AVVISI DI SEMINARI

martedi' 22-11-2005 (14:00) - sala conferenze del Centro di Ricerca Matematica Ennio de Giorgi Yutaka ISHII ((Kyushu University)) : Hyperbolic polynomial diffeomorphisms of C^2

Abstract.1 (ISHII): In this talk I will explain a general framework for verifying hyperbolicity of holomorphic dynamical systems in C^2. This framework in particular enables us to construct the first example of a hyperbolic complex H'enon map which cannot be topologically conjugate on its Julia set to a small perturbation of any expanding polynomial in one complex variable. Some applications to the analysis of (the maximal entropy and horseshoe) parameter loci for the H'enon family in R^2 will be also given. **************************************************************************** **************************** mercoledi' 23-11-2005 (15:30) - sala seminari Elisabetta Colombo (Milano) : Superfici cubiche marcate

Si discutono risultati recenti sullo spazio dei moduli delle superfici cubiche di P3 marcate con al piu' nodi, identificato da Allcock, Carlson Toledo con un quoziente della palla complessa 4-dimensionale. Si illustrano in particolare l'embedding proiettivo in P9, il gruppo di Chow e modelli della famiglia universale

**************************************************************************** **************************** lunedi' 28-11-2005 (09:30) - Sala delle Riunioni Roberto Lucchetti (Politecnico di Milano) : Well posed problems in quadratic and convex programming

Abstract: A minimum problem is said to be well posed whenever it has a solution towards every minimizing sequence converges. Being a noteworthy property, both from a theoretical and a computational point of view, it is interesting to know when well posedness is a generic property, in selected classes of problems. In this talk I will present results showing that the majority (in a strong sense) of the convex and quadratic problems are well posed.

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28-11-2005 (11:00) - Sala delle Riunioni Fabio Tardella (Università di Roma "La Sapienza") : An extension of the fundamental theorem of Linear Programming and applications

Abstract: We describe an extension of the fundamental theorem of Linear Programming on the existence of a global minimum in a vertex of a polyhedron for lower bounded linear programs to Quadratic Programming and beyond. Our extension implies and strengthens the Frank-Wolfe (fundamental) theorem on the existence of the minimum of a lower bounded quadratic programming problem. We then show that several known and new results providing continuous formulations for discrete optimization problems can be easily derived and generalized with our result. These include the Quadratic Programming formulation of the maximum clique problem by Motzkin and Straus and its weighted extension by Gibbons et al., the equivalence between the minimization of a multilinear function on the continuous and discrete unit hypercube by Rosenberg, and a recent continuous polynomial formulation of the maximum independent set problem by Abello et al. Furthermore, we use our extension of the fundamental theorem of Linear Programming to obtain combinatorial formulations and polynomiality results for some nonlinear problems with simple polyhedral constraints, like nonconvex (standard) quadratic programming. Finally, we characterize those functions that have a polyhedral convex envelope on a polyhedron.

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Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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