Meetings usually take place at 2pm on Tuesdays in the second floor seminar room in Howard House.

We are using the following material:

• Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards, G. Forni and C. Matheus, Journal of Modern Dynamics, 8(3-4), 271-436, 2014.
• A Primer on Mapping Class Group, B. Farb and D. Margalit, Princeton Univeristy Press, 2011.
• The scenery flow for geometric structures on the torus: the linear setting, P. Arnoux and A.M. Fisher, Chinese Annals of Mathematics, 22B(4), 427-470, 2001. (Preprint available here).
• Deviation for interval exchange transformations, A. Zorich, Ergodic Theory and Dynamical Systems, 17(6), 1477-1499, 1997.
• Flat surface models of ergodic systems, K. Lindsey and R. Trevino. (Preprint available here).
• The visits to zero of a random walk driven by an irrational rotation, A. Avila, D. Dolgopyat, E. Duryev and O. Sarig, Israel Journal of Mathematics, 207(2), 653-717, 2015.

Short courses and special seminars

Short course by Dr. Alexandra Skripchenko
National Research University Higher School of Economics (visiting from 31 January to 06 February)

1. Novikov's problem on plane sections of periodic surfaces; exeptional chaotic behaviour.
2. Reduction to systems of isometries, minimality.
3. Analogous of Rauzy Induction for systems of isometries.
4. Thermodynamic formalism and existence of a natural invariant measure on the set of admissible parameters.

Short course by Dr. Elise Goujard
Laboratoire de Mathématiques d'Orsay (visiting from 09 to 17 February)

1. Siegel-Veech constants for strata of Abelian differentials.
2. Diffusion rate and Lyapunov exponents for the Ehrenfest wind-tree model.
3. Generating functions associated to counting ramified torus covers are quasimodular forms; examples for the strata H(2) and H(1,1).

Seminar by Mr. Przemysław Berk
Nicolaus Copernicus University in Torun (visiting from 07 to 14 March)

1. Non-isomorphism criterion for flows with their inverses via joinings.
2. Applications to suspension flows over irrational rotations.

Seminar by Dr. Kathryn Lindsey
University of Chicago (visiting from 13 to 25 March)

1. Examples of cutting and stacking constructions and Bratteli diagrams: Hajian-Kakutani skyscraper and Pascal-adic transformations.
2. Horocycle orbit closure of translation surfaces.

Seminar by Dr. Adam Kanigowski
PennState University (visiting from 11 to 21 May)

1. Singular spectrum for Kochergin flows.

Seminar by Prof. Omri Sarig
Weizmann Institute of Science (visiting from 19 to 25 June)

1. A generalisation of Beck's Theorem to rotations of bounded type.

Meetings

1. Tuesday 20th October 2015: Grötzsch Theorem for quasiconformal maps, definitions of moduli space and of Teichmüller space.
2. Tuesday 27th October 2015: Moduli space of Riemann surfaces as the quotient of the Teichmüller space modulo the Mapping Class Group. Abelian, quadratic and Beltrami differentials. Beltrami differentials and quasiconformal maps.
3. Tuesday 03rd November 2015: Duality between Beltrami and quadratic differentials. Stratification of the space of Abelian differentials. Period coordinates on the Teichmüller space of Abelian differentials.
4. Wednesday 11th November 2015: Kontsevich-Zorich cocycle and its relations with Rauzy-Veech Induction for zippered rectangles.
5. Wednesday 18th November 2015: The scenery flow over the space of 2-dimensional affine lattices.
6. Wednesday 2nd December 2015: Symbolic coding for the scenery flow: Sturmian sequences and Ostrowsky expansion.
7. Wednesday 9th December 2015: Directional flows in planar periodic configurations of Eaton lenses.
8. Tuesday 15th December 2015: Adic transformations on Markov compacta.
9. Tuesday 12th January 2016: Zorich's result on deviation of ergodic averages for interval exchange transformations.
10. Wednesday 20th January 2016: Counting problems for flat surfaces. Siegel-Veech transform and Siegel-Veech constant.
11. Tuesday 26th January 2016: Computing volumes of strata of Abelian differentials via counting square tiled surfaces.
12. Tuesday 2nd February 2016: Short course by A. Skripchenko.
13. Wednesday 3rd February 2016: Short course by A. Skripchenko.
14. Tuesday 9th February 2016: Short course by E. Goujard.
15. Tuesday 16th February 2016: Short course by E. Goujard.
16. Friday 4th March 2016: Bratteli diagrams, tail equivalence relation and invariant measures, cutting and stacking constructions.
17. Tuesday 8th March 2016: Bi-infinite Bratteli diagrams ans translation surfaces; renormalisation.
18. Wednesday 9th March 2016: Special seminar by P. Berk.
19. Tuesday 15th March 2016: Special seminar by K. Lindsey.
20. Thursday 21st April 2016: First and second Lyapunov exponent of the Kontsevich-Zorich cocycle w.r.t. any invariant ergodic probability measure.
21. Tuesday 26th April 2016: Limit theorems for a random walk driven by an irrational rotation (part I).
22. Tuesday 3rd May 2016: Limit theorems for a random walk driven by an irrational rotation (part II).
23. Tuesday 10th May 2016: Limit theorems for a random walk driven by an irrational rotation (part III).
24. Tuesday 17th May 2016: Special seminar by A. Kanigowski.
25. Wednesday 08th June 2016: Transformations with finite non simple spectrum.
26. Tuesday 21st June 2016: Special seminar by O. Sarig.

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