March 2018 - Seminaire.calin

Seminaires CALIN a 11h et 14h aujourd'hui
by Thierry Monteil 27 Mar '18

27 Mar '18

Bonjour, Ce matin mardi 27 mars à 11h00 en B107, Gleb Koshevoy nous parlera de : Combinatorial bases of KZ_n (discussion). Cet après-midi, à 14h00 en B107, le même Gleb Koshevoy nous parlera de : Cluster relations among Schur functions and a positivity conjecture Résumé : 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. Bonne journée, Thierry

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Seminaire CALIN ce mardi : matin et apres-midi
by Thierry Monteil 19 Mar '18

19 Mar '18

Bonjour, ce mardi 20 mars 2018 à 10h30 en B107, Sergey Dovgal nous parlera de : Pólya enumeration theorem from scratch III Résumé : I am going to talk about very popular combinatorial connection between ordinary and exponential generating functions which is called cycle index function. I am going to define the combinatorial species according to the book "Theory of Species" by Bergeron, Labelle, Leroux, and present their beautiful proof of the cycle index composition theorem. The proof relies on the theory of symmetric functions in infinitely many variables. This proof is a beautiful example of Grothendieck's concept: in order to prove something particular, one should make a more general statement and prove it. L'après-midi, à 14h00 en B107, Antoine Deza nous parlera de : On lattice polytopes, convex matroid optimization, and degree sequences of hypergraphs Résumé : We introduce a family of polytopes, called primitive zonotopes, which can be seen as a generalization of the permutahedron of type Bd. We discuss connections to the largest diameter of lattice polytopes and to the computational complexity of multicriteria matroid optimization. Complexity results and open questions are also presented. In particular, we answer a question raised in 1986 by Colbourn, Kocay, and Stinson by showing that deciding whether a given sequence is the degree sequence of a 3-hypergraph is computationally prohibitive. Based on joint works with Asaf Levin (Technion), George Manoussakis (Paris Sud), Shmuel Onn (Technion). À demain, Thierry

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Seminaire CALIN ce mardi : matin et apres-midi
by Thierry Monteil 05 Mar '18

05 Mar '18

Bonjour, ce mardi 06 mars 2018 à 10h30 en B107, Sergey Dovgal nous parlera de : Pólya enumeration theorem from scratch II + discussion Résumé : I am going to talk about very popular combinatorial connection between ordinary and exponential generating functions which is called cycle index function. I am going to define the combinatorial species according to the book "Theory of Species" by Bergeron, Labelle, Leroux, and present their beautiful proof of the cycle index composition theorem. The proof relies on the theory of symmetric functions in infinitely many variables. This proof is a beautiful example of Grothendieck's concept: in order to prove something particular, one should make a more general statement and prove it. L'après-midi, à 14h00 en B107, Sidi Mohamed Sedjelmaci nous parlera de : Two fast parallel GCD algorithms of many integers Résumé : On montre que le calcul du PGCD de 𝑚 integers de 𝑂(𝑛) bits peut se faire en parallèle en temps 𝑂(𝑛 / log 𝑛) avec 𝑂(𝑚𝑛1+𝜖 ) processors, pour tout 2 ≤ 𝑚 ≤ 𝑛3/2 / log 𝑛, c'est-à-dire que le temps de calcul en parallèle ne dépend pas dépend du nombre d'entiers m considéré dans cet intervalle. À demain, Thierry

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