One Day Workshop on "Trieste Tangles: From Topology to Fractals to Complex Dynamics" - Wednesday 13 September, from 10:30 to 16:00

[ICTP Math Section]

*_One Day Workshop on "Trieste Tangles: From Topology to Fractals to 
Complex Dynamics"_*


Wednesday 13 September


*WORKSHOP VENUES*: Fibonacci lecture room (morning) and Luigi Stasi 
seminar room (afternoon)


/Morning (10:30 - 12:30) - Venue: Fibonacci lecture room (Galileo Guest 
House)/


10:30 *Jernej Činč* /(ICTP, Italy and University of Maribor, Slovenia)/

Title: *Lebesgue measure-preserving maps on one-dimensional manifolds*

*Abstract:* In this talk I will survey recent advances in the study of 
Lebesgue measure-preserving maps on one-dimensional compact connected 
manifolds with particular emphasis on the circle case. If time permits I 
will also argue that there exists an open dense set of Lebesgue 
measure-preserving circle maps which satisfy a very strong topological 
expansion property. The talk is based on joint works with Jozef Bobok 
(CVUT Prague), Serge Troubetzkoy (Aix-Marseille) and Piotr Oprocha (AGH 
Krakow & IRAFM Ostrava).


11:30 *Siniša Miličić* /(University of Pula, Croatia)/

Title: *Box dimensions of stuffed sets*

Abstract: This seminar delves into the behaviour of box 
(Minkowski-Bouligand) dimensions of stuffed sets - sets with locally 
stable dimension and a compact core part with a dimensional jump 
(spirals, chirps etc.). We define stuffed sets and analyse how that 
property drives the box dimension, with the ultimate aim of justifying 
intuitive shortcuts in computing dimensions.


/Afternoon (14:00 - 16:00) - Venue: Luigi Stasi seminar room (Leonardo 
Da Vinci Building)
/


14:00 *Shaun Bullett* /(Queen Mary University of London, UK)/


Title: *Dynamics of holomorphic correspondences I: a guided tour of a 
family of examples

*


15:00*Luna Lomonaco* /(IMPA, Rio de Janeiro, Brazil)/


Title: *Dynamics of holomorphic correspondences II: matings between 
quadratic maps and the modular group*

*
*

*Joint Abstract for the above two talks:*
A holomorphic correspondence on the Riemann sphere is a multivalued map 
z->w defined by a polynomial relation P(z,w)=0. This definition 
generalises those of a rational map and of a finitely generated Kleinian 
group, putting them into a common framework. An iterated correspondence 
may simultaneously exhibit the behaviour of a rational map of one part 
of the Riemann sphere and of a Kleinian group on another, in which case 
we describe it as a mating between the map and the group.

The first talk will describe the dynamical behaviour of the simplest 
2-parameter family of holomorphic correspondences. With Christopher 
Penrose the speaker identified certain members of this family as matings 
between quadratic polynomials and the modular group, and in their 1994 
Inventiones paper these authors made a series of conjectures concerning 
the family of such matings. The second speaker introduced a new tool to 
the problem: the theory of parabolic-like mappings. In her talk she will 
give an overview of how she and the first speaker have together resolved 
all the 1994 conjectures.

/https://indico.ictp.it/event/10533/

All are welcome to attend

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela