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Ergodic theory and dynamical systems

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Frühjahrssemester 2022

Datum / Zeit Referent:in Titel Ort
28. Februar 2022
14:05-15:05 		Prof. Dr. Corinna Ulcigrai
Universität Zürich
Details

Ergodic theory and dynamical systems seminar

Titel Rigidity of Poincare sections of higher genus flows
Referent:in, Affiliation Prof. Dr. Corinna Ulcigrai, Universität Zürich
Datum, Zeit 28. Februar 2022, 14:05-15:05
Ort HG G 43
Abstract A celebrated result in the theory circle diffeomorphisms proved by Michael Herman and Jean-Christophe Yoccoz shows that (smooth) circle diffeomorphisms with a Diophantine rotation numbers are smoothly conjugated to their linear model, namely a rotation of the circle with the same rotation number. In terms of foliations on surfaces, this result shows that, under a full measure condition, smooth, orientable minimal foliations on surfaces of genus one are geometrically rigid, i.e. when they are topologically conjugated to a linear foliation, the conjugacy is also differentiable (and actually smooth). We prove a generalization of this result to higher genus, by showing that, under a full measure condition, smooth, orientable minimal foliations with Morse saddles on a surfaces of genus two are differentiably conjugated to their linear model (and actually the conjugacy can be shown to be C^{1+\alpha}). The result can be rephrased in terms of generalized interval exchange maps (GIETs), namely piecewise diffeomorphisms which appear as Poincare' sections, and conjugacy to their linear models, namely (standard) interval exchange maps (IETs) and is proved using renormalization and proving a dynamical dichotomy for the renormalization operator (which is valid in any genus). This result proves a conjecture on GIETs by Marmi-Moussa and Yoccoz in genus two. The talk is based on joint works with Selim Ghazouani.
Rigidity of Poincare sections of higher genus flowsread_more
HG G 43
7. März 2022
14:05-15:05 		Dr. Lei Yang
Sichuan University
Details

Ergodic theory and dynamical systems seminar

Titel Khintchine's theorem on manifolds
Referent:in, Affiliation Dr. Lei Yang, Sichuan University
Datum, Zeit 7. März 2022, 14:05-15:05
Ort Online Seminar
Abstract In this talk, we will prove the convergence part of Khintchine's theorem on non-degenerate manifolds. This confirms a conjecture of Kleinbock and Margulis in 1998. Our approach uses geometric and dynamical ideas together with a new technique of `major and minor arcs'. In particular, we establish sharp upper bounds for the number of rational points of bounded height lying near `major arcs' and give explicit exponentially small bounds for the measure of `minor arcs'. This is joint work with Victor Beresnevich.
Khintchine's theorem on manifoldsread_more
Online Seminar
14. März 2022
14:05-15:05 		Prof. Dr. Anish Ghosh
Tata Institute of Fundamental Research
Details

Ergodic theory and dynamical systems seminar

Titel Hausdorff dimension estimates in dynamics and number theory
Referent:in, Affiliation Prof. Dr. Anish Ghosh, Tata Institute of Fundamental Research
Datum, Zeit 14. März 2022, 14:05-15:05
Ort Online Seminar
Abstract I will discuss some recent work estimating, and in some instances computing, the Hausdorff dimension of natural sets arising in Diophantine approximation and dynamics. -- talk on Zoom: https://ethz.zoom.us/j/65329488712 Meeting ID: 653 2948 8712
Hausdorff dimension estimates in dynamics and number theoryread_more
Online Seminar
21. März 2022
14:05-15:05 		Dr. Yotam Smilansky
Rutgers University
Details

Ergodic theory and dynamical systems seminar

Titel Order and disorder in multiscale substitution tilings
Referent:in, Affiliation Dr. Yotam Smilansky, Rutgers University
Datum, Zeit 21. März 2022, 14:05-15:05
Ort Online Seminar
Abstract The study of aperiodic order and mathematical models of quasicrystals is concerned with ways in which disordered structures can nevertheless manifest aspects of order. In the talk I will describe examples such as the aperiodic Penrose and pinwheel tilings, together with several geometric, dynamical, functional and spectral properties that enable us to measure how far such constructions are from demonstrating lattice-like behavior. A particular focus will be given to new results on multiscale substitution tilings, a class of tilings that was recently introduced jointly with Yaar Solomon. -- talk on Zoom: https://ethz.zoom.us/j/65329488712 Meeting ID: 653 2948 8712
Order and disorder in multiscale substitution tilingsread_more
Online Seminar
28. März 2022
14:05-15:05 		Prof. Dr. David Damanik
Rice University
Details

