Category Archives: News

Giornata Analisi Armonica, Probabilita’, e Sistemi Dinamici (16 aprile 2018)

Giornata di Analisi Armonica, Probabilita’, e Sistemi Dinamici

Location: Aula 1E (palazzina E)
Dipartimento SBAI (Universita’ di Roma “La Sapienza”)
via A. Scarpa 14, Roma

Lunedi’ 16 aprile:

ore 14:30

ore 15:30

ore 16:30

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement N°647133)”

PhD in Pisa

In case you are looking for a PhD position in Mathematics at the University of Pisa for you or your students, I’m forwarding useful information from the PhD School Coordinator.

Dear colleagues,

in our department we are looking for students from outside Italyt hat might be interested in doing their PhD in Pisa, starting nextacademic year (that is, October/November 2018).
I ask your help to bring this message to the attention of students in your department that might be interested.

Concerning support: this year we have 5 positions, 1 of which is
reserved for students who got a Master degree out of Italy.
We expect the call for these positions will open in June, it will be
announced on our webpage

and on the university webpage

Moreover students from abroad can also apply to the following

*Note that the call for this last program is already open, and the **
**deadline is May 31st.*

Note that

* all these positions come with a three-year fellowship that
can fully support a student in Pisa, and some funds for
research travels;
* candidates are supposed to get their master degree by
October 2018 at the latest;
* advanced courses in Pisa are usually taught in English
(at least if there are non-Italian students in the class)
and learning Italian is not mandatory;
* even though the Scuola Normale is a separate institution
from the University of Pisa, we share courses and all types
of activities; indeed students from the University can have
an advisor at the Scuola, and viceversa;
* students that can secure themselves financial support
from other sources can apply for further positions.

Best regards,

Prof. Giovanni Alberti


Summer School in Dynamics at ICTP, 16-27 July 2018

A Summer School in Dynamical Systems which will be held at ICTP, Trieste (Italy) on 16-27 July 2018.
The school is targeted to Masters and beginning PhD students and aims at introducing a variety of fundamental ideas and techniques in dynamics. The first week will not assume prior knowledge in the field of dynamical systems. Students can also register for the second week only.
Female students are especially encouraged to apply. A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries.
Organizers and lectures:
-Jana RODRIGUEZ-HERTZ (Southern University of Science and Technology of China)
-Corinna ULCIGRAI (University of Bristol, UK)
-Amie WILKINSON (University of Chicago, USA)
Local organizer: Stefano Luzzatto (ICTP)
Week 1
A circle of concepts and methods in dynamics.
Basic concepts in dynamics will be introduced, with many examples, especially in the setting of circle maps. Topics include rotations of the circle, doubling map, Gauss map and continued fractions and an introduction to the basic ideas of symbolic codings and invariant measures. At the end of the week we will discuss some simple examples of structural stability and renormalization.
Week 2
Ergodicity in smooth dynamics (10h, Jana Rodriguez-Hertz and Amie Wilkinson)
The concept of ergodicity is a central hypothesis in statistical mechanics, one whose origins can be traced to Boltzmann’s study of ideal gases in the 19th century. Loosely speaking, a dynamical system is ergodic if it does not contain any proper subsystem, where the notion of “proper” is defined using measures. A powerful theorem of Birkhoff from the 1930’s states that ergodicity is equivalent to the property that “time averages = space averages:” that is, the average value of a function taken along an orbit is the same as the average value over the entire space. The property of ergodicity is the first stepping stone in a path through the study of statistical properties of dynamical systems, a field known as Ergodic Theory.
We will develop the ergodic theory of smooth dynamical systems, starting with the fundamental, linear examples of rotations and doubling maps on the circle introduced in Week 1. We will develop some tools necessary to establish ergodicity of nonlinear smooth systems, such as those investigated by Boltzmann and Poincaré in the dawn of the subject of Dynamical Systems. Among these tools are distortion estimates, density points, invariant foliations and absolute continuity. Closer to the end of the course, we will focus on the ergodic theory of Anosov diffeomorphisms, an important family of “toy models” of chaotic dynamical systems.
Renormalization in entropy zero systems (5h, Corinna Ulcigrai)
Rotations of the circle are perhaps the most basic examples of low complexity (or “entropy zero”) dynamical systems. A key idea to study systems with low complexity is renormalization. The Gauss map and continued fractions can be seen as a tool to renormalize rotations, the behaviour of a rotation on finer and finer scales. We will see two more examples of renormalization in action.
The first is the characterization of Sturmian sequences, which arise as symbolic coding of trajectories of rotations (and hint at more recent developments, such as the characterization of cutting sequences for billiards in the regular octagon). The second concerns interval exchange maps (IETs), which are generalizations of rotations. We will introduce the Rauzy-Veech algorithm as a tool to renormalize IETs. As applications, we will give some ideas of how it can be used (in some simplified settings) to study invariant measures and (unique) ergodicity and deviations of ergodic averages for IETs.
Tutorial and exercise sessions will be held regularly and constitute an essential part of the school.
Tutors: Oliver BUTTERLEY (ICTP), Irene PASQUINELLI (Durham University, UK), Davide RAVOTTI, (University of Bristol, UK), Lucia SIMONELLI (ICTP), Kadim WAR (Ruhr-Universität, Bochum, Germany).
Women in Mathematics: Activities directed to encourage and support women in mathematics, such as panel discussions and small groups mentoring and networking, will be organized during the event.
Deadlines for applications:
2 April 2018 (for applicants requesting financial support)
25 June 2018 (for applicants NOT requesting financial support)

