Sala Conferenze (Puteano, Centro De Giorgi)

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: 
0000 - 16:30
Affiliazione: 
Universidade de São Paulo
Ora Inizio: 
0000 - 15:30

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: 
0000 - 15:00
Affiliazione: 
University of Vienna
Ora Inizio: 
0000 - 14:00

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: 
0000 - 16:15
Affiliazione: 
University of Vienna
Ora Inizio: 
0000 - 15:15

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: 
0000 - 15:00
Affiliazione: 
Centro De Giorgi
Ora Inizio: 
0000 - 14:00

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: 
0000 - 12:00
Affiliazione: 
SNS
Ora Inizio: 
0000 - 11:00

Quasiperiodic sums and products

Relatore: 
Paul Verschueren

Quasiperiodic Sums and Products arise in many areas of mathematics including the study of Strange Non-Chaotic Attractors, Critical KAM Theory, Quantum Chaos, q-series, Partition Theory, and Diophantine Approximation.

The graphs of these functions form intriguing geometrically strange and self-similar structures. They are easy and rewarding to investigate numerically, and suggest many avenues for investigation. However they prove resistant to rigorous analysis.

Data Seminario: 
Tuesday, September 20, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
0000 - 15:00
Affiliazione: 
Open University
Ora Inizio: 
0000 - 14:00

Integrability of bi-homogeneous potentials

Relatore: 
Thierry Combot

We present a new notion of homogeneity for rational potentials in the plane, we called rotation homogeneity. These potentials can be seen as singular limits of rational potentials, and in particular, a necessary condition for integrability is that the dominant term and lower order term should be integrable. This new notion of homogeneity can combine with the classical one, producing a bihomogeneous case, which is a 2-integer parameter family.

Data Seminario: 
Wednesday, September 14, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
0000 - 15:30
Affiliazione: 
Centro Fibonacci e Université de Bourgogne
Ora Inizio: 
0000 - 14:30

PERMUTABLE ENTIRE FUNCTIONS AND MULTIPLY CONNECTED WANDERING DOMAINS

Relatore: 
Anna Miriam Benini
Let f and g be permutable transcendental entire functions. It is a long standing question whether the Julia sets of f and g are equal. The conjecture is true in the case that f,g are rational functions, and in the transcendental case the main issues are due to the presence of Baker Domains and Wandering Domains.
Data Seminario: 
Wednesday, January 27, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Universita' Roma Tor Vergata
Ora Inizio: 
0000 - 15:00

Pluripotential theory and C^n capacities

Relatore: 
Karim Rakhimov
In this talk, after a short history of Pluripotential theory and $C^n$ capacities, I shall describe our results on capacity dimension of Brjuno and Perez-Marco set, giving a sketch of the proof of the fact that the complement of Brjuno set has zero sigma-capacity.
Data Seminario: 
Wednesday, January 27, 2016
Aula: 
Sala Conferenze (Puteano, Centro De Giorgi)
Ora Fine: 
0000 - 15:00
Affiliazione: 
National University of Uzbekistan, Tashkent
Ora Inizio: 
0000 - 14:00

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