Ergodic theory and dynamical systems seminar

Titel The Structure of the Spectrum of a Dynamically Defined Schrödinger Operator
Referent:in, Affiliation Prof. Dr. David Damanik, Rice University
Datum, Zeit 28. März 2022, 14:05-15:05
Ort HG G 43
Abstract We consider Schrödinger operators whose potentials are defined by sampling the orbits of a homeomorphism of a compact metric space with a continuous function. Motivated by the phenomenon of spectral pseudo-randomness we discuss mechanisms that allow one to show that the gap structure of such a spectrum is very simple under suitable assumptions. Specific instances include applications of Johnson's approach to the gap labelling theorem and the effects of small random perturbations of a given background.
The Structure of the Spectrum of a Dynamically Defined Schrödinger Operatorread_more
HG G 43
4. April 2022
14:05-15:05 		Dr. Florian Richter
EPFL
Details

Ergodic theory and dynamical systems seminar

Titel On a sumset conjecture of Erdos and its generalizations
Referent:in, Affiliation Dr. Florian Richter, EPFL
Datum, Zeit 4. April 2022, 14:05-15:05
Ort HG G 43
Abstract In this talk we will investigate the question -- based on problems attributed to Erdos -- of whether every subset of the integers with positive density contains a sumset B_1+...+B_k where B_1,...,B_k are infinite sets. We will present a purely ergodic-theoretic approach to this topic. Our method relies on a newfound connection between k-fold sumsets in the integers and return times of orbits in k-fold joinings of measure preserving systems arising from the Host-Kra structure theory. This talk is based on joint work with Bryna Kra, Joel Moreira, and Donald Robertson.
On a sumset conjecture of Erdos and its generalizationsread_more (ABGESAGT)
HG G 43
11. April 2022
14:05-15:05 		Prof. Dr. Claire Burrin
Universität Zürich
Details

Ergodic theory and dynamical systems seminar

Titel Windings of closed geodesics around cusps of hyperbolic surfaces
Referent:in, Affiliation Prof. Dr. Claire Burrin, Universität Zürich
Datum, Zeit 11. April 2022, 14:05-15:05
Ort HG G 43
Abstract In his 2006 ICM lecture, Ghys made the following observation. The winding of a closed geodesic around the cusp of the modular surface can be computed using a function from the theory of modular forms: the Rademacher function. In joint work with Flemming von Essen, we studied how and when Rademacher functions also encode the winding for closed geodesics around the cusps of hyperbolic surfaces. For certain families of surfaces, we use a Selberg trace formula argument to obtain precise statistical results on these winding numbers.
Windings of closed geodesics around cusps of hyperbolic surfacesread_more
HG G 43
28. April 2022
14:15-15:15 		Dr. Roberto Castorrini
University of Pisa
Details

Ergodic theory and dynamical systems seminar

Titel Quantitative statistical properties for a class of partially hyperbolic systems
Referent:in, Affiliation Dr. Roberto Castorrini, University of Pisa
Datum, Zeit 28. April 2022, 14:15-15:15
Ort HG G 5
Abstract In the last few years, an extremely powerful method has been developed to study the statistical properties of a dynamical system: the functional approach. It consists of the study of the spectral properties of transfer operators on suitable Banach spaces. In this talk I will discuss how to further such a point of view to a class of two dimensional partially hyperbolic systems, not necessarily skew products, in order to provide explicit conditions for the existence of finitely many physical measures and prove exponential decay of correlations for mixing measures. To illustrate the scopes of the theory, I will discuss how to apply the results to a family of fast-slow partially hyperbolic maps. This is a joint work with Carlangelo Liverani.
Quantitative statistical properties for a class of partially hyperbolic systemsread_more (ABGESAGT)
HG G 5
2. Mai 2022
14:05-15:05 		Dr. Florian Richter
EPFL
Details

Ergodic theory and dynamical systems seminar

Titel On a sumset conjecture of Erdos and its generalizations
Referent:in, Affiliation Dr. Florian Richter, EPFL
Datum, Zeit 2. Mai 2022, 14:05-15:05
Ort HG G 43
Abstract In this talk we will investigate the question -- based on problems attributed to Erdos -- of whether every subset of the integers with positive density contains a sumset B_1+...+B_k where B_1,...,B_k are infinite sets. We will present a purely ergodic-theoretic approach to this topic. Our method relies on a newfound connection between k-fold sumsets in the integers and return times of orbits in k-fold joinings of measure preserving systems arising from the Host-Kra structure theory. This talk is based on joint work with Bryna Kra, Joel Moreira, and Donald Robertson.
On a sumset conjecture of Erdos and its generalizationsread_more
HG G 43
2. Mai 2022
15:30-16:30 		Jiajie Zheng
Brandeis University
Details

