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Autumn Semester 2024

Date / Time Speaker Title Location
3 October 2024
16:15-17:15 		Marie Abadie
University of Luxembourg
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Geometry Graduate Colloquium

Title Surfaces, graphs and complexes
Speaker, Affiliation Marie Abadie, University of Luxembourg
Date, Time 3 October 2024, 16:15-17:15
Location HG G 19.2
Abstract The goal of this talk is to provide a brief overview of the interactions between hyperbolic surfaces and certain combinatorial objects. Specifically, we will explore Brock's combinatorial approach to understanding the coarse geometry of Teichmüller space equipped with the Weil-Petersson metric. This approach revolves around using the pants graph as a combinatorial tool for navigating Teichmüller space. Along the way, we will also encounter the hexagons graph and other related questions.
Surfaces, graphs and complexesread_more
HG G 19.2
10 October 2024
16:15-17:15 		Raphael Appenzeller
Heidelberg University
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Geometry Graduate Colloquium

Title Hyperbolicity and winning strategies in Cops and Robbers games
Speaker, Affiliation Raphael Appenzeller, Heidelberg University
Date, Time 10 October 2024, 16:15-17:15
Location HG G 19.2
Abstract Cops and Robbers is a two-player game played on graphs, where one player tries to catch the other, while the other tries to escape. Recently, a version of this game was introduced, where the existence of a winning strategy is invariant under quasi-isometry. This allows to play the game on Cayley-graphs of groups and gives new group invariants. We spotlight some connections between Gromov-hyperbolicity and the existence of winning strategies.
Hyperbolicity and winning strategies in Cops and Robbers gamesread_more
HG G 19.2
17 October 2024
16:15-17:15 		Sophie Schmidhuber
University of Zurich
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Geometry Graduate Colloquium

Title Billiard dynamics and Masur’s Criterion
Speaker, Affiliation Sophie Schmidhuber, University of Zurich
Date, Time 17 October 2024, 16:15-17:15
Location HG G 19.2
Abstract In this talk, we will show how the trajectory of a billiard ball on a billiard table with rational angles can be understood via the straight line flow on a translation surface. We will define the geodesic flow for the moduli space of translation surfaces and provide a simple but elegant proof for Masur's Criterion, which states that if the trajectory of a translation surface under the geodesic flow is recurrent, then the vertical straight line flow on the translation surface is uniquely ergodic.
Billiard dynamics and Masur’s Criterionread_more
HG G 19.2
24 October 2024
16:15-17:15 		Cynthia Bortolotto
ETH Zurich
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Geometry Graduate Colloquium

Title On distribution of random chords in the plane
Speaker, Affiliation Cynthia Bortolotto, ETH Zurich
Date, Time 24 October 2024, 16:15-17:15
Location HG G 19.2
Abstract In 1961, Jovan Karamata proved a remarkable identity involving the Dilogarithm function and intersection of diagonals of regular polygons. We reframe the problem and give different proofs for the result. We also investigate what happens when we consider different approaches to it.
On distribution of random chords in the planeread_more
HG G 19.2
31 October 2024
16:15-17:15 		Layne Hall
University of Warwick
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Geometry Graduate Colloquium

Title The correspondence between pseudo-Anosov flows and veering triangulations.
Speaker, Affiliation Layne Hall, University of Warwick
Date, Time 31 October 2024, 16:15-17:15
Location HG G 19.2
Abstract We will describe how a family of dynamical systems can be studied using combinatorial topology. The systems in question are pseudo-Anosov flows, an abundant class of continuous dynamical systems on three-manifolds. The combinatorics comes from an object of a different flavour: veering triangulations. Both of these objects, in their own right, are closely related to the geometry and topology of the underlying manifold. We will start by introducing pseudo-Anosov flows and veering triangulations. Then, we will discuss a deep correspondence between the two.
The correspondence between pseudo-Anosov flows and veering triangulations.read_more
HG G 19.2
7 November 2024
16:15-17:15 		Huaitao Gui
University of Copenhagen
Details

Geometry Graduate Colloquium

Title Injective metric spaces and locally elliptic action
Speaker, Affiliation Huaitao Gui, University of Copenhagen
Date, Time 7 November 2024, 16:15-17:15
Location HG G 19.2
Abstract Can hyperbolic groups act on spaces exhibiting nonpositive curvature in a noncoarse way? The quest to understand this has led to the study of injective metric spaces. In this talk, we will discuss some basic properties of such spaces and explore their connection to nonpositive curvature. Then, we will shift to combinatorial dimension, a closely related notion which finds application in describing locally elliptic actions.
Injective metric spaces and locally elliptic actionread_more
HG G 19.2
14 November 2024
16:15-17:15 		Laura Lankers
Max Planck Institute for Mathematics in the Sciences, Leipzig
Details

Geometry Graduate Colloquium

Title Higher Teichmüller spaces and Positivity
Speaker, Affiliation Laura Lankers, Max Planck Institute for Mathematics in the Sciences, Leipzig
Date, Time 14 November 2024, 16:15-17:15
Location HG G 19.2
Abstract In the classical Teichmüller space, representations admit positive boundary maps. We will recall some hyperbolic geometry in order to understand this positivity at the boundary at infinity of the hyperbolic plane. Then we move to higher rank and talk about what positivity means in this case and why it is useful to find higher Teichmüller spaces.
Higher Teichmüller spaces and Positivityread_more
HG G 19.2
21 November 2024
16:15-17:15 		Panagiotis Papadopoulos
Universität München
Details

Geometry Graduate Colloquium

Title Knotting, motions and symmetries
Speaker, Affiliation Panagiotis Papadopoulos, Universität München
Date, Time 21 November 2024, 16:15-17:15
Location HG G 19.2
Abstract Three well-studied (classes of) objects in low-dimensional topology are knots (in various settings), mapping class groups of manifolds, and motion groups. We will see how these can be related to each other, and illustrate these connections using the example of braids and links. We will then introduce the Goeritz group, which may be thought of as a higher-dimensional analogue of the (spherical) braid group, and conclude with open problems around it.
Knotting, motions and symmetriesread_more
HG G 19.2
28 November 2024
16:15-17:15 		Erick Gordillo
Heidelberg University
Details

Geometry Graduate Colloquium

Title Brattelli-Verschik diagrams and Rudolph’s-like representation theorem
Speaker, Affiliation Erick Gordillo, Heidelberg University
Date, Time 28 November 2024, 16:15-17:15
Location HG G 19.2
Brattelli-Verschik diagrams and Rudolph’s-like representation theorem
HG G 19.2
5 December 2024
16:15-17:15 		Clemens Bannwart
University of Modena and Reggio Emilia
Details

Geometry Graduate Colloquium

Title Persistent homology and vector fields
Speaker, Affiliation Clemens Bannwart, University of Modena and Reggio Emilia
Date, Time 5 December 2024, 16:15-17:15
Location HG G 19.2
Persistent homology and vector fields
HG G 19.2

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