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Seminari de Geometria Algebraica UPC-UB
http://www.ub.edu/sga/
Álvaro del Pino Gómez (CSIC-ICMAT)

Open problems in Engel geometry http://www.ub.edu/sga/seminari1516/delpino.pdf

Divendres 29 d'abril, 15 h, Aula B1, Facultat de Matemàtiques, Edifici Històric, Universitat de Barcelona

Title: Graphs, hypergraphs and dominating sets
Speaker: MERCÈ MORA

Thursday, April 28, 2016, 13:15-14:15 (15 minutes delayed with respect to the usual schedule)
Room S215 Omega Building, Campus Nord UPC (equiv.: Room 215 Floor -2) 

Abstract: A 'simple hypergraph' is a collection of non-comparable subsets of a set of vertices. The elements of the hypergraph are called 'hyperedges'. A graph can be viewed as a hypergraph with hyperedges of size 2.

Many concepts of graphs give rise to a collection of subsets of vertices that allows us to consider hypergraphs associated with the graph by considering the collection of minimal or maximal elements. Namely, we will handle with the collection of closed neighborhoods, dominating sets, vertex covering sets and independent sets. We study the relationships between them by using some hypergraph operations.

Finally, we focus on the case of dominating sets. A hypergraph is a 'domination hypergraph' if it is the collection of the minimal dominating sets of some graph. We are interested in determining when a hypergraph is a domination hypergraph and, if it is not the case, we seek domination hypergraphs close to it, the domination completions. Moreover, we prove that the hypergraph is univocally characterized by some domination completions, the 'minimal domination completions'.

We discuss in more detail the case of k-uniform complete 'hypergraphs', that is, hypergraphs containing all the k-subsets of a set of vertices. 

Joint work with Jaume Martí-Farré and José Luis Ruiz.

Abstract: A simple hypergraph is a collection of non-comparable subsets of a set of vertices. The elements of the hypergraph are called hyperedges. A graph can be viewed as a hypergraph with hyperedges of size 2. 

Many concepts of graphs give rise to a collection of subsets of vertices that allows us to consider hypergraphs associated with the graph by considering the collection of minimal or maximal elements. Namely, we will handle with the collection of closed neighborhoods, dominating sets, vertex covering sets and independent sets. We study the relationships between them by using some hypergraph operations.
Finally, we focus on the case of dominating sets. A hypergraph is a domination hypergraph if it is the collection of the minimal domination sets of some graph. We are interested in determining when a hypergraph is a domination hypergraph and, if it is not the case, we seek domination hypergraphs close to it, the domination completions. Moreover, we prove that the hypergraph is univocally characterized by some domination completions, the minimal domination completions. We discuss in more detail the case of k-uniform complete hypergraphs/, that is, hypergraphs containing all the k-subsets of a set of vertices.

Joint work with Jaume Martí-Farré and José Luis Ruiz.

Activities are regularly announced a
http://www-ma2.upc.edu/dccg/upc-seminar-on-computational-geometry/

This two-day conference will feature talks by graduate and post-graduate students from different universities. The common theme is symplectic geometry and dynamical systems. More details can be found on our website http://juniorgesta.wordpress.com/

Attention: change of room. The conference will take place in Sala de Graus (EPSEB).

 List of speakers

* Roisin Braddell (Université de Bordeaux)
* Damien Bouloc (Université Toulouse Paul Sabatier)
* Álvaro del Pino Gomez (ICMAT Madrid)
* Anna Kiesenhofer (UPC Barcelona)
* Cédric Oms (Université Libre de Bruxelles)
* Jose Luis Perez Garcia (ICMAT Madrid)
* Samuel Ranz (ICMAT Madrid)
* Abdó Roig (UPC Barcelona)
* Carles Sáez (Universitat de Barcelona)
* Rodrigo Schaefer (UPC Barcelona)

This two-day conference will feature talks by graduate and post-graduate students from different universities. The common theme is symplectic geometry and dynamical systems. More details can be found on our website http://juniorgesta.wordpress.com/.

List of speakers

• Roisin Braddell (Université de Bordeaux)
• Álvaro del Pino Gomez (ICMAT Madrid)
• Anna Kiesenhofer (UPC Barcelona)
• Cédric Oms (Université Libre de Bruxelles)
• Jose Luis Perez Garcia (ICMAT Madrid)
• Samuel Ranz (ICMAT Madrid)
• Abdó Roig (UPC Barcelona)
• Carles Sáez (Universitat de Barcelona)
• Rodrigo Schaefer (UPC Barcelona)

Given some random variables X_1, ... , X_n, one can form a vector of size 2^n-1 with the entropies of subsets of variables: [H(X_1), H(X_2), H(X_1,X_2), ... , H(X_1,...,X_n)]. The set of all possible such vectors is an object in the Euclidean space delimited by hyperplanes: information inequalities. Perhaps the most famous inequality is Shannon's basic inequality H(A,C) + H(B,C) = H(A) + H(A,B,C). We will see which role do these inequalities play in problems like secret sharing. I will also discuss a recent result on the geometry of inequalities based on duality of polymatroid.

by Folco Casadei from formerly At Joint Research Centre, Ispra, Italy Institute for the  Protection And Security of the Citizen European Laboratory for Structural Assessment