ALGANT Student seminar – Thursday, May 26th, 2pm, Aula 6

ALGANT Student seminar – Commutative Algebra

Date and time: Thrusday, May 26th, at 2pm
Room: Aula 6

Lecture 1: Riccardo Ghezzi
Title: Cohen-Macaulay rings and Gorenstein rings.
Abstract: In this lecture we will show the main properties of Cohen-Macaulay rings, as their good behaviour in terms of dimension, and of Gorenstein rings. In particular, introducing the definition of injective hull, we will characterize Gorenstein rings as Cohen-Macaulay rings of type 1.

Lecture 2: Francesco Monopoli
Title: Unique factorization in regular local rings
Abstract: The goal of this seminar is to prove that any local regular ring is a unique factorization domain. To prove this theorem I will use methods and results coming from commutative and homological algebra.

Anyone interested is invited.

ALGANT Student seminar: May 25th 16:00 Aula Dottorato

ALGANT Student seminar – Commutative Algebra

Date and time: Wednesday, May 25th, at 4pm

Room: Aula Dottorato

Lecture 1: Federico Binda
Title: the Intersection formula (PDF)
The goal of this lecture is to present the minimum background material that is necessary to understand Serre’s definition of intersection multiplicity, at least in the case of two irreducible subvarieties of an n-dimensional affine space. Following [2], we will quickly review Samuel’s definition of multiplicity of an ideal. Then we will see how the homology modules of the Koszul complex are related to the Tor functor and in which way they can be used to give a “new” definition of multiplicity, as in [1]. We will conclude the talk proving that Serre’s definition is the “right one”, at least in the case of plane curves, and, if time permits, we will also give an example that should convince that the higher Tor are actually useful.
References:
[1] J. P. Serre (2000), Local Agebra, revised edition. Springer Monographs in Mathematics.
[2] P. Roberts (1998), Multiplicities and Chern Classes in Local Algebra. Cambridge Univ. Press. Cambridge.

Lecture 2: Ziyang Gao
Title: Grothendieck-Serre Duality (PDF)
Abstract: This lecture can be viewed as a preliminary part for the next lecture I will give about global Grothendieck duality. In this seminar, we will talk about Koszul complexes of both local and global versions. At the end of the talk, a non-trivial theorem about the canonical bundle of a regular closed immersion will be presented.

Anyone interested is invited.

Seminario Kutoyants (9 giugno) – SEMINARIO MATEMATICA APPLICATA

ANNUNCIO DI SEMINARIO

Il giorno 9 Giugno 2011 alle ore 11.00 presso la Sala di Rappresentanza del Dipartimento di Matematica via Saldini 50, Milano

il

Prof. Yuri Kutoyants, Université du Maine, France

terra’ il seguente seminario:

On identification of threshold diffusion processes

Abstract. We consider several problems of threshold estimation for ergodic diffusion processes. It is shown that the maximum likelihood and bayesian estimators are consistent, have singular rate of convergence and the bayesian estimators are asymptotically efficient. The properties of these estimators are described in non regular situations too.

SemMatFis – MAURI

SEMINARIO MATEMATICO E FISICO DI MILANO

AVVISO DI CONFERENZA

Lunedi’ 23 maggio 2011, ore 17:00, presso l’Aula Seminari del VI piano del Dipartimento di Matematica del Politecnico di Milano, in via Bonardi 9

Prof. ROBERTO MAURI Dipartimento di Ingegneria Chimica, Chimica Industriale e Scienze dei Materiali Universita’ di Pisa

terra’ la conferenza

“Mean Field Modeling of Multiphase Systems”

Abstract. The theory of multiphase systems was developed at the beginning of the 19th century assuming that different phases are at local equilibrium and are separated by a sharp (i.e. with zero thickness) interface. This approach breaks down when the real interface thickness is comparable to the lengthscale of the phenomenon that is being studied, as it happens near a contact line or in the breakup or coalescence of liquid droplets. A different approach consists in treating the interface as a finite (although thin) region where the density, or the composition, of the mixture varies from one value (not necessarily of equilibrium) to the other. The drawback of this approach is that we have to add a mass conservation equation to the equation of conservation of momentum and of energy, as we need to determine the density (or concentration) profile of the mixture in the interface region. The advantage is that the position of the interface is automatically determined through the concentration profile and so no interface tracking is required. This approach, which is generally referred to as the diffuse interface method, is based on one of the many intuitions by Van der Waals and was later generalized by Ginzburg and Landau to formulate the mean field theory. After deriving the basic equations of the model, results of several recent simulations are presented and commented. In particular, we will describe spinodal decomposition and nucleation of both liquid binary mixtures and single component, vapor-liquid systems.

Cordiali saluti, Franco Tomarelli Direttore del Seminario Matematico e Fisico di Milano

Per ulteriori informazioni sulle attività del seminario: http://www.mate.polimi.it/smf

seminario Ding

Mercoledì  18 Maggio alle ore 14.30 in Aula di Rappresentanza

del Dipartimento di Matematica (Via Saldini, 50)

Yanheng Ding
(Chinese Academy of Sciences, Pechino)

terrà un seminario dal titolo

"On semi-classical solutions of the nonlinear Dirac equation"

Tutti gli interessati sono invitati a partecipare