[Todos] Charla de Daniele Mundici en el coloquio del Depto de MatemátiMatemática

[Juan José Guccione]

Hola: el jueves 25 de agosto a las 16 hs, en el aula 2, expondrá en el
Coloquio del Departamento de Matemática el Profesor Daniele Mundici
de Departmento de Matemática "Ulisse Dini" de la Universidad de Florencia.

Título: Polyhedra, fans and logic.

Resumen: C.C.Chang's MV-algebras stand to boolean algebras as Lukasiewicz
infinite-valued logic stands to classical logic. Up to categorical
equivalence, MV-algebras have many counterparts,  e.g., lattice-ordered
abelian groups with a distinguished archimedean element, called unit.
Further, Grothendieck's K_0 functor induces a one-one correspondence 
between AF C*-algebras whose Murray-von Neumann order of projections is a
lattice., and countable MV-algebras. States on MV-algebras correspond to
unit preserving order preserving real valued functionals of unital
l-groups, and also correspond to tracial states of AF C*-algebras. Last,
but not least, finitely presented MV-algebras are categorically equivalent
to rational polyhedra, (=finite unions of simplexes with rational
vertices). The arrow-theoretic counterpart of an MV-algebraic isomorphism 
j  is a Z-homeomorphism j', i.e., a PL-homeomorphism  where each linear
piece of both j' and its inverse has integer coefficients. Z-homeomorphism
invariant measures on rational polyhedra yield  invariant states on
MV-algebras, unital l-groups and AF C*-algebras. To construct such
measures we will combine the solution by Morelli and Wlodarczyk of the
weak Oda conjecture, and the de Concini-Procesi theorem on the elimination
of points of indeterminacy in toric varieties.

Background references.

R.Cignoli, I.D'Ottaviano, D.Mundici, "Algebraic Foundations of
Many-valued Reasoning", Kluwer-Springer, 2000.

D.Mundici, "Advanced Lukasiewicz Calculus and MV-algebras",
Springer, 2011.




Están todos cordialmente invitados.
Saludos, Juan José Guccione


Para más información sobre los coloquios del Departamento de Matemática ir a

http://cms.dm.uba.ar/actividades/coloquios/