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Autumn Semester 2018

Date / Time Speaker Title Location
19 September 2018
15:45-16:45 		John Parker
Durham University
Event Details

Geometry Seminar

Title Cusp regions for parabolic ends of hyperbolic manifolds
Speaker, Affiliation John Parker, Durham University
Date, Time 19 September 2018, 15:45-16:45
Location HG G 43
Abstract A hyperbolic manifold or orbifold can be written as the quotient of hyperbolic space by a discrete group of isometries. A cusp end of the orbifold corresponds to parabolic elements in the group. A consequence of discreteness is that these cusp ends contain regions of a certain shape. In dimensions two and three this is classical. More complicated things can happen in higher dimensions. In this talk I will survey the classical results, then I will discuss some more recent results in dimension four which show how continued fractions and Diophantine approximation come into play.
Cusp regions for parabolic ends of hyperbolic manifoldsread_more
HG G 43
26 September 2018
15:45-16:45 		Dr. Matthew Cordes
ETH Zurich, Switzerland
Event Details

Geometry Seminar

Title Quasi-möbius maps of Morse boundaries
Speaker, Affiliation Dr. Matthew Cordes, ETH Zurich, Switzerland
Date, Time 26 September 2018, 15:45-16:45
Location HG G 43
Abstract Boundaries of hyperbolic groups can tell you a great deal about the group. For instance, one can show two groups are not quasi-isometric by showing their boundaries are not homeomorphic. Paulin showed that under the right conditions you can show that two groups with homeomorphic boundaries are quasi-isometric. By restricting to rays satisfying the Morse property, one can define an analogous boundary for more general groups. Inspired by the theorem of Paulin, we give precise conditions for when a homeomorphism between the Morse boundaries of two groups is induced by a quasi-isometry of the groups themselves. This is joint work with Ruth Charney and Devin Murray.
Quasi-möbius maps of Morse boundariesread_more
HG G 43
3 October 2018
15:45-16:45 		Livio Liechti
Institut de Mathématiques de Jussieu, Paris
Event Details

Geometry Seminar

Title Minimal pseudo-Anosov dilatations in the extended mapping class group
Speaker, Affiliation Livio Liechti, Institut de Mathématiques de Jussieu, Paris
Date, Time 3 October 2018, 15:45-16:45
Location HG G 43
Abstract For any orientable closed surface of genus larger than one, it is an open problem to determine the minimal dilatation among pseudo-Anosov mapping classes in the extended mapping class group. We discuss this problem, with a particular emphasis on the comparison of orientation-preserving and orientation-reversing mapping classes. In particular, for every surface of odd genus, we consider a simple candidate which conjecturally minimises the dilatation among orientation-reversing pseudo-Anosov mapping classes with orientable invariant foliations. This is joint work with Balázs Strenner.
Minimal pseudo-Anosov dilatations in the extended mapping class groupread_more
HG G 43
10 October 2018
15:45-16:45 		Dominik Francoeur
University of Geneva
Event Details

Geometry Seminar

Title On the existence of free subsemigroups in automata groups
Speaker, Affiliation Dominik Francoeur, University of Geneva
Date, Time 10 October 2018, 15:45-16:45
Location HG G 43
Abstract Groups generated by automata have attracted a lot of attention since their introduction, partly because despite their simple combinatorial description, they can possess many interesting properties. For instance, one can find among this class finitely generated infinite torsion groups, just infinite groups and groups of intermediate growth. There is also a connection, discovered by Glasner and Mozes, between these groups and square complexes. An important question in the study of automata groups is how the properties of the automaton are reflected in the properties of the group that it generates. We will discuss one such connection, namely the link between reversibility of the automaton and the existence of free subsemigroups. This is joint work with Ivan Mitrofanov.
On the existence of free subsemigroups in automata groupsread_more
HG G 43
17 October 2018
15:45-16:45 		Dr. Konstantin Golubev
ETH Zurich, Switzerland
Event Details

