Departement Mathematik

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Ergodic theory and dynamical systems

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Herbstsemester 2019

Datum / Zeit Referent:in Titel Ort
23. September 2019
14:00-15:00 		Dr. Cagri Sert
Universität Zürich
Details

Ergodic theory and dynamical systems seminar

Titel Measure classification and (non)-escape of mass for horospherical actions on regular trees
Referent:in, Affiliation Dr. Cagri Sert, Universität Zürich
Datum, Zeit 23. September 2019, 14:00-15:00
Ort HG G 43
Abstract Let T be a d-regular tree (d > 2), R < Aut(T) be a lattice and U < Aut(T) the stabilizer of some end on the boundary of T, that do not contain hyperbolic elements (horospherical subgroup). In a first part, we study U-invariant ergodic probability measures on Aut(T)/ R and prove an Hedlund theorem when R is geometrically finite. In a second part, given a closed transitive subgroup G < Aut(T) and lattice R < G, we study non-escape of mass phenomenon for the U-action on G/R and we construct examples of R with escape of mass for the U-action using subgaussian concentration inequalities. Finally, we make connections between the geometric diophantine behaviour of ends and the speed of equidistribution of dense U-orbits in the aforementioned Hedlund theorem. Joint work with Corina Ciobotaru and Vladimir Finkelshtein.
Measure classification and (non)-escape of mass for horospherical actions on regular treesread_more
HG G 43
30. September 2019
14:00-15:00 		Dr. Pengyu Yang
ETH Zürich
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Ergodic theory and dynamical systems seminar

Titel Translates of curves in homogeneous spaces and Dirichlet improvability on matrices
Referent:in, Affiliation Dr. Pengyu Yang, ETH Zürich
Datum, Zeit 30. September 2019, 14:00-15:00
Ort HG G 43
Abstract We will show that in homogeneous spaces, the expanding translates of a generic analytic curve under a flow get equidistributed with respect to the Haar measure. This also has an application to Diophantine approximation on matrices. The proof relies on Ratner's theorem on unipotent rigidity, linearization technique, and a new ingredient coming from geometric invariant theory.
Translates of curves in homogeneous spaces and Dirichlet improvability on matricesread_more
HG G 43
7. Oktober 2019
15:15-16:15 		Prof. Dr. Peter Varju
University of Cambridge
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Ergodic theory and dynamical systems seminar

Titel The dimension of Bernoulli convolutions
Referent:in, Affiliation Prof. Dr. Peter Varju, University of Cambridge
Datum, Zeit 7. Oktober 2019, 15:15-16:15
Ort HG F 26.1
Abstract The Bernoulli convolution with parameter lambda in (0, 1) is the measure nu_lambda on the real line that is the distribution of the random power series sum of +/-lambda^n , where +/- are independent fair coin tosses. These measures are natural objects from several points of view including fractal geometry, dynamics and number theory. I will discuss recent results about their dimension.
The dimension of Bernoulli convolutionsread_more
HG F 26.1
14. Oktober 2019
14:00-15:00 		Prof. Dr. Sophie Grivaux
CNRS, Lille
Details

Ergodic theory and dynamical systems seminar

Titel Fourier coefficients of continuous measures on the Furstenberg sequence
Referent:in, Affiliation Prof. Dr. Sophie Grivaux, CNRS, Lille
Datum, Zeit 14. Oktober 2019, 14:00-15:00
Ort HG G 43
Abstract We will present a negative answer to a conjecture of Lyons, related to Furstenberg $x2$-$x3$ conjecture, concerning the existence of a continuous probability measure on the unit circle with large Fourier coefficients on the Furstenberg set {2^p3^q ; p,q \geq 0}. The proof involves rigidity sequences for weakly mixing dynamical systems, and a generalization of a recent construction of such sequences by Fayad and Thouvenot. This is joint work with Catalin Badea.
Fourier coefficients of continuous measures on the Furstenberg sequenceread_more
HG G 43
17. Oktober 2019
15:30-16:30 		Dr. Wenyu Pan
University of Chicago
Details

