Workshop «Hyperbolic dynamical systems, geometry and spectral theory» in Peyresq

1 The place

• Enter in the village with google street. A precise (IGN) map that you can (de)zoom by using the +/- on the top left.
• Informations on the association that welcome us are here or (here in french). Some images of the village.
• Beware the altitude is 1500 meters. Evenings are cold. The weather can be cold (or not). Take good clothes. Here is the forecast.

2 Scientific program

• Participant presents a paper(s) (not from him) that she (he) finds interesting. A subject can be presented in tandem by two persons.
• or we present some open problems the first day(s) of the conference, and we discuss, work on them together, the next days.
• Large place for discussions among participants.
• We encourage the presence and participation of students and young researchers.

2.1 We have 9 propositions of talks (the program is full)

1. Proposition from Baptiste Cercle: durée ?
   • sujet qui tournerait autour de la quantification géométrique, des orbites co-adjointes et des modèles Wess-Zumino-Witten (voir l'article https://arxiv.org/abs/1801.07963 d'Alekseev et Shatashvili) ,
2. Proposition from Malo Jezequel: durée >= 2h
   • Waves in 2 dimensional domains from the recent paper of Dyatlov, Wang, Zworski https://arxiv.org/abs/2112.10191 and related papers from Laure Saint-Raymond, Yves Colin de Verdière, Galkowski-Zworski and other articles in physics.
3. Proposition from Vivek Dewan: durée >= 1h15
   • “GOE STATISTICS ON THE MODULI SPACE OF SURFACES OF LARGE GENUS” by Rudnick.
   • https://arxiv.org/pdf/2202.06379.pdf
4. Proposition from Ioannis Iakovoglou: durée >= 2h
   • https://arxiv.org/abs/2012.11811 “Orbit equivalences of R-covered Anosov flows and applications” from Thomas Barthelmé, Kathryn Mann. In this article the authors prove among others that two R-covered Anosov flows on the same manifold M having periodic orbits in the exact same free homotopy classes of M are orbitally equivalent. I believe that the proof of the previous result can be explained in the duration of one talk modulo some black boxes from Anosov flow theory and also that this would allow us to state some interesting open problems in Anosov flow theory.
5. Julien Boulanger et Charles Fougeron: durée: 1h15 + 1h15
   • Translation surfaces and entropy, from recent papers of Colognese/Pollicott.
     • https://arxiv.org/abs/2107.14058.pdf
     • https://arxiv.org/pdf/2107.14078.pdf
     • https://arxiv.org/pdf/2107.14078.pdf
6. Lucas Vacossin: durée >= 1h15
   • Mathematics of magic angles in a model of twisted bilayer graphene, (Simon Becker, Mark Embree, Jens Wittsten, Maciej Zworski), from https://arxiv.org/abs/2008.08489.
7. Félix Lequen: durée >=2h
   • L'article de Bourgain, Furman, Lindesntrauss, Mozes sur les mesures stationnaires pour les marches aléatoires linéaires sur le tore https://www.ams.org/journals/jams/2011-24-01/S0894-0347-2010-00674-1/. C'est une preuve par l'analyse de Fourier, très quantitative et qui utilise des idées de géométrie fractale.
   • L'article de Lindenstrauss-Mohammadi qui montre un cas particulier effectif de Ratner (pour la densité d'orbites). https://arxiv.org/abs/2112.14562. La preuve est par certains égards semblables (et inspirée de) à l'article de Bourgain, Furman, Lindenstrauss, Mozes ci-dessus (mais c'est sans doute plus technique encore).
8. Colin Guillarmou: durée ?
   • je propose l’étude de ce papier https://arxiv.org/abs/2111.12716 . Ce sont des phycisiens à l’IAS qui appliquent les idées du bootstrap conforme pour les petites valeurs propres du laplacien sur les surfaces hyperboliques. Ils ont aussi appliqué cette méthode de bootstrap et ils retrouvent des resultats de Viazwoska.

2.2 Schedule

• On morning 9h-10h15, pause, 10h45-12h: one talk with two parts of 1h15 each, or 2 talks of 1h15 each.
• On afternoon 17h-19h: one talk of 2 hours.

3 Participants

• There are 9 places in the mini-van grenoble<->Peyresq.
• There are 2 places with Yves Colin de Verdiere in his car, grenoble<->Peyresq.

4 Transport information

4.1 Arrival: in Peyresq will be sunday 19 june 2022 in the afternoon or the evening.

• Bus: Nice -> Peyresq?
  • There will be a special bus from Nice's airport to Peyresq, Departure sunday 19 june 2022 at 16h30 from Nice Airport. To be confirmed.
• Minibus: Grenoble -> Peyresq, sunday 19 june 2022
  • We will have a minibus with 9 places starting from Grenoble. So you can join us in Grenoble.
  • We will start around 13h from grenoble, train station, side of "palais de justice", exactly here, so that we can wait the train Paris 8h59 -> Grenoble 12h39. If the weather is good, we will buy a picnic in grenoble and take the lunch on the road.
  • Possibility to stop at train station "Chateaux Arnoud or sisteron".
• Train + Foot-path: Nice -> Peyresq, for people who like walking on a nice small path in the mountain, with a backpack (no suitcase)
  • Informations for Nice airport -> "Train des pignes" station in Nice.
  • Train des pignes from Nice to Peyresq station
    • "Train des pignes" station in Nice: here is on google map. (This is close to but different from the national SNCF train station).
    • Here are the time table for the "train des pignes": Nice -> Peyresq
  • Then for people who like walking on a nice small path in the mountain, with a backpack (no suitcase): stop at the train station called "arrêt de Peyresq" (you have to ask to the train driver) and follow the path on this map that goes to the north. You start above and along the right side of the river "Vaïre". After walking flat 2km, you arrive at the ruins of Moulin du Ray", then the path goes up. You will have 500 meters elevation, may be 2h.

4.2 Departure on friday 24th june:

• Bus: Peyresq -> Nice.
  • There will be a special bus to Nice's airport from Peyresq, arrival at Nice's airport, friday 24th at 14h30. To be confirmed.
• Minibus: Peyresq -> Grenoble friday 24th june
  • a minibus from Preyresq to grenoble with 9 places that can reach grenoble before 17h to catch a train Grenoble 17h19 -> Paris 20h18. Possibility to stop at train station "Chateaux Arnoud or sisteron".

5 Other activities

• Just look at the view and think or discuss about mathematics.
• Look at mountain flowers. This will the full season of blowing flowers. Here is a list and a useful app. Make a tour around Peyresq and try to recognize them!
• Walk in the moutain around Peyresq. Bring good clothes and shoes. Here is a map . There is a local summit (2693m = Peyresq + 1170m): "le grand coyer" and a more local one (2157m = Peyresq + 620m) "le courradour". There is a small cave to visit, bring your lights. La grotte de Meailles
• Climbing at annot, pictures, topo.
• Music: there are some musicians and singers among us. I will bring a guitare. There will be a piano, you can bring your instrument, sheet music, song lyrics, to share with us.
• Mountain bike. Bring your mountain bike (there will be 3 places on the minibus). Here are the topo.
• Look for fossiles.
• Other ideas?