Oriol Serra
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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: oserra@ma4.upc.edu |
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Jordi
Girona, 1 |
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E-08034 Barcelona, Spain |
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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,
in the board of the Societat
Catalana de Matemàtiques,
member of the Council of EMS, Editor of the Butlletí de l'SCM and in the
editorial board of Integers and Electronic Journal of Graph Theory and
Applications
I am also involved in the
following activities
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
Seminar Combinatorics, Graph Theory and Applications
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
Recent preprints and papers
O.
Serra and L. Vena, On
the number of monochromatic solutions of integer linear systems on Abelian groups, submitted to 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, submitted to 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, to
appear in 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, submitted to 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,
submitted to Discrete Appl. Math
Asymptotic almost
sure values of the
treedepth of random graphs
A.
Montejano
and O. Serra, Counting patterns in
colored orthogonal arrays, submitted to 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 , submitted to 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, to appear in 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, to appear 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, to appear in 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, to appear in 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.
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