Workshop 

Spectral Geometry, Graphs, Semiclassical Analysis and Dynamics in Peyresq

saturday 21 may 2016 -> saturday 28 may 2016.

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.

Other  here.   or (here in french)

Beware the altitude is 1500 meters. Evenings are cold. The weather can be cold (or not).

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.
We will take time for each presentation if needed. (may be half a day).

Propositions of talks

• Frédéric Naud: (M1)

• Maxime Ingremeau and Martin Vogel (A2)

• will present Johannes Sjöstrand's paper: " Asymptotic distribution of eigenfrequencies for damped wave equation"
• Abstract:The eigenfrequencies associated to a damped wave equation, are known to belong to a band parallel to the real axis. We establish Weyl asymptotics for the distribution of the real parts of the eigenfrequencies, we show that up to a set of density 0, the eigenfrequencies are confined to a band determined by the Birkhoff limits of the damping coefficient. We also show that certain averages of the imaginary parts converge to the average of the damping coefficient.

• Sebastien Gouezel (M2)

  • article de Ledrappier et Lim, "Local Limit Theorem in negative curvature"
  • Abstract: describing very precisely the asymptotics of the heat kernel p_t(x,y) on a simply connected riemannian manifold of negative curvature with a compact quotient, when x y are fixed and t tends to infinity. The asymptotics are of the form C(x,y) e^{-\lambda_0 t} / t^{3/2}, where \lambda_0 is the bottom of the spectrum of the laplacian.
  • Slides of Ledrappier.  Video by F. Ledrappier.

• Francoise Truc (A3)

• article of  Davies et Pushnitski de 2010
• Title : "Non Weyl resonances asymptotics for quantum graphs",   arxiv:1003.0051v1
• abstract: we consider the resonances of a  quantum graph G that consists of a compart part with infinite leads attached to it. We discuss the leading term of the aymptotics oçf the number of  resonancesof G in a disc of large radius. We call G a Weyl graph if the coefficient in front of this leading term coincides with the volume of the compact part of G. We give an explicit topological criterion for a graph to be Weyl.

• Dima Jakobson (A3')

• article of Chatterjee and Galkowski,
• Title "ARBITRARILY SMALL PERTURBATIONS OF DIRICHLET LAPLACIANS ARE QUANTUM UNIQUE ERGODIC".
• Abstract: Given an Euclidean domain with very mild regularity properties, we prove that there exist arbitrarily small perturbations of the Dirichlet Laplacian of the form with whose high energy eigenfunctions are quantum unique ergodic (QUE). Moreover, if we impose stronger regularity on the domain, the same result holds with for depending on the domain. The method of proof is entirely probabilistic. A local Weyl law for domains with rough boundaries is obtained as a byproduct of the proof.
• Notes by D. Jakobson

• Alejandro Rivera and Luc Gossart (A5)

• article de Nazarov & Sodin (2007) "On the number of nodal domains of random spherical harmonics".
  
  The authors prove that the number of connected components of the zero set of a random spherical harmonic of high degree d concentrates in probability at an exponential rate around a.d for some constant a>0. We will provide an overview of the proof with some emphasis on the probabilistic arguments employed therein.

• Colin Guillarmou (M5)
  

• Article de Otal. "Le Spectre Marque des Longueurs des Surfaces a Courbure Negative" détermine la métrique à isométrie près.

• Vincent Beffara (M3)
  

• Travaux de Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond "The Brownian motion as the limit of a deterministic system of hard-spheres"
• Video . Texte

• Erwann Lanneau (M4)
  

• We will present a paper by McMullen "Entropy and the clique polynomial" and its connection to surface dynamics (entropy and pseudo-Anosov maps).
• If time and energy permit we will try to explain some ideas of a related paper by W. Thurston on Perron numbers: "Entropy in Dimension One".

• Nikhil Savale (A4)

• the paper of Montgomery on the magnetic Laplacian: "Hearing the zero locus of a magnetic field".  I might also use the book of Montgomery and the recent paper of Colin de Verdière-Hillairet-Trélat as a joint reference.

• Tobias Weich (A1):  

• Article récent de JF Bony et al. sur les chaines de resonances.

• Joachim Hilgert (A1'):  

• Les anciens articles de Bunke Olbrich  liés au résultat de Patterson-Perry sur les résonances sur la surface de Schottky.

Tentative schedule (we will see on place)

Transport information

Arrival:  in Peyresq will be saturday 21 may 2016 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:
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, so that we can wait the train from Paris 9h45-> Grenoble 12h47.

Car1 (Colin de V.) has 2 places. Departure 21/5 from Grenoble.

Car3 (Francoise) has 3 places. Departure 22/5 from Grenoble.

Departure: saturday 28 may 2016

• 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" 28/5/2016:  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->Paris TGV at 17h16 (the next is at19h16). Possibility to stop at train station "Chateaux Arnoud or sisteron".

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?