Departement Mathematik

Ergodic theory and dynamical systems

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Herbstsemester 2018

Datum / Zeit Referent:in Titel Ort
27. September 2018
09:00-10:00 		Manuel Lüthi
ETH Zurich, Switzerland
Details

Ergodic theory and dynamical systems seminar

Titel Talk in ETDS working seminar
Referent:in, Affiliation Manuel Lüthi, ETH Zurich, Switzerland
Datum, Zeit 27. September 2018, 09:00-10:00
Ort HG G 19.1
Abstract We formulate bounds on Kloosterman sums as an effective equidistribution problem in the unit tangent bundle of the modular surface – giving rise to effective equidistribution of primitive rational points. Using this interpretation, we obtain a natural generalization of this question and show how to prove effective equidistribution of primitive rational points in products of the torus and the unit tangent bundle to the modular surface using effective mixing for congruence quotients.
Talk in ETDS working seminarread_more
HG G 19.1
1. Oktober 2018
15:30-16:30 		Prof. Dr. Martin Möller
Goethe-Universität Frankfurt
Details

Ergodic theory and dynamical systems seminar

Titel Siegel-Veech constants and intersection numbers on moduli space
Referent:in, Affiliation Prof. Dr. Martin Möller, Goethe-Universität Frankfurt
Datum, Zeit 1. Oktober 2018, 15:30-16:30
Ort Y27 H 25
Abstract Siegel-Veech constants are quantities that control the dynamics of the straight line flow on flat surfaces. We show how to relate these quantities to algebraic intersection numbers on the Hodge bundle over the moduli space of curves.
Siegel-Veech constants and intersection numbers on moduli spaceread_more
Y27 H 25
8. Oktober 2018
15:30-16:30 		Prof. Dr. Amos Nevo
Technion, Israel Institute of Technology
Details

Ergodic theory and dynamical systems seminar

Titel Effective solution count in intrinsic Diophantine approximation
Referent:in, Affiliation Prof. Dr. Amos Nevo, Technion, Israel Institute of Technology
Datum, Zeit 8. Oktober 2018, 15:30-16:30
Ort Y27 H 25
Abstract In his 1965 "Report on Diophantine approximation" Serge Lang raised the problem of establishing the approximation properties of rational points on homogeneous algebraic varieties, singling out in particular the questions of establishing Diophantine approximation exponents, an analog of Khinchin's dichotomy theorem and an analog of W. Schmidt's solution counting theorem. In recent years a systematic approach to Lang's problems has been developed for varieties homogeneous under an action of semisimple groups, and some progress towards answering the questions mentioned above has been obtained, with the answers in certain special cases being optimal. The methods involve lattice actions, ergodic theorems and spectral estimate in the automorphic representation. Based on joint work with Anish Ghosh and Alex Gorodnik.
Effective solution count in intrinsic Diophantine approximationread_more
Y27 H 25
11. Oktober 2018
09:05-10:05 		Dr. Roland Prohaska
ETH Zurich, Switzerland
Details

Ergodic theory and dynamical systems seminar

Titel Morning Seminar: Equidistribution of Markov Random Walks on Homogeneous Spaces
Referent:in, Affiliation Dr. Roland Prohaska, ETH Zurich, Switzerland
Datum, Zeit 11. Oktober 2018, 09:05-10:05
Ort HG G 43
Abstract We show that under an expansion condition, typical trajectories of finite state Markov random walks on homogeneous spaces equidistribute. Our results add to previous work in the iid case by Benoist--Quint and Simmons--Weiss and have applications to Diophantine approximation on graph-directed fractals. Joint work with Cagri Sert.
Morning Seminar: Equidistribution of Markov Random Walks on Homogeneous Spaces read_more
HG G 43
15. Oktober 2018
15:30-16:30 		Prof. Dr. Giovanni Forni
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel On twisted translation flows
Referent:in, Affiliation Prof. Dr. Giovanni Forni, University of Maryland
Datum, Zeit 15. Oktober 2018, 15:30-16:30
Ort Y27 H 25
Abstract We study cohomological equations and ergodic integrals for twisted translation flows, define as products of a translation flow on a translation surface and a linear flow on a circle. By standard Fourier analysis the questions we consider reduce respectively to non-homogeneous cohomology equations with purely imaginary constant zero-order term (twisted cohomological equation) and to ergodic integrals of functions times an exponential of time with purely imaginary phase (twisted ergodic integrals). The motivation is two-fold: on the one hand we want to understand a simple example of 3-dimensional translation flow, on the other hand there is a well-known close connection between twisted ergodic integrals and spectral measures of translation flows, already exploited in the work of Bufetov-Solomyak. In this respect our aim is to cast their work in more geometric terms and to generalize it.
On twisted translation flowsread_more
Y27 H 25
19. Oktober 2018
09:00-10:00 		Yiftach Dayan
Tel Aviv University
Details

