1 Luglio, 2011 14:45 oclock

Bivariate Splines for Ozone Concentration Forecasting

Bree Ettinger, University of Georgia (USA)

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

For ground level ozone prediction, we use past spatially distributed measurements and the functional linear regression model. We use bivariate splines defined over triangulations of a relevant region of the U.S.A. to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with penalty to the principal components regression approach.
We apply these two functional linear models to ground level ozone forecasting over the south eastern United States to illustrate the predictive skills of the two methods. If time allows, we will also discuss a naive extension of these models for Hurricane Path prediction where both the explanatory and response variables are random surfaces.

30 Giugno, 2011 15:00 oclock

Bootstrap & Finite Population Complex Sampling

Fulvia Mecatti, University of Milano-Bicocca

Aula Seminari F. Saleri VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano

abstract

abstract

Since being first introduced by Efron in 1979, the
Bootstrap has quickly become one of the most largely studied, developed and applied resampling method. As a consequence of its simplicity and generality there has been much theoretical and empirical research and the bootstrap is nowadays a well established computer intensive method for assessing the precision of an estimator, confidence intervals and p-values. In its
original version the bootstrap applies in the classical non-parametric inferential context, under the customary assumption of independency and identical distribution (iid) of the sample observations from an unknown probability model. Non-iid situation are also of interest in statistical theory and practice and suitable
modifications of the original bootstrap able to address a weaker or stronger dependency structure in sample data are needed. In the seminar first the development of bootstrap method is briefly reviewed and then the non-iid finite population case is focused. Main proposals of bootstrap algorithms for complex sample are discussed and
some new results for probability proportional to size sampling are presented. Open issues and development challenges are also enlightened.

29 Giugno, 2011 14:15

Sezione di Fisica Matematica

The challenge of the Supersolid state of matter

Maurizio Rossi, Dipartimento di Matematica, Politecnico di Milano

Aula Seminari III piano, dipartimento di Matematica, Politecnico di Milano

abstract

abstract

The supersolid is a fascinating state of matter in which the long-range
order, typical of the solid phase, coexists with some form of
superfluidity, where atoms are free to flow without any dissipation. The
first experimental evidence of supersolidity comes in 2004 in solid 4He.
The true mechanism leading to supersolidity is still unknown and there
is the diffuse believing that disorder plays a fundamental role. We
study via the Path Integral Ground State technique the properties of 2D
solid 4He. We find that perfect crystals do not display Bose-Einstein
condensation, and thus no superfluidity. Otherwise vacancies are really
efficient at inducing a condensate fraction. But vacancies are shown to
be attractive, leading to the conviction that they phase-separate out of
the solid. However, we find that when many vacancies are inserted into
the crystal, they tend to transform themselves into dislocations able to
sustain a condensate fraction in the simulated systems.

27 Giugno, 2011 17:00

Seminario Matematico e Fisico di Milano

RECENT DEVELOPMENTS IN THE THEORY OF COMPLEX MULTIPLICATION

EYAL GOREN, McGill University

Università di Milano, Dipartimento di Matematica, Via Saldini 50, Sala Rappresentanza

abstract

abstract

Our story begins more than a century ago with Kronecker Jugendtraum and Hilbert 12th problem, where complex multiplication appears as a way to understand Galois extensions of number fields - a problem still at the heart of number theory. Our lecture will have a strong historical flavour; we shall attempt to survey the development of the theory of complex multiplication and the philosophy behind it. On this background, we will present some exciting recent results, some of which build in an essential way on Borcherds theory. Finally, we shall sketch some of the key challenges of the theory of complex multiplication today and future directions.

21 Giugno, 2011 16:30

Lezioni Leonardesche

EXPANSION IN LINEAR GROUPS, SPECTRAL GAPS AND APPLICATIONS

JEAN BOURGAIN, Institute for Advanced Study, Princeton

Luogo: Dipartimento di Matematica, V. Saldini, 50, Aula Chisini

abstract

abstract

This talk is a partial survey of some developments over recent years around the expansion theory ofthe Cayley graphs of linear groups and spectral gaps of the corresponding Hecke operators. A sample resultis the extension of Selberg's theorem for congruence subgroups of SL2(Z) to the setting of arbitrary non-elementary subgroups. Underlying these advances are techniques from arithmetic combinatorics that will be briefly indicated. The main emphasis of this (non-technical) presentation will be rather the applications however. They are quite diverse and relate to a variety of different issues in various fields: hyperbolic lattice point counting, number theory, geometry and questions from computer science.

