Date/Time : 14 Sep 2023 15:30
Venue : S17 #05-11 (SR5)
Speaker : Daniel Huson, University of Tubingen

This talk has four parts. In the first part – topology -, we recall the classification of two-dimensional manifolds and orbifolds, and introduce their Conway-Macbeath notation. In the second part – geometry -, we discuss two-dimensional periodic tilings and their classification. In the third part – combinatorics -, we introduce Delaney-Dress symbols and indicate how they can be used to systematically enumerate periodic tilings. Finally, in the fourth part – algorithms and software -, we present Tegula

(https://ddec1-0-en-ctp.trendmicro.com:443/wis/clicktime/v1/query?url=http%3a%2f%2ftegula.husonlab.org&umid=7c8bc7cd-aafa-4ab0-9fe7-ed56d83a50f7&auth=8d3ccd473d52f326e51c0f75cb32c9541898e5d5-113b232b1017a668b66ec7edf1b8b0f54e074fb4),

a new computer program that can be used the explore the “galaxy” of all 2.4 billion periodic tilings of the euclidean plane, sphere and hyperbolic plane, of low Dress-complexity. This is joint work with Olaf Delgado and Rüdiger Zeller.

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Date/Time : 07 Sep 2023 15:30
Venue : S17 #05-11 (SR5)
Speaker : Wei Darren, National University of Singapore

Two flows are said to be Kakutani equivalent if one is isomorphic to the other after time change, or equivalently if there are Poincare sections for the flows so that the respective induced maps are isomorphic to each other. Ratner showed that if G=SL(2,R) and \Gamma is a lattice in G, and if U is a one parameter unipotent subgroup in G then the U action on G equipped with Haar measure is loosely Bernoulli, i.e. Kakutani equivalent to a circle rotation. Thus any two such systems SL(2,R)/\Gamma are Kakutani equivalent to each other. On the other hand, Ratner showed that if G’=SL(2,R) x SL(2,R) and \Gamma’ is a reducible lattice, and U’ is the diagonally embedded one parameter unipotent subgroup in G’, then (G’/\Gamma’, U’, m) is not loosely Bernoulli. We show that in fact in this case and many other situations one cannot have Kakutani equivalence between such systems unless they are actually isomorphic. This is a joint work with Elon Lindenstrauss.

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Date/Time : 17 Aug 2023 15:00
Venue : S17 #04-06 (SR1)
Speaker : Jia Jia, Tsinghua University

TopoloAn automorphism of a compact complex space is called wild if there is no non-trivial proper invariant analytic subset. In this talk, I will show that a compact complex surface admitting a wild automorphism is either a complex torus or an Inoue surface of certain type, and this wild automorphism has zero entropy. This is based on a joint work with Long Wang.gy and geometry

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Date/Time : 17 Aug 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Yap Jit Wu, Harvard University

Let K be a number field, S a finite set of places containing all Archimedean places and f a rational map defined over K of degree d >_ 2. Given a non-preperiodic point a and non-exceptional b, both in P^1(K), Silverman has shown that there are only finitely many points among {a,f(a),f^2(a),…} that are S-integral relative to b. More recently, Hsia and Silverman showed an upper bound of the form O(4^|S|) on the number of such points as S varies. In this talk we will improve this upper bound to |S|^(1+o(1)) and show it is possible to get O(|S|) for certain rational maps.

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Date/Time : 16 Jun 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Zhu Feng, University of Wisconsin

Putting a hyperbolic metric on a complete finite-type surface gives us a linear representation (the holonomy representation) with many nice geometric and dynamical properties: for instance it is discrete and faithful, and in fact stably quasi-isometrically embedded. This picture can be generalised in (at least) two ways. First, the notion of geometric finiteness generalises this picture in the context of rank-one Lie groups such as PSL(2,R) or PSL(2,C). Second, Anosov representations generalise this picture to higher-rank Lie groups such as PSL(d,K) for d>2.

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Date/Time : 03 May 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Marco Abate, University of Pisa

In this talk we shall describe the asymptotic behaviour of sequences of functions obtained by iteratively left-composing or right-composing holomorphic self-maps of a hyperbolic Riemann surface $X$. We shall consider in detail two cases: when the holomorphic self-maps to be composed have values in a Bloch subdomain of~$X$; and when the holomorphic self-maps to be composed are sufficiently close to a given self-map. This is a joint work with Argyrios Christodoulou and Ian Short.

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Date/Time : 19 Apr 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Lucas Kaufmann, University of Orleans

Consider a (singular) holomorphic foliation F on a complex manifold. In the 1970s, Baum-Bott constructed residue classes associated with each singular component of F. These classes satisfy an index theorem, which computes characteristic classes of F.

A natural question since their work is how to compute or find natural representatives of such cohomology classes. Apart from the case where the foliation is of rank one and has isolated singularities, no general result is known. In this talk I will show that each Baum-Bott class can be naturally represented by a residue current supported by the singular component of F. This is a joint work with Richard Lärkäng and Elizabeth Wulcan.

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Date/Time : 08 Feb 2023 15:30
Venue : S17 #04-04 (SR3)
Speaker : Fabrizio Bianchi, University of Lille

We show that every Hölder observable satisfies the Central Limit Theorem (CLT) with respect to the measure of maximal entropy of every complex Hénon map. The proof is based on a general criterion to ensure the validity of the CLT, valid for abstract measurable dynamical systems. This is a joint work with Tien-Cuong Dinh.

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Date/Time : 25 Jan 2023 15:30
Venue : S17 #04-05 (SR2)
Speaker : Wang Tianqi, National University of Singapore

Minsky shows that there is an open set of PSL(2,C) characters of a free group F_n, namely the primitive-stable character, which is strictly larger than the convex-cocompact character and on which the action of Out(F_n) is properly discontinuous. In this talk, we introduce the notion of simple Anosov representations of closed surface groups and give an analogue of Minsky’s theorem, that is, the set of simple Anosov representations of the fundamental group of a closed hyperbolic surface into a higher rank Lie group is open in the character variety, which is strictly larger than the set of Anosov representations, with the mapping class group action properly discontinuous. This is joint work with Nicholas Tholozan.

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