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Spring Semester 2025

Date / Time Speaker Title Location
26 February 2025
13:30-14:30 		Prof. Dr. Chris Judge
Indiana University
Details

Ergodic theory and dynamical systems seminar

Title Shrinking targets for affine self-diffeomorphisms of translation surfaces
Speaker, Affiliation Prof. Dr. Chris Judge, Indiana University
Date, Time 26 February 2025, 13:30-14:30
Location HG E 33.1
Abstract The affine self-diffeomorphism group of a translation surface can be rather large. For example, the affine diffeos of a 2-torus contain a lattice.  In the case of a torus $T$, Ghosh, Gorodnik, and Nevo proved that for any $\eta > 0$, for almost every $y \in T$ and for every $x \in T$, there exist infinitely many $\gamma \in SL_2(Z)$ so that $\| \gamma x- y \|\leq \|\gamma\|^{-1-\eta}$. We show that a similar result holds for translation surfaces with the lattice property. This is joint work with Josh Southerland.
Shrinking targets for affine self-diffeomorphisms of translation surfacesread_more
HG E 33.1
5 March 2025
13:30-14:30 		Dr. Marc Abboud
Université de Neuchâtel
Details

Ergodic theory and dynamical systems seminar

Title Unlikely intersections problem for automorphisms of Markov surfaces
Speaker, Affiliation Dr. Marc Abboud, Université de Neuchâtel
Date, Time 5 March 2025, 13:30-14:30
Location HG G 19.1
Abstract The family of Markov surfaces M_D is a family of cubic affine surfaces parametrised by the complex line (here D is the parameter) that is related to the character variety of the punctured torus. It has sparked a lot of work in algebraic geometry, algebraic differential equations and low-dimensional topology. The mapping class group of the punctured torus acts on the character variety and preserves this family. Its image is a finite index subgroup of the group of automorphisms of M_D for every parameter D. We show the following result: for certain algebraic parameters D if two automorphisms of M_D with positive entropy share a Zariski dense set of periodic points then they share a common iterate. The proof uses tools from arithmetic dynamics such as the arithmetic equidistribution theorem of Yuan and Zhang and tools from quasi-Fuchsian representation theory.
Unlikely intersections problem for automorphisms of Markov surfacesread_more
HG G 19.1
12 March 2025
13:30-14:30 		Dr. Mihajlo Cekic
Universität Zürich
Details

Ergodic theory and dynamical systems seminar

Title Quasi-Fuchsian flows and the coupled vortex equations
Speaker, Affiliation Dr. Mihajlo Cekic, Universität Zürich
Date, Time 12 March 2025, 13:30-14:30
Location HG G 19.1
Abstract In 1992, Ghys introduced a remarkable class of flows called quasi-Fuchsian flows. Namely, for a pair of metrics g_1 and g_2 of constant curvature -1 on a closed surface M, corresponding to points in Teichmueller space [g_1] and [g_2], respectively, he constructed an Anosov flow \phi_{[g_1], [g_2]} on the bundle of positive half-lines over M, whose weak stable and unstable foliations are smoothly conjugated to that of the geodesic flows of g_1 and g_2, respectively. In fact, in 1993 Ghys also showed that any Anosov flow on a 3-manifold with smooth weak stable/unstable bundles is smoothly conjugate to a quasi-Fuchsian flow or a suspension of a diffeomorphism of the 2-torus. In this talk, I will give an alternative 'PDE theoretic' description of quasi-Fuchsian flows as certain thermostat flows on the unit tangent bundle of the Blaschke metric uniquely determined by a conformal class on M and a holomorphic quadratic differential, satisfying `coupled vortex equations'. Joint work with Gabriel Paternain.
Quasi-Fuchsian flows and the coupled vortex equationsread_more
HG G 19.1
19 March 2025
13:30-14:30 		Dr. Tanja Schindler
Jagiellonian University/University of Exeter
Details

Ergodic theory and dynamical systems seminar

Title Trimmed laws of large numbers for different dynamical systems
Speaker, Affiliation Dr. Tanja Schindler, Jagiellonian University/University of Exeter
Date, Time 19 March 2025, 13:30-14:30
Location HG G 19.1
Abstract Trimming, i.e. removing the largest summands of a sum of identically distributed (iid) random variables, has a long tradition to prove limit theorems which are not valid if one considers the untrimmed sum - one example is the strong law of large numbers for random variables with an infinite mean or in case of ergodic transformations Birkhoff's ergodic theorem. In this talk I will compare different dynamical systems, e.g. piecewise expanding interval maps and irrational rotations with the results for iid random variables regarding weak and strong laws of large numbers after trimming. This will be a somewhat expository talk.
Trimmed laws of large numbers for different dynamical systemsread_more
HG G 19.1
26 March 2025
13:30-14:30 		Prof. Dr. Nattalie Tamam
Imperial College London
Details