Please note the fast-approaching DEADLINE (2 April 2018) for applicants requesting financial support!

Postdoctoral position in São Carlos, Brazil

The University of São Paulo campus São Carlos invites potential candidates for a two-year Postdoctoral position, renewable up to four years. Looking for candidates whose research is related to the interests of the Dynamical Systems group (see
Equilibrium states for partially hyperbolic diffeomorphisms (in particular measures of maximal entropy), Stable ergodicity for conservative diffeomorphisms, Comparing classical partially hyperbolic dynamical systems and random walks, Equilibrium states for action of groups, Piecewise expanding transformations with low regularity, Renormalization Theory and universality in one-dimensional dynamics Deformation theory in one- dimensional dynamics Dynamics defined by action of groups: Anosov (sub)systems and their representations in SL(n,R).

The funding is provided by FAPESP (Thematic Project 17/06463-3), the research funding agency of the state of São Paulo, and benefits include:

– Monthly stipend of 7,174.00 BRL (tax free; around US$2100 ),
– Additional 15% of yearly income for research related expenses,
– Start-up costs, including air travel and one extra month of pay,
– Maternity and paternity leave as described on

Applicants should have a Ph.D. degree by the start date of the scholarship and should have graduated no longer than seven year ago. To apply, candidates should send an email to
– CV,
– Research Project,
– Two letters of recommendation.
Deadline to apply: 15th april 2018
Result: The last week of April.
The selected candidate will begin research no later than August 2018.

About University of São Paulo, campus São Carlos: University of São Paulo (USP) is the major Institution of higher learning and research in Brazil. ICMC (Instituto de Ciências Matemáticas e de Computação) is one of the two campi of USP with graduate program in Mathematics. It is located in the city of São Carlos at the distance of 230 km to São Paulo (capital) where the main campus of university is found. The excellence of the scientific level of the Mathematical program at São Carlos Campus has been recognized in the evaluation of CAPES (Coordination for the Improvement of Higher Education Personnel, ministry of Education-Brazil), which assigned it note 7, the maximum concept in Brazil. São Carlos is an academic city with two main Public universities (USP and UFscar) and one the highest index of Ph.D per capita in Latin America. The weather is pleasant with average annual temperature of 20.5 C and the city provides an excellent condition of life.