Room C3-113, Campus Nord
Universitat
Politècnica de Catalunya
Jordi Girona,1
E-08034 Barcelona, Spain
Tel.
+34 934 015 996
FAX
+34 934 015 981
e-mail: oriol.serra at upc.edu
|
Address Room C3-113, Campus Nord Universitat
Politècnica de Catalunya Jordi Girona,1 E-08034 Barcelona, Spain |
Tel.
+34 934 015 996 FAX
+34 934 015 981 e-mail: oriol.serra at upc.edu |
Short
Bio
I am or have been involved as organizer, member of program committee or invited speaker in the following activities in the last five years
European
Conference in Combinatorics, Graph Theory and applications,
September 2021, Barcelona
2nd GAPCOMB Workshop,
July 2021, Montserrat
Combinatorial
and Additive Combinatorics, CANT 2021, May 2021, New York
Colloquia
in Combinatorics, May 2021, London
Combinatorial
and Additive Combinatorics, CANT 2020, May2020, New York
European
Conference in Combinatorics, Graph Theory and applications, August
2019, Bratislava
British
Combinatorial Conference, Birmingham, July 2019
1st GAPCOMB Workshop,
Campelles, June 2019
DIAMANT
Symposium, April 2019, Eindhoven
Joint
meeting of the Czech, Slovak, Austrian, Slovenian and Catalan Math
societies, September 2018, Bratislava
7th
Polish Combinatorial conference, Bedlewo, 2018
21st
International Workshop for Young Mathematicians, Krakow 2018
Discretaly:
A Workshop on Discrete Mathematics, Roma, February 2018
Journées
Combinatoire et Algorithmes du Littoral Méditerranéen,
Barcelona, 2018
The
Music of Numbers: a tribute to Javier Cilleruelo, September 2017,
Madrid
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
Alberto Espuny
Díaz, Patrick Morris, Guillem Perarnau, Oriol Serra Speeding
up random walk mixing by starting from a uniform vertex (Arxiv,
2022)
The mixing time of random walks is usually affected by local
bottlenecks which may distort its general performance, that may be
better reflected by average mixing times. A general framework for
analyzing average mixing times in graphs with small bottlenecks is
introduced and two main applications are given, reducing to log n the
mixing times of randomly perturbed graphs with bounded degeneracy and
of percolated expander graphs.
Jan
Hubička, Jaroslav Nešetřil, Pablo Oviedo, Oriol Serra On
the Homomorphism Order of Oriented Paths and Trees (Arxiv,
2022)
Universality of homomorphism orders is an amazing property that
illustrates its richness: it contains every countable partial order.
Here universality is proved for the class of oriented paths and
trees of height at least four, completing a program in this direction
started some decades ago.
Marcelo
Campos, Matthew Coulson, Oriol Serra, Maximilian Wötzel The
typical approximate structure of sets with bounded sumset (Arxiv
2021)
Sets of
integers with small sumset are structured in multidimensional
progresions. To what extent this general theorem of Freiman extends to
not so small sumsets is witnessed by analyzing the typical structure
of such sets. Campos showed that not too small sets with doubling only
relatively small are typically mostly dense in short intervals. The
paper extends the result to its asymmetric version with two distinct
sets. The setting is interesting as sampling sets with small sumset is
a nontrivial task, which is achieved by the containers method.
Díaz,
Josep; Diner, Öznur Yaşar; Serna, Maria; Serra, Oriol The
multicolored graph realization problem, Discrete Applied
Mathematics (2022) (online version)
We introduce a natural clustering problem: given a colored graph
ask if a given graph can be realized as a multicolored subgraph. The
complexity of the problem is analyzed and a dicothomy with respect
to the cluster size is obtained.
Fiz
Pontiveros, Gonzalo; Griffiths, Simon; Secco, Matheus; Serra, Oriol Deviation
probabilities for arithmetic progressions and other regular discrete
structures. Random Structures Algorithms 60 (2022), no. 3,
367–405.
Inspired by a
paper by Goldsmith, Griffiths and Scott which study moderate
deviations in subgraph counts in the G(n,m) model we study the
similar problem for arithmetic structures. We give
essentially tight bounds for the deviation probabilities by
counting edges in random subhypergraphs of hypergraphs with
apropriate regularity conditions.
Bosek, Bartłomiej; Grytczuk, Jarosław; Gutowski, Grzegorz; Serra, Oriol; Zając, Mariusz Graph polynomials and group coloring of graphs. European J. Combin. 102 (2022), Paper No. 103505, 11 pp.