Ergodic theory and dynamical systems seminar

Titel Morning Seminar: Diophantine approximations on random fractals
Referent:in, Affiliation Yiftach Dayan, Tel Aviv University
Datum, Zeit 19. Oktober 2018, 09:00-10:00
Ort Y27 H 28
Abstract We will present a model for the construction of random fractals which is called fractal percolation. The result that will be presented in this talk states that a typical fractal percolation set E intersects every set which is winning for a certain game that is called the "hyperplane absolute game", and the intersection has the same Hausdorff dimension as E. A motivating example of such a winning set is the set of badly approximable vectors in dimension d. In order to prove this theorem one may show that a typical fractal percolation set E contains a sequence of Ahlfors-regular subsets with dimensions approaching the dimension of E, where all the subsets in this sequence are also "hyperplane diffuse", which means that they are not concentrated around affine hyperplanes when viewed in small enough scales. If time permits, we will discuss the method of the proof of this theorem as well as a generalization to a more general model for random construction of fractals which is given by projecting Galton-Watson trees against any similarity IFS whose attractor is not contained in a single affine hyperplane.
Morning Seminar: Diophantine approximations on random fractalsread_more
Y27 H 28
22. Oktober 2018
15:30-16:30 		Dr. Christopher Daw
University of Reading
Details

Ergodic theory and dynamical systems seminar

Titel Convergence of measures on compactifications of locally symmetric spaces
Referent:in, Affiliation Dr. Christopher Daw, University of Reading
Datum, Zeit 22. Oktober 2018, 15:30-16:30
Ort Y27 H 25
Abstract In this talk, we will explain our conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space S is compact. To be more precise, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components. We will discuss some tools that we have used to study this conjecture as well as some partial results.
Convergence of measures on compactifications of locally symmetric spacesread_more
Y27 H 25
29. Oktober 2018
15:30-16:30 		Prof. Dr. Raphael Krikorian
Université de Cergy-Pontoise
Details

Ergodic theory and dynamical systems seminar

Titel On the divergence of Birkhoff Normal Forms
Referent:in, Affiliation Prof. Dr. Raphael Krikorian, Université de Cergy-Pontoise
Datum, Zeit 29. Oktober 2018, 15:30-16:30
Ort Y27 H 25
Abstract An analytic hamiltonian system (or a symplectic diffeomorphism) admitting an elliptic fixed point is always formally conjugated to a formal integrable normal form, the Birkhoff Normal Form. It is known since Siegel (1954) that the formal conjugacy cannot in general converge and H. Eliasson asked whether the Birkhoff Normal Form itself could be divergent. Perez-Marco (2001) proved that for any given frequency vector at the origin, one has the following dichotomy: either the BNF always converges or it generically diverges and Gong (2012) exhibited a divergent example with Liouville frequency vector. I will explain in this talk the proof of the following theorem: given any diophantine frequency vector at the origin, the BNF is generically divergent.
On the divergence of Birkhoff Normal Formsread_more
Y27 H 25
5. November 2018
15:30-16:30 		Prof. Dr. Bassam Fayad
Institut de Mathématiques de Jussieu-Paris Rive Gauche
Details

Ergodic theory and dynamical systems seminar

Titel Stabilities and Instabilities in quasi-periodic Hamiltonian motions
Referent:in, Affiliation Prof. Dr. Bassam Fayad, Institut de Mathématiques de Jussieu-Paris Rive Gauche
Datum, Zeit 5. November 2018, 15:30-16:30
Ort Y27 H 25
Abstract We introduce a new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom. Using this mechanism, we obtain the first examples of real analytic Hamiltonians that have a Lyapunov unstable non-resonant elliptic equilibrium. We also give examples of real analytic invariant quasi-periodic tori of arbitrary frequency vectors that are Lyapunov unstable but have a polynomial Birkhoff normal form.
Stabilities and Instabilities in quasi-periodic Hamiltonian motionsread_more
Y27 H 25
12. November 2018
15:30-16:30 		Dr. Lucia Dora Simonelli
ICTP (International Centre for Theoretical Physics)
Details

Ergodic theory and dynamical systems seminar

Titel Resonances of Nilmanifold Automorphisms and Properties of Nilflows
Referent:in, Affiliation Dr. Lucia Dora Simonelli, ICTP (International Centre for Theoretical Physics)
Datum, Zeit 12. November 2018, 15:30-16:30
Ort Y27 H 25
Abstract We start by considering the Heisenberg nilflow renormalized by a partially hyperbolic automorphism of the nilmanifold. Through this renormalization, we show that the spectrum of the transfer operator of the partially hyperbolic map gives information about the (parabolic) nilflow - in particular, information about deviation of ergodic averages and regularity of the cohomological equation. Then we discuss the spectral information of more general partially hyperbolic systems and their relationship to a larger class of parabolic flows. (Joint work with Oliver Butterley.)
Resonances of Nilmanifold Automorphisms and Properties of Nilflowsread_more
Y27 H 25
21. November 2018
15:45-16:45 		Prof. Dr. Tamar Ziegler
Einstein Institute of Mathematics, Hebrew University
Details