Ergodic theory and dynamical systems seminar

Titel Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay
Referent:in, Affiliation Dr. Wenyu Pan, University of Chicago
Datum, Zeit 17. Oktober 2019, 15:30-16:30
Ort Y13 L 11/13
Abstract We will start with the notion of Fourier dimension of a subset of $\mathbb{R}^d$. We will then focus on the particular case of the limit sets of Kleinian Schottky groups and show the the Fourier transform of the associated Patterson-Sullivan measures enjoy polynomial decay. This generalizes a result of Bourgain-Dyatlov for convex co-compact Fuchsian groups. The proof includes an estimate on the decay of exponential sums and a regularity estimate for stationary measures of certain random walks on linear groups. This is a joint work with Jialun Li and Fréderic Naud.
Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decayread_more
Y13 L 11/13
28. Oktober 2019
14:00-15:00 		Prof. Dr. Amir Mohammadi
Department of Mathematics, UC San Diego
Details

Ergodic theory and dynamical systems seminar

Titel Geodesic planes in hyperbolic 3-manifolds and arithmeticity
Referent:in, Affiliation Prof. Dr. Amir Mohammadi, Department of Mathematics, UC San Diego
Datum, Zeit 28. Oktober 2019, 14:00-15:00
Ort HG G 43
Abstract Let M be a hyperbolic 3-manifold, a geodesic plane in M is a geodesic immersion of the hyperbolic plane into M. It is quite rare for a totally geodesic plane to be a closed subset of M; indeed, it was proved recently that if M contains infinitely many closed geodesic planes, then M is arithmetic, i.e., the fundamental group of M is an arithmetic lattice in PGL(2, C). We will discuss a proof in this talk. This is based on a joint work with G. Margulis.
Geodesic planes in hyperbolic 3-manifolds and arithmeticityread_more
HG G 43
7. November 2019
16:30-17:30 		Yoav Gat
Technion
Details

Ergodic theory and dynamical systems seminar

Titel On the analogue of the Gauss circle problem for Cygan-Koranyi norm balls.
Referent:in, Affiliation Yoav Gat, Technion
Datum, Zeit 7. November 2019, 16:30-17:30
Ort Y13 L 11/13
Abstract In this talk, I shall present a generalization of the lattice point counting problem for Euclidean balls in the context of a certain type of homogeneous groups, the so-called Heisenberg groups. I will begin by describing the counting problem at hand, and how it relates to the Euclidean case both from the group-theoretic perspective as well as the analytic methods needed to tackle it. I shall then proceed by presenting the main results regarding the lattice point discrepancy for Heisenberg-dilates of the Cygan-Koranyi norm ball, and for the rest of the talk I will survey the various stages and metods which appear in the course of the proof of these results.
On the analogue of the Gauss circle problem for Cygan-Koranyi norm balls.read_more
Y13 L 11/13
11. November 2019
14:00-15:00 		Dr. Nguyen-Thi Dang
Université Rennes 1
Details

Ergodic theory and dynamical systems seminar

Titel Topological dynamics of the Weyl Chamber flow
Referent:in, Affiliation Dr. Nguyen-Thi Dang, Université Rennes 1
Datum, Zeit 11. November 2019, 14:00-15:00
Ort HG G 43
Abstract Let G be a connected, real linear, semisimple Lie group of non-compact type. Consider a Cartan subgroup A, a closed Weyl chamber A^+ in A and a maximal compact subgroup K for which the Cartan decomposition G = KA^+K holds. Denote by M the centralizer subgroup of A in K. Let D be a discrete subgroup of G. In this talk, we will assume that the real rank of G is higher than 2 and that D is Zariski dense (not necessarily a lattice). I am interested in dynamical systems of the form D\G/M x a_t, where a_t is a Weyl chamber flow. One can ask: when do they have non-diverging orbits? orbits that are dense in their A-orbit? is there topological mixing in a suitable subset of D\G/M? For G = SL(2, R), they identify with the action of the geodesic flow on the unit tangent bundle of D\H^2. The latter's topological dynamics are rather well understood due to the works of many people among which Hopf, Hedlund, Eberlein, Dal'bo... In particular, it is topologically mixing on its non-wandering set. In this talk, I will first state the main results on Weyl chamber flows of my thesis. Then I will sketch a proof of a joint work with O. Glorieux, a necessary and sufficient condition for topological mixing for regular Weyl chamber flows. Time permitting, I will present a generalization of this criteria for actions on D\G for SL(n, R) or SL(n, C).
Topological dynamics of the Weyl Chamber flowread_more
HG G 43
18. November 2019
14:00-15:00 		Prof. Dr. Sylvain Crovisier
CNRS, Orsay
Details

