Workshop
24-26 May 2023, ISEG-Lisbon School of Economics & Management, Universidade de Lisboa
The LxDS-Lisbon Dynamical Systems group, the Mathematics Department of ISEG, CEMAPRE, REM and CMAFcIO are organizing a 3-day spring school (24th to 26th May 2023) on dynamical systems to be held at ISEG/ULisboa. The school will consist of three mini-courses in specific areas of dynamical systems lectured by specialists of recognized international merit.
REGISTRATION is required to confirm participation. Please fill the form on this web page.
Those wishing to give a 20-minute talk should mention it in the comments section of the registration form, indicating the corresponding title and abstract.
The spring school will have a limited number of participants.
PhD students can apply for financial support.
Diophantine approximations and the space of lattices (Nicolas Chevallier) |
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| The objective of the course is to show the fruitful relations between Diophantine approximations, lattices and the action of the diagonal flow in the space of unimodular lattices. We will start with the classics: continued fractions in one dimension, Dirichlet`s theorem in one dimension and Dirichlet`s theorem in simultaneous approximation. Then we will introduce lattices, the space of unimodular lattices, the shortest vector function and the diagonal flow. We will reinterpret the notions of badly approximable and singular vectors (Dani correspondence). We will also reinterpret the notion of best Diophantine approximation in terms of minimal vectors in lattices. Finally we will give applications of the ergodicity of the diagonal flow to Diophantine approximations. |
Statistical properties for certain dynamical systems (Silvius Klein) |
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| The main objective of this mini-course is the study of some recent topics in ergodic theory about limit laws (i.e. the large deviations principle and the central limit theorem) for certain types of dynamical systems. The main tool in this study is the existence of the spectral gap of the Markov transition operator or the Ruelle transfer operator in an appropriate space of observables. |
TBA |
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| Time | 24th May | 25th May | 26th May |
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| 09h30 | Registration | ||
| 10h00 - 11h30 | Course 1 (Part 1) | Course 1 (Part 2) | Course 1 (Part 3) |
| 11h30 - 11h45 | Coffee break | Coffee break | Coffee break |
| 11h45 - 13h15 | Course 2 (Part 1) | Course 2 (Part 2) | Course 2 (Part 3) |
| 13h15 - 15h00 | Lunch | Lunch | Lunch |
| 15h00 - 16h30 | Course 3 (Part 1) | Course 3 (Part 2) | Course 3 (Part 3) |
| 16h30 - 17h00 | Coffee break | Coffee break | |
| 17h00 - 17h30 | talk 1 | talk 3 | |
| 17h30 - 18h00 | talk 2 | talk 4 | |
| 20h00 |
PhD students, post-docs and researchers.
For more information please contact us.
The organizers are grateful for the sponsorship of the CIM - Centro Internacional de Matemática.
CEMAPRE - Centre for Applied Mathematics and Economics
Rua do Quelhas, n.º 6
1200-781 Lisboa
Portugal
Email: cemapre@iseg.ulisboa.pt
Tel: (+351) 213 925 876