Ergodic theory and dynamical systems seminar

Title Markoff triples and their connection to orbits of the mapping class group
Speaker, Affiliation Prof. Dr. Nattalie Tamam, Imperial College London
Date, Time 26 March 2025, 13:30-14:30
Location HG G 19.1
Abstract The Markoff triples are the natural solutions of the Markoff relation $x^2+y^2+z^2=3xyz$. They can be viewed as points in the orbit of the mapping class group acting on the character variety of the punctured torus. In this case the action is transitive. However, when considering surfaces with a higher genus or number of holes, this is no longer the case. We will discuss the possible orbits closures of the general case; the algebraic relations that are preserved under the action and the exceptional cases. This is a joint work with Alireza Salehi-Golsefidy.
Markoff triples and their connection to orbits of the mapping class groupread_more
HG G 19.1
2 April 2025
13:30-14:30 		Constantin Kogler
University of Oxford
Details

Ergodic theory and dynamical systems seminar

Title On dimension and absolute continuity of self-similar measures
Speaker, Affiliation Constantin Kogler, University of Oxford
Date, Time 2 April 2025, 13:30-14:30
Location HG G 19.1
Abstract I will present my recent joint work with Samuel Kittle. We establish numerous novel explicit examples of absolutely continuous self-similar measures. In fact, we give the first inhomogenous examples in dimension 1 and 2 and construct examples for essentially any given rotations and translations, provided they have algebraic coefficients. Moreover we strengthen Varju's result for Bernoulli convolutions and Lindenstrauss-Varju's result in dimension >= 3. We also generalise Hochman's result to contracting on average measures and show that a separation condition weaker than exponential separation is sufficient.
On dimension and absolute continuity of self-similar measuresread_more
HG G 19.1
9 April 2025
13:30-14:30 		Prof. Dr. Kostiantyn Drach
Universitat de Barcelona/CRM-Barcelona
Details

Ergodic theory and dynamical systems seminar

Title (Unmarked) Length spectral rigidity for expanding circle maps
Speaker, Affiliation Prof. Dr. Kostiantyn Drach, Universitat de Barcelona/CRM-Barcelona
Date, Time 9 April 2025, 13:30-14:30
Location HG G 19.1
Abstract For a smooth expanding map of the circle, its (unmarked) length spectrum is defined as the set of logarithms of multipliers along all periodic orbits. This set is analogous to the set of lengths of all closed geodesics on negatively curved surfaces -- the classical length spectrum. In the talk, I will present a length spectral rigidity result for expanding circle maps. Namely, I will show that a smooth expanding circle map, under certain assumptions on the sparsity of its length spectrum, cannot be perturbed with an arbitrarily small smooth perturbation (depending on the map) so that the length spectrum stays the same. The proof uses the Whitney extension theorem, a quantitative Livcis-type theorem, and a novel iterative scheme. This is joint work with Vadim Kaloshin.
(Unmarked) Length spectral rigidity for expanding circle mapsread_more
HG G 19.1
16 April 2025
13:30-14:30 		Prof. Dr. Tobias Hartnick
TU
Details

Ergodic theory and dynamical systems seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Tobias Hartnick, TU
Date, Time 16 April 2025, 13:30-14:30
Location HG G 19.1
Title T.B.A.
HG G 19.1
30 April 2025
13:30-14:30 		Konstantin Andritsch
ETHZ
Details

Ergodic theory and dynamical systems seminar

Title Title T.B.A.
Speaker, Affiliation Konstantin Andritsch, ETHZ
Date, Time 30 April 2025, 13:30-14:30
Location HG G 19.1
Title T.B.A.
HG G 19.1
7 May 2025
13:30-14:30 		Prof. Dr. David Aulicino
Brooklyn College (CUNY)
Details

Ergodic theory and dynamical systems seminar

Title Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces
Speaker, Affiliation Prof. Dr. David Aulicino, Brooklyn College (CUNY)
Date, Time 7 May 2025, 13:30-14:30
Location HG E 33.1
Abstract We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given.  This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.
Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfacesread_more
HG E 33.1
14 May 2025
13:30-14:30 		Prof. Dr. Caroline Series
University of Warwick
Details

Ergodic theory and dynamical systems seminar

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Caroline Series, University of Warwick
Date, Time 14 May 2025, 13:30-14:30
Location HG F 5
Title T.B.A.
HG F 5
21 May 2025
13:30-14:30 		TBA
Details

Ergodic theory and dynamical systems seminar

Title Title T.B.A.
Speaker, Affiliation TBA,
Date, Time 21 May 2025, 13:30-14:30
Location HG E 33.1
Title T.B.A.
HG E 33.1
28 May 2025
13:30-14:30 		René Pfitscher
Université Sorbonne Paris Nord
Details

Ergodic theory and dynamical systems seminar

Title Title T.B.A.
Speaker, Affiliation René Pfitscher, Université Sorbonne Paris Nord
Date, Time 28 May 2025, 13:30-14:30
Location HG E 33.1
Title T.B.A.
HG E 33.1

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