Ergodic theory and dynamical systems seminar

Titel Extending weakly polynomial functions from high rank varieties
Referent:in, Affiliation Prof. Dr. Tamar Ziegler, Einstein Institute of Mathematics, Hebrew University
Datum, Zeit 21. November 2018, 15:45-16:45
Ort HG G 43
Abstract Let k be a field, V a k-vector space, X in V a subset. Say that f: X --> k is weakly polynomial of degree a if its restriction to any isotropic subspace is a polynomial degree of a. We show that if X is a high rank variety then any weakly polynomial function of degree a is the restriction to X of a polynomial of degree a on V. Equidistribution properties of high rank polynomials play an important role. Joint work with D. Kazhdan.
Extending weakly polynomial functions from high rank varietiesread_more
HG G 43
26. November 2018
15:30-16:30 		Prof. Dr. Tanja Eisner
University of Leipzig
Details

Ergodic theory and dynamical systems seminar

Titel Weighted Ergodic Theorems
Referent:in, Affiliation Prof. Dr. Tanja Eisner, University of Leipzig
Datum, Zeit 26. November 2018, 15:30-16:30
Ort Y27 H 25
Abstract We present an overview on good weights for the pointwise ergodic theorem.
Weighted Ergodic Theoremsread_more
Y27 H 25
3. Dezember 2018
15:30-16:30 		Prof. Dr. Emmanuel Breuillard
Details

Ergodic theory and dynamical systems seminar

Titel The joint spectrum
Referent:in, Affiliation Prof. Dr. Emmanuel Breuillard,
Datum, Zeit 3. Dezember 2018, 15:30-16:30
Ort Y27 H 25
Abstract The notion of joint spectral radius of a set S of matrices was introduced by Rota and Strang in the 60's and encodes the maximum asymptotic rate of spatial growth of a product of elements from S. It is intimately related to the maximal growth of eigenvalues of products of elements from S by theorems of Berger-Wang and Bochi. In this talk I will present a multi-dimensional version of this notion, where one looks at the full vector of eigenvalues leading naturally to the notion of joint spectrum of S. This is a compact subset of the Weyl chamber that can sometimes be explicitly computed and has connections with the asymptotic shape of large balls in Cayley graphs of Lie groups, with Lyapunov exponents for stationary processes, large deviations for random matrix products and with ergodic optimization. Joint work with Cagri Sert.
The joint spectrumread_more
Y27 H 25
10. Dezember 2018
15:30-16:30 		Prof. Dr. Jean-François Quint
CNRS - Université de Bordeaux
Details

Ergodic theory and dynamical systems seminar

Titel Complementary series
Referent:in, Affiliation Prof. Dr. Jean-François Quint, CNRS - Université de Bordeaux
Datum, Zeit 10. Dezember 2018, 15:30-16:30
Ort Y27 H 25
Abstract Complementary series are families of unitary representations of certain (rank 1) simple Lie groups, as well as of groups of automorphisms of regular trees. I will explain their construction and show how to extend it in order to get new representations of free groups.
Complementary seriesread_more
Y27 H 25
17. Dezember 2018
15:30-16:30 		Dr. Adam Kanigowski
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel Bernoulli property for homogeneous systems
Referent:in, Affiliation Dr. Adam Kanigowski, University of Maryland
Datum, Zeit 17. Dezember 2018, 15:30-16:30
Ort Y27 H 25
Abstract We study homogeneous systems on irreducible quotients of semi simple Lie groups. We show that positive entropy implies that the system is Bernoulli.
Bernoulli property for homogeneous systemsread_more
Y27 H 25
9. Januar 2019
11:00-12:00 		Dr. Michael Björklund
Chalmers University, Schweden
Details

Ergodic theory and dynamical systems seminar

Titel Almost almost homogeneous dynamics
Referent:in, Affiliation Dr. Michael Björklund, Chalmers University, Schweden
Datum, Zeit 9. Januar 2019, 11:00-12:00
Ort HG G 19.1
Abstract The plan is to survey some recent developments about approximate lattices, which are "large" approximate subgroups of lcsc groups. After setting up definitions, we will discuss the close analogy with "classical" lattices. Based on joint works with Tobias Hartnick (Giessen).
Almost almost homogeneous dynamicsread_more
HG G 19.1
9. Januar 2019
13:00-14:00 		Dr. Krzysztof Fraczek
Nicolaus Copernicus University
Details

Ergodic theory and dynamical systems seminar

Titel Billiard flows in nibbled ellipses
Referent:in, Affiliation Dr. Krzysztof Fraczek, Nicolaus Copernicus University
Datum, Zeit 9. Januar 2019, 13:00-14:00
Ort HG G 19.1
Abstract I plan to present some basic properties of the billiard flow on nibbled ellipses. The boundary of a nibbled ellipse consist of a chain of elliptic and hyperbolic arcs, all coming from confocal conics. The main aim of the talk is to present some steps and tools in the proof of equidistribution for almost all invariant sets determined by caustics of the billiard.
Billiard flows in nibbled ellipsesread_more
HG G 19.1

Organisatoren:innen: Menny Akka Ginosar, Artur Ávila, Ofir David, Manfred Einsiedler, Alexander Gorodnik, Corinna Ulcigrai

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18

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