Ergodic theory and dynamical systems seminar

Titel Renormalization of Hénon maps with zero entropy
Referent:in, Affiliation Prof. Dr. Sylvain Crovisier, CNRS, Orsay
Datum, Zeit 18. November 2019, 14:00-15:00
Ort HG G 43
Abstract De Carvalho, Lyubich and Martens have built a renormalization for the (real) Hénon maps with very small Jacobian and described the boundary of the parameters with zero entropy. With E. Pujals and C. Tresser we extend some of these results up to Jacobian 1/4: any Hénon map with zero entropy can be renormalized. As a consequence, we also obtain a characterization of the sets of periods (answering a conjecture by Tresser).
Renormalization of Hénon maps with zero entropyread_more
HG G 43
25. November 2019
14:00-15:00 		Dr. Liviana Palmisano
Uppsala University
Details

Ergodic theory and dynamical systems seminar

Titel Coexistence of attractors and their stability
Referent:in, Affiliation Dr. Liviana Palmisano, Uppsala University
Datum, Zeit 25. November 2019, 14:00-15:00
Ort HG G 43
Abstract In unfoldings of rank-one homoclinic tangencies, there exist codimension 2 laminations of maps with infinitely many sinks. The sinks move simultaneously along the leaves. As consequence, in the space of real polynomial maps, there are examples of: Hénon maps, in any dimension, with infinitely many sinks, quadratic Hénon-like maps with infinitely many sinks and a period doubling attractor, quadratic Hénon-like maps with infinitely many sinks and a strange attractor. The coexistence of non-periodic attractors, namely two period doubling attractors or two strange attractors, and their stability is also discussed.
Coexistence of attractors and their stabilityread_more
HG G 43
2. Dezember 2019
14:00-15:00 		Dr. Zhiyuan Zhang
IAS, Princeton
Details

Ergodic theory and dynamical systems seminar

Titel Exponential mixing of 3D Anosov flows
Referent:in, Affiliation Dr. Zhiyuan Zhang, IAS, Princeton
Datum, Zeit 2. Dezember 2019, 14:00-15:00
Ort HG G 43
Abstract We show that a transitive C^\infty Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential if and only if E^s and E^u are not jointly integrable. This is a joint work with Masato Tsujii.
Exponential mixing of 3D Anosov flowsread_more
HG G 43
9. Dezember 2019
14:00-15:00 		Dr. Menny Akka
ETHZ
Details

Ergodic theory and dynamical systems seminar

Titel Joinings of diagonal flows and application to elliptic curves
Referent:in, Affiliation Dr. Menny Akka, ETHZ
Datum, Zeit 9. Dezember 2019, 14:00-15:00
Ort HG G 43
Abstract I will shortly discuss the classification of joinings for certain diagonal actions by Einsiedler and Lindenstrauss and some of its applications. Then I will detail a recent application to elliptic curves that shows the following: The simultaneous reduction with respect to several distinct inert primes of the set of complex multiplication curves of discriminant D is surjective on the set of isomorphism classes of supersingular curves, as D goes to infinity under two "external" congruence conditions. This is a joint work with Manuel Luethi, Philippe Michel, and Andreas Wieser.
Joinings of diagonal flows and application to elliptic curvesread_more
HG G 43
16. Dezember 2019
14:00-15:00 		Or Landesberg
The Hebrew University
Details

Ergodic theory and dynamical systems seminar

Titel Horospherically invariant measures on geometrically infinite quotients
Referent:in, Affiliation Or Landesberg, The Hebrew University
Datum, Zeit 16. Dezember 2019, 14:00-15:00
Ort HG G 43
Abstract We consider a locally finite (Radon) measure on SO(d,1)/Gamma invariant under a horospherical subgroup of SO(d,1) where Gamma is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not observe any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable flow (geodesic flow). Measure classification results are deduced, in particular for the case of a normal subgroup of a geometrically finite Zariski dense discrete group. This is joint work with Elon Lindenstrauss.
Horospherically invariant measures on geometrically infinite quotientsread_more
HG G 43

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