Sala Conferenze (Puteano, Centro De Giorgi)

Il teorema di Szego

Tipo Seminario: 
Relatore: 
Alexander Bufetov

#ENG
Gabor Szego proved the first version of this theorem when he was 20, and he proved it in a stronger version when he was 57.
He established asymptotic properties of Toeplitz determinants  which nowadays are of crucial importance in many fields.

In fact, Szego theorem can be proved in many ways: via mathematical analysis (Szego, Ibragimov, Widom, Basor-Helton, Deift), with an algebraic approach (Geronimo-Case-Borodin-Okounkov), or else using  representation theory arguments  (Bump-Diaconis) or statistical mechanics (Johansson). 

Data Seminario: 
Thursday, April 5, 2018
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 18:15
Affiliazione: 
CNRS I2M, Marseille and Steklov Mathematical Institute, Moscow
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

On the fractal geometry of the Lagrange and Markov spectra.

Relatore: 
Carlos Matheus

After the remarkable works of Markov in 1879 and 1880, the Lagrange and Markov spectra (coding arithmetic properties of irrational numbers and indefinite binary quadratic forms) were studied by several authors (including Perron, Hall, Freiman, Cusick, Flahive, ...).

Data Seminario: 
Wednesday, November 22, 2017
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 17:30
Affiliazione: 
Paris XIII
Ora Inizio: 
Saturday, January 1, 0000 - 16:30

On mixing rates for time-changes of Heisenberg nilflows

Relatore: 
Giovanni Forni

We construct Bufetov functionals for nilpotent flows on (compact) Heisenberg nilmanifolds. Such functionals were first constructed by Bufetov for Interval Exchange Transformations and Translation flows, and later for horocycle flows by Bufetov and myself with the goal of proving limit theorems. In the Heisenberg case we generalize results of Griffin and Marklof, and Cellarosi and Marklof on the related question of limit distributions of theta sum.

Data Seminario: 
Wednesday, November 22, 2017
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Affiliazione: 
University of Maryland
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

The Mandelbrot set and its satellite copies

Relatore: 
Luna Lomonaco
For a polynomial on the Riemann sphere, infinity is a (super) attracting fixed point, and the filled Julia set is the set of points with bounded orbit. Consider the quadratic family $P_c(z)=z^2+c.$ The Mandelbrot set M  is the set of parameters c such that the filled Julia set of $P_c$ is connected. Douady and Hubbard, using polynomial-like mappings, proved the existence of homeomorphic copies of M inside of M, which can be primitive (if, roughly speaking, they have a cusp) or satellite (if they don't). They
Data Seminario: 
Monday, February 27, 2017
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 15:30
Affiliazione: 
Universidade de São Paulo
Ora Inizio: 
Saturday, January 1, 0000 - 14:30

A randomized version of the Littlewood Conjecture - Part I

Relatore: 
Henna Koivusalo

The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by a random amount which depends on the denominator of the corresponding rational. Using a randomized covering argument we prove that, not only is this randomized version of the Littlewood Conjecture true for almost all choices of centers, but an even stronger statement with an extra factor of a logarithm also holds.

Data Seminario: 
Wednesday, December 7, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 14:00
Affiliazione: 
University of Vienna
Ora Inizio: 
Saturday, January 1, 0000 - 13:00

A randomized version of the Littlewood Conjecture - Part II: discussion

Relatore: 
Henna Koivusalo

The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by a random amount which depends on the denominator of the corresponding rational. Using a randomized covering argument we prove that, not only is this randomized version of the Littlewood Conjecture true for almost all choices of centers, but an even stronger statement with an extra factor of a logarithm also holds.

Data Seminario: 
Wednesday, December 7, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 15:15
Affiliazione: 
University of Vienna
Ora Inizio: 
Saturday, January 1, 0000 - 14:15

Lagrange Spectrum of Veech surfaces

Relatore: 
Mauro Artigiani

The Lagrange spectrum is a classical object in Diophantine approximation on the real line that has been generalised to many
different settings. In particular, recently it has been generalised to a similar object for translation surfaces, which attracted quite some
attention in the field. We study the Lagrange spectrum in the contest of Veech translation surfaces. These are particular translation surfaces
with many symmetries, that can be thought as a dynamical equivalent of the torus in higher genera.

Data Seminario: 
Tuesday, October 25, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 14:00
Affiliazione: 
Centro De Giorgi
Ora Inizio: 
Saturday, January 1, 0000 - 13:00

When panic makes you blind: a chaotic route to systemic risk

Relatore: 
Piero Mazzarisi

We introduce a slow-fast dynamical system to study the role of the expectation feedbacks on systemic stability of financial markets. We study a simple stylization of a financial market, that is a set of financial institutions having capital requirements in the form of the Value at Risk constraint, following standard mark-to-market and risk management rules and investing in some risky assets.

Data Seminario: 
Tuesday, October 25, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
SNS
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Linearization of multi-dimensional dynamical systems through tree-expansions

Relatore: 
David Sauzin

joint work with F.Fauvet and F.Menous

Data Seminario: 
Wednesday, October 19, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
CNRS e Laboratorio Fibonacci
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

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