Mardi 27 Mars


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Mardi 27 Mars
Heure: 11:00 - 12:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Combinatorial bases of KZn
Description: Gleb Koshevoy TBA (discussion)
Heure: 12:30 - 13:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Complexity of the cluster deletion problem on cographs and subclasses of chordal graphs
Description: Mario Valencia Pabon We consider the following vertex-partition problem on graphs,
known as the CLUSTER DELETION (CD) problem: given a graph with real
nonnegative edge weights, partition the vertices into clusters (in this
case, cliques) to minimize the total weight of edges outside the
clusters. The decision version of this
optimization problem is known to be NP-complete even for unweighted
graphs and has been studied extensively. In this talk, I will focus on
the complexity of the decision CD problem for the family of chordal
graphs, showing that it is NP-complete for weighted split graphs,
weighted interval graphs and unweighted chordal graphs. We will also see
that the problem is NP-complete for weighted cographs. Some
polynomial-time solvable cases of the optimization problem will be
identified, in particular CD for unweighted cographs, split graphs,
unweighted proper interval graphs and weighted block graphs.

This is a joint work with Flavia Bonomo and Guillermo Duràn (University
of Buenos Aires).
Heure: 14:00 - 15:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Cluster relations among Schur functions and a positivity conjecture
Description: Gleb Koshevoy Cluster algebras, invented by Sergey Fomin and Andrei Zelevinsky around 2000,
are commutative algebras whose generators and relations are constructed in a recursive manner.
Due to cluster recursion we obtain Laurent polynomials in the initial variables, so-called Laurent
phenomenon of cluster algebras. The coordinate ring of base affine space C[N_-SL_n] plays an important role in representation theory and is endowed with a cluster algebra structure. We show that under specialization of minors to Schur functions, Laurent polynomials of this cluster algebra turn into 'homogeneous' sums of Schur function. A positivity conjecture says that these sums have positive coefficients. This conjecture is true for finite cluster subalgebras.