Ergodic theory and dynamical systems seminar

Titel Dynamical Borel--Cantelli Lemma for Lipschitz Twists
Referent:in, Affiliation Jiajie Zheng, Brandeis University
Datum, Zeit 2. Mai 2022, 15:30-16:30
Ort HG G 43
Abstract In the study of some dynamical systems, the limit superior of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limit superior sets. However, the zero-one laws for the shrinking targets and recurrence are usually treated separately and proved differently. In this talk, we construct a generalized definition that can specialize into the shrinking targets and recurrence and our approach gives a unified proof to the zero-one laws for the two problems.
Dynamical Borel--Cantelli Lemma for Lipschitz Twistsread_more
HG G 43
9. Mai 2022
14:05-15:05 		Prof. Dr. Alfonso Sorrentino
Details

Ergodic theory and dynamical systems seminar

Titel On the persistence of periodic tori for symplectic twist maps
Referent:in, Affiliation Prof. Dr. Alfonso Sorrentino,
Datum, Zeit 9. Mai 2022, 14:05-15:05
Ort HG G 43
Abstract In this talk, I shall discuss the persistence of Lagrangian periodic tori for symplectic twist maps of the -dimensional annulus and the rigidity of completely integrable maps. This is based on a joint work with Marie-Claude Arnaud and Jessica Elisa Massetti.
On the persistence of periodic tori for symplectic twist mapsread_more
HG G 43
16. Mai 2022
14:05-15:05 		Dr. Cheng Zheng
Jiao Tong University
Details

Ergodic theory and dynamical systems seminar

Titel A shrinking target problem in rank one homogeneous spaces
Referent:in, Affiliation Dr. Cheng Zheng, Jiao Tong University
Datum, Zeit 16. Mai 2022, 14:05-15:05
Ort HG G 43
Abstract The Khintchine's theorem in the metric theory of Diophantine approximation says that the subset of Diophantine numbers of type r > 1 has full Lebesgue measure. The Jarník-Besicovitch theorem states further that its complement has Hausdorff dimension 2/(1 + r). A dynamical point of view on the Jarník-Besicovitch theorem is the shrinking target problem proposed by Hill and Velani. In this talk, we will discuss our work about a shrinking target problem in rank one homogeneous spaces and a result of Jarník-Besicovitch theorem in the metric theory of Diophantine approximation on Heisenberg groups. If time permits, we will also discuss the connection between our work and sparse equidistribution problem. Zoom link: https://ethz.zoom.us/j/65329488712
A shrinking target problem in rank one homogeneous spacesread_more
HG G 43
23. Mai 2022
14:05-15:05 		Prof. Dr. Uri Bader
Weizmann Institute of Science
Details

Ergodic theory and dynamical systems seminar

Titel Around higher property (T)
Referent:in, Affiliation Prof. Dr. Uri Bader, Weizmann Institute of Science
Datum, Zeit 23. Mai 2022, 14:05-15:05
Ort HG G 43
Abstract For a finitely generated group, property (T) is equivalent to the vanishing of all first cohomology groups whose coefficient modules are unitary representations. In my talk I will discuss various analogue properties stemming from consideration of higher degree cohomologies. In particular, I will discuss vanishing results for lattices in semisimple groups. The talk will be based on a joint work with Roman Sauer.
Around higher property (T)read_more
HG G 43
30. Mai 2022
14:05-15:05 		Prof. Dr. Jean-Claude Picaud
Université de Tours
Details

Ergodic theory and dynamical systems seminar

Titel Complementary series and Riesz operators for hyperbolic groups
Referent:in, Affiliation Prof. Dr. Jean-Claude Picaud, Université de Tours
Datum, Zeit 30. Mai 2022, 14:05-15:05
Ort HG G 43
Abstract We investigate the set of (equivalence classes) of representations ? : ? -> B(H) where ? is an hyperbolic group, non virtually abelian and B(H) is the space of bounded operators of a separable Hilbert space H. To each geometric action of ? on a metric space (X, d) we associate a family (?t)t?[0,1] of boundary representations, analog to complementary series for SL(2, R). We discuss their irreducibility as well as the role of Riesz operators as intertwinners between representations. We will make an effort for the part of the audience not familiar with representation theory of infinite discrete groups. Joint work with Adrien Boyer (Paris University).
Complementary series and Riesz operators for hyperbolic groupsread_more
HG G 43

Archiv: HS 24 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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