Geometry Seminar

Title Spectral Methods: from hyperbolic surfaces to graphs and back
Speaker, Affiliation Dr. Konstantin Golubev, ETH Zurich, Switzerland
Date, Time 17 October 2018, 15:45-16:45
Location HG G 43
Abstract A number of results of the algebraic graph theory were influenced by the spectral theory of Riemann surfaces. We pay it back, and consider some new and classical notions and results for graphs in the continuous setting. In particular, I will talk about colorings, average distance and discrete random walks on surfaces. Based on joint works with E. DeCorte and A. Kamber.
Spectral Methods: from hyperbolic surfaces to graphs and backread_more
HG G 43
7 November 2018
15:45-16:45 		Waltraud Lederle
ETH Zurich, Switzerland
Event Details

Geometry Seminar

Title Almost automorphisms of trees and completions of Thompson's V
Speaker, Affiliation Waltraud Lederle, ETH Zurich, Switzerland
Date, Time 7 November 2018, 15:45-16:45
Location HG G 43
Abstract Thompson's V was one of the first examples of a finitely presented, infinite, simple group. It can be seen in a natural way as a group of almost automorphisms of the binary tree, and thus embeds densely into a nice locally compact group. Using that V can also be written as topological full group of a one-sided shift in the sense of Matui, we construct infinitely many more completions of V, answering a question of Le Boudec and Wesolek.
Almost automorphisms of trees and completions of Thompson's Vread_more
HG G 43
14 November 2018
15:45-16:45 		Michele Triestino
Université de Bourgogne, Dijon
Event Details

Geometry Seminar

Title The geometry of discrete groups of circle diffeomorphisms
Speaker, Affiliation Michele Triestino, Université de Bourgogne, Dijon
Date, Time 14 November 2018, 15:45-16:45
Location HG G 43
Abstract Fuchsian groups (discrete subgroups of PSL(2,R)) are among the most interesting objects in mathematics, for their connections with geometry, dynamical systems, topology and number theory. In a long term project we want to describe how much discrete subgroups of the group of circle diffeomorphisms behave like Fuchsian groups. All known results suggest a very neat and nice description. Is this just a lack of imagination?
The geometry of discrete groups of circle diffeomorphismsread_more
HG G 43
21 November 2018
15:45-16:45 		Tamar Ziegler
Hebrew University
Event Details

Geometry Seminar

Title Extending weakly polynomial functions from high rank varieties
Speaker, Affiliation Tamar Ziegler, Hebrew University
Date, Time 21 November 2018, 15:45-16:45
Location HG G 43
Abstract Let k be a field, V a k-vector space, X in V a subset. Say that f: X —> k is weakly polynomial of degree a if its restriction to any isotropic subspace is a polynomial degree of a. We show that if X is a high rank variety then any weakly polynomial function of degree a is the restriction to X of a polynomial of degree a on V. Equidistribution properties of high rank polynomials play an important role. Joint work with D. Kazhdan.
Extending weakly polynomial functions from high rank varietiesread_more
HG G 43
12 December 2018
15:45-16:45 		Stefan Wenger
Université de Fribourg
Event Details

Geometry Seminar

Title Constructing Hölder maps to Carnot groups
Speaker, Affiliation Stefan Wenger, Université de Fribourg
Date, Time 12 December 2018, 15:45-16:45
Location HG G 43
Abstract Carnot groups equipped with a Carnot metric are subriemannian manifolds. These exhibit interesting (local) geometry that is far from Euclidean. In this talk we mainly focus on the special case of the first Heisenberg group $H$ and study its geometry through Hölder mappings. By a theorem of Züst, which strengthens a result of Gromov and Pansu, every $\alpha$-Hölder map with $\alpha>2/3$ from a Euclidean ball to $H$ factors through some tree. We show that Züst's result is sharp by constructing topologically non-trivial $\alpha$-Hölder maps from the Euclidean $2$-ball and $3$-ball to $H$ for every $\alpha<2/3$. Some of our results generalize to general Carnot groups. Joint work with Robert Young.
Constructing Hölder maps to Carnot groupsread_more
HG G 43

Organizers: Marc Burger, Manfred Einsiedler, Alessandra Iozzi, Urs Lang, Viktor Schröder, Alessandro Sisto

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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