15 Giugno, 2011 12:15

Seminari di Cultura Matematica

Évariste Galois e la nascita dell’algebra moderna

Renato Betti, Politecnico di Milano

Aula B.2.1 (edificio 14 - Nave ) via Bonardi, 9, Milano

This talk is a partial survey of some developments over recent years around the expansion theory ofthe Cayley graphs of linear groups and spectral gaps of the corresponding Hecke operators. A sample resultis the extension of Selberg's theorem for congruence subgroups of SL2(Z) to the setting of arbitrary non-elementary subgroups. Underlying these advances are techniques from arithmetic combinatorics that will be briefly indicated. The main emphasis of this (non-technical) presentation will be rather the applications however. They are quite diverse and relate to a variety of different issues in various fields: hyperbolic lattice point counting, number theory, geometry and questions from computer science.

14 Giugno, 2011 14:30

Seminario Matematico e Fisico di Milano

DNA TOPOLOGY

DE WITT L. SUMNERS, Florida State University

Dipartimento di Matematica, Università di Milano Bicocca, aula seminari 3014

abstract

abstract

This lecture will give an introduction to the topology and geometry of DNA. Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate and carefully control the geometry and topology of cellular DNA perform many important cellular
processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This talk is intended for a general scientific audience, and will discuss topological models for DNA strand passage and exchange, including the analysis of topoisomerase experiments on circular DNA using knot theory.

8 Giugno, 2011 12:15

Seminari di Cultura Matematica

Omeopatia, para-psicologia, negazione dei cambiamenti climatici. Le bufale scientifiche: come evitarle.

Silvie Coyaud, Il Sole 24 Ore

Aula B.2.1 (edificio 14 - Nave ) via Bonardi, 9, Milano

This lecture will give an introduction to the topology and geometry of DNA. Cellular DNA is a long, thread-like molecule with remarkably complex topology. Enzymes that manipulate and carefully control the geometry and topology of cellular DNA perform many important cellular
processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity). Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme binding and mechanism can often be characterized. This talk is intended for a general scientific audience, and will discuss topological models for DNA strand passage and exchange, including the analysis of topoisomerase experiments on circular DNA using knot theory.

7 Giugno, 2011 16:30

Lezioni Leonardesche

NONLINEAR DIFFUSION, FROM POROUS MEDIA TO FRACTIONAL DIFFUSION. EVOLUTIONS, FREE BOUNDARIES AND ASYMPTOTICS

JUAN LUIS VAZQUEZ, Universidad Autonoma de Madrid

Dipartimento di Matematica, V. Saldini, 50, Aula Chisini

abstract

abstract

In the talk we will make a presentation of the theory of Nonlinear Diffusion centered on one of the popular models, the porous medium equation and its close relative, the fast diffusion equation. The existence of free boundaries is one of the most peculiar properties of the former equation. Related models and literature will be mentioned.
In the final section, I will present recent work that combines degenerate nonlinear diffusion with nonlocal operators of fractional Laplacian type. Apart from the unexpected existence of free boundaries, the model admits mass preserving self-similar solutions that are found by solving an elliptic fractional-Laplacian obstacle problem. We use entropy methods to show that the asymptotic behaviour is described after renormalization by these self-similar solutions.
This is intended to give an idea of the variety of topics and techniques in the area.

7 Giugno, 2011 10:30 oclock

Sezione di Geometria, Algebra e loro applicazioni

Una costruzione di schemi proiettivi ACM

Roberto Notari, Dipartimento di Matematica, Politecnico di Milano

Aula seminari del terzo piano

abstract

abstract

Intendo presentare una costruzione di schemi proiettivi ACM di codimensione qualsiasi ed alcuni esempi per illustrarla.