Departement Mathematik

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Ergodic theory and dynamical systems

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Herbstsemester 2024

Datum / Zeit Referent:in Titel Ort
25. September 2024
13:30-14:30 		Prof. Dr. Adam Kanigowski
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel Horocycle flows at semi-prime times
Referent:in, Affiliation Prof. Dr. Adam Kanigowski, University of Maryland
Datum, Zeit 25. September 2024, 13:30-14:30
Ort Y27 H 28
Abstract In this joint work with G. Forni and M. Radziwill we study the orbits of horocycle flows when sampled at semi-primes (integers with at most two prime factors). We show that if the lattice is arithmetic then such orbits equidistribute towards Haar measure for every non-periodic point. During the talk I will outline a new criterion for semi-primes, and describe main ideas of the proof.
Horocycle flows at semi-prime timesread_more
Y27 H 28
2. Oktober 2024
13:45-14:45 		Prof. Dr. Roman Sauer
Karlsruhe Institute for Technology
Details

Ergodic theory and dynamical systems seminar

Titel The Kazhdan property donates an extra dimension
Referent:in, Affiliation Prof. Dr. Roman Sauer, Karlsruhe Institute for Technology
Datum, Zeit 2. Oktober 2024, 13:45-14:45
Ort Y27 H 28
Abstract The waist inequality for the sphere by Gromov is wonderful result of geometric measure theory. Formulated appropriately for families of spaces, a (uniform) waist inequality for a family of Riemannian manifolds is the Riemannian analog of higher dimensional expanders. We formulate a conjectural picture for locally symmetric spaces. Finally, we show that the Kazhdan property alone gives rise not only to expanders, which is classical, but also to 2-dimensional expanders. An extra dimension for free! This is joint work with Uri Bader.
The Kazhdan property donates an extra dimensionread_more
Y27 H 28
9. Oktober 2024
13:30-14:30 		Dr. Pouya Honaryar
Universität Zürich
Details

Ergodic theory and dynamical systems seminar

Titel Central limit theorem for homology of simple closed curves
Referent:in, Affiliation Dr. Pouya Honaryar, Universität Zürich
Datum, Zeit 9. Oktober 2024, 13:30-14:30
Ort Y27 H 28
Abstract Fix a hyperbolic surface $X$, and for $L > 0$, let $\mathcal{S}_L(X)$ denote the set of simple closed geodesics of length at most $L$ on $X$. Fixing a norm on $H_1(X, \mathbb{R})$, we may ask what is the statistics of the norm of homology class of $\alpha$, denoted by $[\alpha]$, when $\alpha$ is chosen randomly uniformly from $\mathcal{S}_L(X)$, as $L \rightarrow \infty$? For example, does one expect the norm of $[\alpha]$ to be of order $L$ or smaller? We answer this question by proving a CLT-type result for the norm of homology of a randomly chosen curve in $\mathcal{S}_L(X)$. We discuss the main steps to reduce the desired CLT to a CLT for the Kontsevich-Zorich cocycle obtained by Forni-Saqban. (Joint work with F. Arana-Herrera)
Central limit theorem for homology of simple closed curvesread_more
Y27 H 28
16. Oktober 2024
13:30-14:30 		Dr. Katy Loyd
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel Pointwise Ergodic Averages along Sequences of Slow Growth
Referent:in, Affiliation Dr. Katy Loyd, University of Maryland
Datum, Zeit 16. Oktober 2024, 13:30-14:30
Ort Y27 H 28
Abstract Following Birkhoff's proof of the Pointwise Ergodic Theorem, it is natural to consider whether convergence still holds along various subsequences of the integers. In 2020, Bergelson and Richter showed that in uniquely ergodic systems, pointwise convergence holds along the number theoretic sequence $\Omega(n)$, where $\Omega(n)$ denotes the number of prime factors of $n$, with multiplicities. In this talk, we will see that by removing this assumption, a pointwise ergodic theorem does not hold along $\Omega(n)$. In fact, $\Omega(n)$ satisfies a notion of non-convergence called the strong sweeping out property. We then further classify the strength of this non-convergence behavior by considering weaker notions of averaging. Time permitting, we will introduce a more general criterion for identifying slow growing sequences with the strong sweeping out property (based on joint work with S. Mondal).
Pointwise Ergodic Averages along Sequences of Slow Growthread_more
Y27 H 28
23. Oktober 2024
13:30-14:30 		Prof. Dr. Sobhan Seyfaddini
ETH Zürich
Details

Ergodic theory and dynamical systems seminar

Titel The closing lemma and Lagrangian submanifolds
Referent:in, Affiliation Prof. Dr. Sobhan Seyfaddini, ETH Zürich
Datum, Zeit 23. Oktober 2024, 13:30-14:30
Ort Y27 H 28
Abstract We will discuss the smooth closing lemma for Hamiltonian diffeomorphisms with invariant Lagrangians.  Based on joint work with Erman Cineli & Shira Tanny.
The closing lemma and Lagrangian submanifoldsread_more
Y27 H 28
30. Oktober 2024
13:30-14:30 		Prof. Dr. François Maucourant
Université Rennes I
Details