One
of the features of the Combinatorial Nullstellensatz is to count the
number of nonzero points of a multivariate polynomial on a grid, a
theorem of Alon and Füredi. By applying this method one can improve
the bound on the number of group colorings of a planar graph
established by Langhede and Thomassen, and extend the results to
more general classes and more general types of group colorings.
Candela, Pablo; Catalá, Carlos; Rué, Juanjo; Serra, Oriol On Motzkin's problem in the circle group. (Russian) English version published in Proc. Steklov Inst. Math. 314 (2021), no. 1, 44–63. Tr. Mat. Inst. Steklova 314 (2021), Analiticheskaya i Kombinatornaya Teoriya Chisel, 49–70.
Extensions
to abelian compact groups of problems in discrete groups is an
interesting trend in combinatorics. Here the classical Motzkin
problem on the largest density of sets of integers with given
missing differences is treated in the circle group. When all
differences are rational the problem is related to the independence
ratio of circulant graphs, a problem still wide open.
Lladó,
Anna; Mokhtar, Hamid; Serra, Oriol; Zhou, Sanming Distance-constrained
labellings of Cartesian products of graphs. Discrete Appl. Math.
304 (2021), 375–383.
Distance constrained labellings L(2,1) require that vertices at
distance 1 are at least 2 apart and vertices at distance two
are distinct. This parameter has been widely studied and can be
generalized to a larger number of parameters requiring
prescribed separation of labels for vertices at given distances.
This paper studies these parameters in Cartesian products of graphs,
in particular the Hamming graphs and the n-cube. In particular a
problem of computing the chromatic number of powers of the n-cube is
solved.
Díaz,
Josep; Diner, Öznur Yaşar; Serna, Maria; Serra, Oriol On
list k-coloring convex bipartite graphs. Graphs and
combinatorial optimization: from theory to applications—CTW2020
proceedings, 15–26, AIRO Springer Ser., 5, Springer, Cham, [2021],
©2021.
List k-Coloring (Li k-Col) is the decision problem asking if a
given graph admits a proper coloring compatible with a given list
assignment to its vertices with colors in {1,2,..,k}. The problem is
known to be NP-hard even for k=3 within the class of 3-regular
planar bipartite graphs and for k=4 within the class of chordal
bipartite graphs. In 2015, Huang, Johnson and Paulusma asked for the
complexity of Li 3-Col in the class of chordal bipartite graphs. In
this paper we give a partial answer to this question by showing that
Li k-Col is polynomial in the subclass of convex bipartite graphs.
Matolcsi and
Ruzsa suggested an attractive discrete version of the Brunn-Minkowski
inequality in the plane. In this paper an extension of this conjecture
for arbitrary dimensions is proposed and several particular cases are
proved. The proof reveals intriguing difficulties in the proof of this
natural version.
Gregory A.
Freiman, Oriol Serra, Christoph Spiegel Additive
Volume of Sets Contained in Few Arithmetic Progressions, Integers
19 (2919)
A conjecture of Freiman gives an exact formula for the largest volume
of a finite set A of integers with given cardinality k=|A| and
doubling T=|2A|. The formula is known to hold when T≤3k−4, for some
small range over 3k−4 and for families of structured sets called
chains. In this paper we extend the formula to sets of every dimension
and prove it for sets composed of three segments, giving structural
results for the extremal case. A weaker extension to sets composed of
a bounded number of segments is also discussed.
Christine Bachoc,
Oriol Serra, Gilles Zémor, Revisiting
Kneser’s theorem for field extensions, Combinatorica 38 (2018),
no. 4, 759–777.
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.
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
result which uses some particularly chosen random subgraphs.
See all papers in
Mathscinet and in Arxiv
Oriol Serra, Límits
de graphs (Catalan) , Butlletí de la Societat Catalana de
Matemàtiques, Vol. 35 (1) 2020
Marc Noy, Oriol Serra. Perspectivas
en combinatoria (in Spanish). Boletín de la Real Sociedad Española
de Matemáticas 19 (2016)
Plagne, Alain; Lladó, Anna; Serra, Oriol. Yahya Ould Hamidoune,
1948–2011. (Catalan) SCM Not. No. 32 (2012), 14–17.
