The University of Pisa offers an online Ph.D. course taught by Mauro Artigiani (Universidad del Rosario, Colombia) and Paolo Giulietti (Università di Pisa) titled “Translation Surfaces: From Geometry to Spectral Theory”.
Description: Translation surfaces are a generalization of flat tori to higher genuses, with rich and interesting geometrical and dynamical properties. In fact, they can be seen both from a complex geometry point of view, stemming from the works of Teichmüller, Ahlfors and Bers, and also from a Euclidean geometry point of view, connecting to the works of the Russian school on low dimensional dynamics. These two different point of views have been fruitfully exploited in the last 50 years to obtain many deep and beautiful results.
In this course, we will introduce translation surfaces motivating their interest. Then, we will survey some of the classical results about them, focusing on the dynamical point of view: the geodesic flow on a translation surface is an important example of a parabolic system, in which nearby points diverge slowly from each other. We will stress the general philosophy of renormalization, which connects the study of the geodesic flow on a surface with the study of the geodesic flow on the moduli space of translation surfaces, which has a chaotic behavior that can be exploited to obtain many information on our initial flow.
Prerequisites are measure theory, some familiarity with complex analysis and functional analysis.
A sketch of the course is as follows:
- Introduction, motivation, brief survey of Teichmüller’s theorems;
- Basic definitions, examples, Masur’s criterion, Sketch of Kerkhoff, Masur and Smillie;
- Veech’s dichotomy, Examples of Veech surfaces (without proofs);
- Lyapunov exponents, motivations: Zorich’s asymptotic flag. Forni’s proof of Kontsevich-Zorich conjecture for genus 2;
- Detour, an explicit counterexample: the Eierlegende Wollmilchsau;
- Sketch of the exponential mixing of the Teichmüller flow (following Avila, Gouëzel and Yoccoz);
- An introduction to Transfer Operator Theory;
- Ruelle resonances for Pseudo-Anosov transformations.
Practical info: The course will last 5 weeks, for a total of approximately 30 hours. The first lecture will be on the 4th of June at 15,30 (Rome Time). From the 7th of June to the 10th of July the schedule is:
Monday 11,30 – 13,30;
Wednesday 15,30 – 17,30;
Friday 15,30 – 17,30
BEWARE: Due to the Italian tradition of “quarto d’ora accademico” lectures begin 15 minutes after the scheduled time.
The course will be held virtually on Teams, hosted by the University of Pisa. Some of the lectures will be streamed and recorded (for the teachers’ use) via Zoom. Accordingly, the links will be provided both by mailing list and the Teams channel.
If you would like to attend the lectures, write to [email protected] or [email protected].
“Uniformly and non-uniformly hyperbolic dynamics”
“Systèmes dynamiques uniformément et
(In honour of Christian Bonatti’s 60th birthday)
14 – 18 June 2021
Plenary talks are planned every afternoon, from 1:30pm to 4:30pm approximately. More information will appear soon on the webpage of the event.
The online graduate school, part of the ANR Project RAW “Random operators Arising in the study of random Walks”, is addressed to master, PhD students and postdocs, and people interested in the topics of random Schrödinger operators and their connection to random walks or stochastic process (in random environments).
The school will take place over 5 days: June 28, 29 and July 5-7, with 4h of lectures every day to accommodate participants from different time zones (mainly CET, GMT-3, GMT+8). It will consist of
- Mini courses with exercise sessions by Martin Vogel (CNRS & U. Strasbourg), Emmanuel Jacob (ENS Lyon),
- Mini courses by Peter Müller (LMU Munich), Oriane Blondel (CNRS & U. Claude Bernard Lyon 1) and Alain Joye (U. Grenoble Alpes)
- Introductory talks by Amine Asselah (U. Paris-Est Créteil), Eman Hamza (Cairo University), Katarzyna Pietruska-Pałuba (U. of Warsaw), Silke Rolles (TU Munich), Christian Sadel (P. Universidad Católica de Chile), Albert H. Werner (U. of Copenhagen).
For more details and registration, see the following link: https://sites.google.com/view/anr-jcjc-raw/raw-graduate-school
This online course is part of the Ph.D. program in Mathematics at University of Rome Tor Vergata.
Title: “Viscosity solutions of the Hamilton-Jacobi equations on non-compact manifolds”
Lecturer: Albert Fathi (Georgia Institute of Technology, USA)
– Lecture 1: Tuesday June 1, 11-13 (UTC+2)
– Lecture 2: Friday June 4, 11-13 (UTC+2)
– Lecture 3: Tuesday June 15, 11-13 (UTC+2)
– Lecture 4: Thursday June 17, 11-13 (UTC+2)
– Lecture 5: Tuesday June 22, 11-13 (UTC+2)
Lectures will be streamed by the platform Microsoft Teams.
– To subscribe to the Team of the course (It is not necessary to register to the Team in order to attend the streaming of the lectures, see next item):The identifying code of the Team is tltqtrm
Otherwise, you can register using the direct link: https://teams.microsoft.com/l/team/19%3a8e116cb44a774a5d83e247df943a2095%40thread.tacv2/conversations?groupId=92c9b6b2-bb3b-4d7e-833f-9a1ec74e9bcb&tenantId=24c5be2a-d764-40c5-9975-82d08ae47d0e
– This is the link to attend the streaming of the lectures (it works also for people that are not-member of the Team and also without downloading the app, but directly via browser): https://teams.microsoft.com/l/meetup-join/19%3a8e116cb44a774a5d83e247df943a2095%40thread.tacv2/1619861879421?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9%22%7d
These lectures are part of the activity of the MIUR Excellence Department Project [email protected] CUP E83C18000100006
For any information, please feel free to contact Alfonso Sorrentino ([email protected])
The Mathematical Institute of the Serbian Academy of Sciences and Arts will host the Belgrade Summer School on Dynamics, July 17-22, 2021, organized by Vladimir Dragović (UTD/MISANU) and Vadim Kaloshin (IST, Austria).
The target audience is undergraduate and graduate students and researchers from Serbia, the region, and around the globe interested in modern dynamics.
The school will be organized online with possible hybrid elements, if the situation with the pandemic permits. The lectures will be given by:
- Marcel Guardia (UPC, Barcelona)
- Hamid Hezari (UC Irvine)
- Vadim Kaloshin (IST, Wien)
- Martin Leguil (UPJV, Amiens)
The event is supported by the Seminars Mathematical Methods of Mechanics and Combinatorics, Geometry, Topology, and Algebra and by the journal Theoretical and Applied Mechanics.
All interested should contact Filip Jevtić by e-mail: [email protected]
by June 17, 2021.
The application material consists of a CV, a short statement of interest and for students a recommendation letter.