Ergodic theory and dynamical systems seminar

Titel Discriminants of periodic geodesics on the modular surface
Referent:in, Affiliation Prof. Dr. François Maucourant, Université Rennes I
Datum, Zeit 30. Oktober 2024, 13:30-14:30
Ort Y27 H 28
Abstract We'll recall how to attach to a periodic geodesic of H^2/PSL(2,Z) an arithmetical quantity, its discriminant. After discussing how to pick a geodesic at random, we will show that 'most' geodesics have large discriminant when ordered by length, and that 42% of them have a fundamental discriminant.
Discriminants of periodic geodesics on the modular surfaceread_more
Y27 H 28
6. November 2024
13:30-14:30 		Dr. Hamid Al-Saqban
Universität Paderborn
Details

Ergodic theory and dynamical systems seminar

Titel A Central Limit Theorem for the Kontsevich-Zorich cocycle
Referent:in, Affiliation Dr. Hamid Al-Saqban, Universität Paderborn
Datum, Zeit 6. November 2024, 13:30-14:30
Ort Y27 H 28
Abstract The Kontsevich-Zorich (KZ) cocycle is a key dynamical system that is closely related to the derivative cocycle of the Teichmüller geodesic flow. We will state and sketch a proof of a central limit theorem for the KZ cocycle, and explain some of the motivations, especially towards the goal of proving the existence of large fluctuations of the Hodge norm of the parallel transport of vectors along Teichmüller horocycles. Such fluctuations were leveraged by Chaika-Khalil-Smillie in their work on the ergodic measures of the Teichmüller horocycle flow. Our work is joint with Giovanni Forni.
A Central Limit Theorem for the Kontsevich-Zorich cocycleread_more
Y27 H 28
13. November 2024
13:30-14:30 		Prof. Dr. Michael Hochman
The Hebrew University of Jerusalem
Details

Ergodic theory and dynamical systems seminar

Titel New results on embedding and intersections of self-similar sets
Referent:in, Affiliation Prof. Dr. Michael Hochman, The Hebrew University of Jerusalem
Datum, Zeit 13. November 2024, 13:30-14:30
Ort Y27 H 28
Abstract I will discuss the problem of affinely embedding self-similar sets in the line into other such sets. Conjecturally, embedding is precluded when the contraction ratios of the defining maps are incommensurable. This is closely related to conjectures on intersections of fractals, but in the open cases even the embedding problem is challenging. I will describe recent joint work with Amir Algom and Meng Wu in which we confirm the conjecture whenever the contraction ratios are algebraic numbers, and also for a.e. choice of parameters. I will discuss the proof. If time permits, I will explain how this is related to the dimension of alpha-beta sets, and describe recent examples that show that the problem is more delicate than anticipated.
New results on embedding and intersections of self-similar setsread_more
Y27 H 28
20. November 2024
13:30-14:30 		Prof. Dr. Daren Wei
National University of Singapore
Details

Ergodic theory and dynamical systems seminar

Titel Time Change Rigidity of Unipotent Flows
Referent:in, Affiliation Prof. Dr. Daren Wei, National University of Singapore
Datum, Zeit 20. November 2024, 13:30-14:30
Ort Y27 H 28
Abstract Two non-isomorphic ergodic measure preserving flows can become isomorphic if one of the systems undergoes an appropriate time change. In this case we will say that these flows are Kakutani equivalent to each other. We say that an ergodic flow is loosely Kronecker if it is Kakutani equivalent to the straight line flow on (say) a two torus in an irrational direction (the exact direction is immaterial as these are all equivalent to each other). Landmark work of Ratner from the late 70s (that paved the way to her even more famous results on orbit closures and equidistribution of unipotent flows) establishes that 1) the horocycle flow on any finite area surface of constant negative curvature is loosely Kronecker. 2) the product of two such flows is not loosely Kronecker. It remained an open problem whether e.g. products of two horocycle flows are Kakutani equivalent to each other. We show unipotent flows are very rigid under time changes, and indeed unless the flows are loosely Kronecker, two unipotent flows are Kakutani equivalent if and only if they are isomorphic as measure preserving flows. This is a joint work with Elon Lindenstrauss
Time Change Rigidity of Unipotent Flowsread_more
Y27 H 28
27. November 2024
13:30-14:30 		Prof. Dr. Dimitry Dolgopyat
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel Title T.B.A.
Referent:in, Affiliation Prof. Dr. Dimitry Dolgopyat, University of Maryland
Datum, Zeit 27. November 2024, 13:30-14:30
Ort Y27 H 28
Title T.B.A.
Y27 H 28
4. Dezember 2024
13:30-14:30 		Prof. Dr. Jens Marklof
University of Bristol
Details

Ergodic theory and dynamical systems seminar

Titel Title T.B.A.
Referent:in, Affiliation Prof. Dr. Jens Marklof, University of Bristol
Datum, Zeit 4. Dezember 2024, 13:30-14:30
Ort Y27 H 28
Title T.B.A.
Y27 H 28
11. Dezember 2024
13:30-14:30 		Dr. Meg Doucette
University of Maryland
Details

Ergodic theory and dynamical systems seminar

Titel Title T.B.A.
Referent:in, Affiliation Dr. Meg Doucette, University of Maryland
Datum, Zeit 11. Dezember 2024, 13:30-14:30
Ort Y27 H 28
Title T.B.A.
Y27 H 28

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