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Mardi 19 Avril
| Heure: |
14:00 - 17:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
On Noncrossing Partitions for the Alternating Groups |
| Description: |
Henri Mühle The lattice of noncrossing set partitions of an n-set can beseen as a subgraph of the Cayley graph of the symmetric group S generated by all transpositions. We mimic thisconstruction for the alternating group A2n+1 generated byall 3-cycles. The resulting poset provides a rich new source ofcombinatorics coming from the alternating groups, which in some senseparallels the combinatorics behind the noncrossing set partitions. Wepresent some enumerative and bijective results, and suggest an extensionof this construction to all finite Coxeter groups. This is joint workwith Philippe Nadeau. |
Vendredi 22 Avril
| Heure: |
11:00 - 12:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
New Results on Morris's Observational Theory: the benefits of separating the inseparable |
| Description: |
Giulio Manzonetto We study the theory of contextual equivalence in the untyped lambda-calculus, generated by taking the normal forms as observables. Introduced by Morris in 1968, this is the original extensional lambda theory H+ of observational equivalence.
On the syntactic side, we show that this lambda-theory validates the omega-rule, thus settling a long-standing open problem. On the semantic side, we provide sufficient and necessary conditions for relational graph models to be fully abstract for H+. We show that a relational graph model captures Morris's observational pre-order exactly when it is extensional and lambda-König. Intuitively, a model is lambda-König when every lambda-definable tree has an infinite path which is witnessed by some element of the model.
Joint work with Flavien Breuvart, Domenico Ruoppolo & Andrew Polonsky |
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