Lugosi, Gábor; Serra, Oriol Endre
Szemerédi, 2012 Abel Prize. (Catalan) Butl. Soc. Catalana Mat. 28
(2013), no. 1, 87–115, 118.
Plagne, Alain; Serra, Oriol; Zémor, Gilles Yahya
Ould Hamidoune's mathematical journey: a critical review of his work.
European J. Combin. 34 (2013), no. 8, 1207–1222.
Serra, Oriol. Endre Szemerédi, 2012 Abel Prize. (Catalan) SCM Not. No.
33 (2013), 42–43.
Serra, Oriol The
Brunn-Minkowski inequality. (Catalan) Butl. Soc. Catalana Mat. 26
(2011), no. 2, 185–220, 223.
Serra, Oriol. 2006 Fields Medal: Terence Tao. (Catalan) SCM Not.
No. 23 (2007), 52–53.
Serra, Oriol. Andrei Nikolaievich Kolmogorov (1903–1987).
(Catalan) SCM Not. No. 19 (2003), 10–12.
Serra, Oriol Problemas
aditivos y grafos de Cayley. (Spanish) Gac. R. Soc. Mat. Esp. 4
(2001), no. 3, 639–648.
Spring 2023
Combinatorics,
Master of Applied Mathematics and Mathematical Engineering, FME
Spring 2023 Complex Analysis, Grau de matemàtiques, FME
Fall 2022 Graph
Theory, Master of Applied Mathematics and Mathematical
Engineering, FME
Fall 2022 Probability
and Statistics 2, Degree in Data Science and Engineering,
FIB/ETSETB/FME
Fall 2022 Probability
and Stochastic Processes, Degree in Electronic Engineering, ETSETB
Spring 2022 Combinatorics,
Master of Applied Mathematics and Mathematical Engineering, FME
Spring 2022 Probability
and Statistics 1, Degree in Data Science and Engineering,
FIB/ETSETB/FME
Fall 2021 Combinatorics and Graph Theory, Grau de Matemàtiques, FME
Fall 2021 Probability and Statistics 2, Degree in Data Science and
Engineering, FIB/ETSETB/FME
Fall 2021, Discrete Mathematics and Optimization, Degree in
Bioinformatics, FIB-UPC/UPF/UAB
Spring 2021, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
Spring 2021, Probability and Statistics 1, Degree in Data Science and
Engineering, FIB/ETSETB/FME
Fall 2020 Combinatorics and Graph Theory, Grau de Matemàtiques, FME
Fall 2020, Discrete Mathematics and Optimization, Degree in
Bioinformatics, FIB-UPC/UPF/UAB
Fall 2020, Probability and Statistics 2, Degree in Data Science and
Engineering, FIB
Spring 2020, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
Spring 2020, Probability and Statistics 1, Degree in Data Science and
Engineering, FIB
Spring 2020, Discrete Mathematics, Degree in Mathematics, FME
Fall 2019, Combinatorics and Graph Theory, Grau de Matem�tiques, FME
Fall 2019, Graph Theory, Master of Applied Mathematics and Mathematical
Engineering, FME
Fall 2019, Discrete Mathematics and Optimization, Degree in
Bioinformatics, FIB-UPC/UPF/UAB
Fall 2019, Probability and Statistics 2, Degree in Data Science and
Engineering, FIB
Spring 2019, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
Spring 2019, Probability and Statistics 1, Degree in Data Science and
Engineering, FIB
Spring 2019, Discrete Mathematics, Degree in Mathematics, FME
Fall 2018, Combinatorics and Graph Theory, Grau de Matemàtiques, FME
Fall 2018, Graph Theory, Master of Applied Mathematics and Mathematical
Engineering, FME
Fall 2018, Discrete Mathematics and Optimization, Degree in
Bioinformatics, FIB-UPC/UPF/UAB
Fall 2018, Probability and Statistics 2, Degree in Data Science and
Engineering, FIB
Spring 2018, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
Spring 2018, Probability and Statistics 1, Degree on Data Science and
Engineering, FIB
Fall 2017, Combinatorics and Graph Theory, Grau de Matemàtiques, FME
Fall 2017, Graph Theory, Master of Applied Mathematics and Mathematical
Engineering, FME
Fall 2017, Discrete Mathematics and Optimization, Degree in
Bioinformatics, FIB-UPC/UPF/UAB
Spring 2017, Combinatorics, Master of Applied Mathematics and
Mathematical Engineering, FME
Spring 2017, Real Analysis, Grau de matemàtiques, FME