Scientific Organisers
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Ian Melbourne, University of Warwick
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Françoise Pène, Université de Brest
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Mike Todd, University of St Andrews
About:
Many physical systems display strong dependence between data points over time, which can be described as, or linked to, intermittency and slow mixing. For example internet packet data, weather and climate data, financial markets and so on can go through long periods of predictable behaviour interspersed with chaotic bursts. Moreover, certain types of data exhibit heavy tails: very large values which occur relatively often and dominate the rest of the observations. Problems of this type have long been important in probability theory and dynamical systems, but it is only recently (particularly in the dynamical setting) that there has been success in developing analytical tools to give a good description of such situations. This workshop will disseminate the most recent results, reinforcing these connections and sparking new ones, and help with identifying and plotting paths to new milestones in the area.
The core of this workshop was slow mixing. Topics based there and in related directions included:
(1) Extreme value theory for dynamical systems with heavy tails
(2) Stable laws and anomalous diffusion in slowly mixing systems
(3) Deterministic homogenisation for fast-slow systems
(4) Geodesic flows on nonpositively curved manifolds
(5) Limit theorems and mixing for infinite measure systems
The speakers represented these different topics with the required background from dynamical systems (including partially hyperbolic dynamics, billiards and geodesic flows), functional analysis, probability theory and stochastic analysis.
Participants:
- Viviane Baladi (ITS-ETH Zurich & CNRS, Paris)
- Peter Balint (Budapest University of Technology and Economics)
- Dylan Bansard-Tresse (Mathematics Center of the University of Porto)
- Bojan Basrak (University of Zagreb)
- Jerome Carrand (Sorbonne Université)
- Ilya Chevyrev (University of Edinburgh)
- Raquel Couto (University of St Andrews)
- Ignacio del Amo (University of Exeter)
- Mark Demers (Fairfield University)
- Nicholas Fleming (University of Warwick)
- Jorge Freitas (Centro de Matemática da Universidade do Porto)
- Ana Cristina Freitas (Universidade do Porto)
- Sebastien Gouezel (CNRS & University of Rennes 1)
- Jérôme Guérizec (Université de Nantes)
- Mark Holland (University of Exeter)
- Natalia Jurga (University of St Andrews)
- Alexey Korepanov (LPSM, Paris)
- Zemer Kosloff (Hevrew University of Jerusalem)
- Tamara Kucherenko (The City College of New York)
- Andrew Larkin (Loughborough University)
- Yuri Lima (Universidade Federal do Ceará)
- Ian Melbourne (University of Warwick)
- Florence Merlevede (University Gustave Eiffel)
- Matthew Nicol (University of Houston)
- David Parmenter (University of Warwick)
- Nicolò Paviato (University of Warwick)
- Françoise Pène (Université de Brest)
- Maxence Phalempin (Université de Bretagne Occidentale)
- Marks Ruziboev (University of Vienna)
- Julien Sedro (CNRS-Sorbonne Université)
- Fanni Sélley (Leiden University)
- Richard Sharp (University of Warwick)
- Carlos Matheus Silva Santos (CNRS & Ecole Polytechnique)
- Terry Soo (UCL)
- Dalia Terhesiu (Mathematical Institute, Leiden)
- Mike Todd (University of St Andrews)
- Paulo Varandas (Federal University of Bahia & CMUP - University of Porto)
- Christian Wolf (The City College of New York)
- Caroline Wormell (CNRS, Sorbonne Université)
- Benthen Zeegers (Leiden University)
Programme
| Monday 6 June 2022 | ||
| Registration and Refreshments | ||
| Lunch | ||
| Opening Remarks | ||
| Florence Merlevède , University Gustave Eiffel | Strong approximations and deviation inequalities for non-uniformly expanding maps | |
| Mark Holland , University of Exeter | Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes | |
| Poster Session with Refreshments | ||
| Sébastien Gouëzel , CNRS & University of Rennes 1 | Phase transition for the minimal distance between orbits in random dynamical systems | |
| Light Supper at ICMS | ||
| Tuesday 7 June 2022 | ||
| Viviane Baladi , ITS-ETH Zurich & CNRS, Paris | Deviation from the average for horocycle flows on surfaces of variable negative curvature | |
| Coffee and Refreshments | ||
| Bojan Basrak , University of Zagreb | Tail process and related limit theorems | |
| Ilya Chevyrev , University of Edinburgh | Path functions and homogenisation of superdiffusive fast-slow systems | |
| Lunch | ||
| Yuri Lima , Universidade Federal do Ceará | Polynomial decay of correlations of geodesic flows on some nonpositively curved surfaces (Part 1) | |
| Refreshments | ||
| Nicholas Fleming-Vázquez, University of Warwick | Optimal iterated moment bounds for nonuniformly hyperbolic maps | |
| Drinks Reception | ||
| Wednesday 8 June 2022 | ||
| Carlos Matheus , CNRS & Ecole Polytechnique | Polynomial decay or correlations of geodesic flows on some nonpositively curved surfaces (Part 2) | |
| Coffee and Refreshments | ||
| Ana Cristina Freitas , Universidade do Porto | Extremes and records for dynamically generated stochastic processes | |
| Zemer Kosloff , Hebrew University of Jerusalem | Sinai factors in nonsingular ergodic theory | |
| Group Photo | ||
| Packed lunch and free afternoon | ||
| Thursday 9 June 2022 | ||
| Mark Demers , Fairfield University | Topological Entropy and Pressure for Sinai Billiards | |
| Coffee and Refreshments | ||
| Natalia Jurga , University of St Andrews | Cover times in dynamical systems | |
| Maxence Phalempin , Université de Bretagne Occidentale | Asymptotic behavior of self-intersection of trajectories from the flow of a Z-periodic Lorentz gaz | |
| Lunch | ||
| Marks Ruziboev , University of Vienna | Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system | |
| Refreshments | ||
| Dalia Terhesiu, Mathematical Institute, Leiden | Local large deviation in the absence of the classical central limit theorem and some applications | |
| Dinner at Blonde Restaurant | ||
| Friday 10 June 2022 | ||
| Alexey Korepanov , LPSM | Polynomial mixing for measure of maximal entropy on dispersing billard maps | |
| Coffee and Refreshments | ||
| Fanni Sélley , Leiden University | Differentiability of the diffusion of coefficient for a family of intermittent maps | |
| Matt Nicol , University of Houston | Stable laws for random dynamical systems. joint with Romain Aimino and Andrew Torok | |
| Packed Lunch and End of Conference |