Workshop 

Spectral Geometry, Graphs, Semiclassical Analysis and Dynamics in Peyresq

sunday 4 june 2017 evening  -> saturday 10 june 2017 morning

organized by the ANR "Geometry,graphs, Semiclassical dynamics".

• The place
• Scientific program
• Transport information
• Participants

• Other activities

The place

A 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.

Scientific program

This meeting will be around the topics  "dynamical systems, geometry and spectral theory",

"semiclassical analysis and applications",
"quantum chaos",

statistical physics", "QFT" ...

 This is a working group:

  - participant presents a paper(s) (not from him) that she (he) finds interesting.

  - or we present some open problems the first day(s) of the conference, and we discuss, work on them together, the next days.

Propositions of talks and/or open problems

• Guillaume Klein 
• propose to present the  article " "Observability properties of the homogeneous wave equation on a closed manifold" by Emmanuel Humbert Yannick Privat  Emmanuel Trélat.

• Alix Deleporte:
• will present a paper on topological isolators.

• Vincent Beffara and Frédéric Faure
• will propose to discuss an open problem: "how to prove Fourier law with a deterministic model?". Is it possible to use recent technics in hyperbolic dynamics (central limit theorem, exponential decay of correlations etc)?

• Jean Lagacé:
•  article de Gregory Berkolaiko and Andrew Comech : "Symmetry and Dirac Points in Graphene Spectrum",
  In the talk, I will focus on the geometric arguments provided but give an idea for all of the results in the paper.

• Laurent Charles:
•  article de Nir Lev, Joaquim Ortega-Cerdà  "Equidistribution estimates for Fekete points on complex manifolds"
  Il s’agit d’échantillonnage/interpolation en quantification kählerienne.

• Nalini Anantharaman:
•  texte de Jean Lacroix. "propriétés spectrales l’opérateur de Schrödinger avec potentiel aléatoire dans un ruban."

• Yves Colin de Verdière:
• I propose to start from (part of) the thesis in physics of Christophe Brouzet   (essentially chapters 1 and 3)  and to describe mathematical models and problems associated to this work.

• Nikhil Savale:
•  papier de Lascar sur la propagation pour les opérateurs hypoelliptiques.

• Emmanuel Schenck:
•  un article récent de Dyatlov-Zworski sur la valeur en zéro de la fonction zeta de Ruelle, avec éventuellement une petite ouverture sur le travail de Chen (qui utilise le laplacien hypoelliptique de Bismut, pour un résultat similaires sur certaines variétés localement symétriques)

• Luc Gossart: 
• Articles of Carlangelo Liverani about "Fast-Slow dynamics":
• I: Fast-slow partially hyperbolic systems: beyond averaging. Part I (Limit Theorems)
• II: Statistical properties of mostly contracting fast-slow partially hyperbolic systems
• III: Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems : We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.

• Loren Coquille: Mathematical models that describe dynamics of populations in ecology.

Tentative schedule (we will see on place)

Transport information

Arrival:  in Peyresq will be sunday 4 june 2017  in the afternoon or the evening.

For people coming from Nice:

• Informations for Nice airport -> "Train des pignes" station in Nice.
• "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 -> Meailles:

http://tourisme.trainprovence.com/horaires-urbains-interurbains/

Since the train station is 30mn from Peyresq by car, it is better if you can arrive simultaneously on Sunday 4th june:
I propose to take the train in Nice a 17h15   -> Meailles  19h20

(or the one before: Nice  13h05 -> Meailles 15h01 but i am not sure to be able to be there)

• Then a car (or some cars) will take you in Meailles to Peyresq.

• An other possibility 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.

For people coming from grenoble:

        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", so that we can wait the train  Paris 9h45 -> Grenoble  12h46. If the weather is good, we will buy a picnic in grenoble and  take the lunch on the road.

                Francoise has 2/3 places in her "car 3" (Grenoble <-> Peyresq (back on friday evening).

Departure:  saturday 10 june 2017

• Since the train station is 30mn from Peyresq by car, it is better if you can leave simultaneously: I propose that  people take the "train des pignes" :  Train Meailles (8h35) –> Nice CP (10h30).
• There will be cars to grenoble, 
• In particular a minibus from Preyresq to grenoble with 9 places that can reach grenoble for the Grenoble 17h16->Paris 20h15.  Possibility to stop at train station "Chateaux Arnoud or sisteron".
•   Yves Colin de Verdieres has 2 places in his "car 1" (Voreppe near Grenoble <-> Peyresq).
• Francoise has 2/3 places in her "car 2" (Peyresq -> grenoble on friday evening).

Participants

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 or here. 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. For technical advices consult Erwann Lanneau.

• 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?