oriol Serra Personal Page
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Address: |
Tel. 34-93 401 5996 |
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FAX: 34-93 401 5981 |
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Mòdul C3, Campus Nord |
e-mail: oriol.serra at upc.edu |
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Jordi Girona, 1 |
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E-08034 Barcelona, Spain |
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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
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, ESF-EMS-ERCOM Conference June 2012
Advanced Course: Combinatorial Convexity, by Imre Leader, May 2012
RSME-SMM Joint Meeting, Jan 2012
Research
Research interests
Recent preprints and papers
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.
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 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.
Juanjo Rué, Oriol Serra, Lluís Vena, Counting 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, 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 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.
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.
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.
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. 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.
Teaching
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
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