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Autumn Semester 2020

Date / Time Speaker Title Location
24 September 2020
13:00-14:00 		Gil Goffer
Weizmann Institute, Israel
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Geometry Graduate Colloquium

Title Lattices in products
Speaker, Affiliation Gil Goffer, Weizmann Institute, Israel
Date, Time 24 September 2020, 13:00-14:00
Location Zoom
Abstract I will give a taste of the rich theory of lattices, and in particular irreducible lattices in a product of locally compact groups. I will briefly review the relevant history, explaining its exceptional importance, and of course present plenty of examples.
Lattices in productsread_more
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1 October 2020
13:00-14:00 		Francesco Fournier Facio
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title What can one do with bounded cohomology?
Speaker, Affiliation Francesco Fournier Facio, ETH Zurich, Switzerland
Date, Time 1 October 2020, 13:00-14:00
Location Zoom
Abstract If you know about singular cohomology and you were asked to define a "bounded version", you would probably come up with the definition of bounded cohomology. However, these two invariants are drastically different. The bad news is that bounded cohomology is really hard to compute, so much so that very few examples are available. The good news is that as soon as one understands the bounded cohomology of a group, this has extremely powerful applications. In this talk I will introduce bounded cohomology of topological spaces and groups, and try to convince you that this is indeed the case. We will focus on the following important applications: 1. The computation of the simplicial volume, which allows to estimate the volume of a Riemannian manifold. 2. The study of group actions on the circle. 3. Time permitting, some rigidity theory.
What can one do with bounded cohomology?read_more
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8 October 2020
13:00-14:00 		Andreas Wieser
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Quantitative non-divergence for orbits of unipotent groups
Speaker, Affiliation Andreas Wieser, ETH Zurich, Switzerland
Date, Time 8 October 2020, 13:00-14:00
Location Zoom
Abstract In this talk, we will discuss a result by Kleinbock and Margulis from the 90's proving quantitative non-divergence for unipotent orbits. Roughly speaking, it states that given a small neighborhood of infinity in a locally homogeneous space a unipotent orbit cannot spend a lot of time in that neighborhood unless there is an algebraic obstruction. The result is quantitative in the sense that the bound on this time is explicit in all parameters (such as the time window for the unipotent flow and the 'size' of the compact set). Our goal will be to see several instances of this result and to understand how this kind of behaviour truly relies on the acting group being unipotent.
Quantitative non-divergence for orbits of unipotent groupsread_more
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15 October 2020
13:00-14:00 		Dr. Patricia Dietzsch
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Lagrangian Hofer metric
Speaker, Affiliation Dr. Patricia Dietzsch, ETH Zurich, Switzerland
Date, Time 15 October 2020, 13:00-14:00
Location Zoom
Abstract In this talk we introduce the Lagrangian Hofer metric, focusing on concrete examples like equators in the 2-disc, the cylinder and the 2-sphere. Then we can discuss the question of (un)boundedness of the Lagrangian Hofer metric in these three examples: M. Khanevsky proved in 2009 that it is unbounded for the disc and the cylinder, but the question is still open for the sphere.
Lagrangian Hofer metricread_more
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22 October 2020
13:00-14:00 		José Pedro Quintanilha
Universität Regensburg
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Geometry Graduate Colloquium

Title Studying 3-manifolds through the finite quotients of their fundamental group
Speaker, Affiliation José Pedro Quintanilha, Universität Regensburg
Date, Time 22 October 2020, 13:00-14:00
Location Zoom
Abstract In recent years there has been growing interest in understanding what features of a 3-manifold are encoded in the finite quotients of its fundamental group. These are broadly known as questions of "profinite rigidity". The fact that 3-manifold groups are residually finite makes them particularly suited to being studied from this viewpoint. We will start by briefly introducing the profinite completion of a group, a construction with origins in Galois theory that neatly packages the information about its finite quotients, and then survey some results that exemplify both profinite rigidity and flexibility among (classes of) 3-manifolds.
Studying 3-manifolds through the finite quotients of their fundamental groupread_more
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29 October 2020
13:00-14:00 		Jonathan Fruchter
University of Oxford, UK
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Geometry Graduate Colloquium

Title Limit groups and compactness
Speaker, Affiliation Jonathan Fruchter, University of Oxford, UK
Date, Time 29 October 2020, 13:00-14:00
Location Zoom
Abstract The opening point of this talk will be a lemma of Gilbert Baumslag, which gives a criterion for the non-triviality of certain elements in a free group. An immediate corollary of this lemma is that surface groups are fully residually free. We will then use Baire's theorem to show that if a compact Hausdorff topological group has a (dense) free subgroup, then it also has a (dense) surface subgroup. To finish, we will discuss how this proof can be generalized and applied to any limit group and to other groups with nice residual properties.
Limit groups and compactnessread_more
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5 November 2020
13:00-14:00 		Dr. Matthias Nagel
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Links between dimensions three and four
Speaker, Affiliation Dr. Matthias Nagel, ETH Zurich, Switzerland
Date, Time 5 November 2020, 13:00-14:00
Location Zoom
Abstract In the talk I will explain how to obtain lower bounds on unlinking numbers through 4-manifold techniques using a generalization of a theorem of Cochran-Lickorish. The method will be illustrated using a link from Kohn's table whose unlinking numbers have only recently been determined through these methods. This is based on joint work with B. Owens.
Links between dimensions three and fourread_more
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12 November 2020
13:00-14:00 		Laurin Köhler-Schindler
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Percolation in the plane and beyond
Speaker, Affiliation Laurin Köhler-Schindler, ETH Zurich, Switzerland
Date, Time 12 November 2020, 13:00-14:00
Location Zoom
Abstract We introduce Bernoulli percolation on an infinite transitive graph, where edges are independently declared open with probability p or closed otherwise. Interestingly, there exists a phase transition at some p_c such that below p_c, all open connected components are finite and above p_c, there exists at least one infinite component. In the plane, we will study this phase transition in more detail and beyond, we will describe links between probabilistic properties of the model and geometric properties of the underlying graph.
Percolation in the plane and beyondread_more
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19 November 2020
13:00-14:00 		Alice Kerr
University of Oxford
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Geometry Graduate Colloquium

Title Tree approximation in quasi-trees
Speaker, Affiliation Alice Kerr, University of Oxford
Date, Time 19 November 2020, 13:00-14:00
Location Zoom
Abstract Quasi-trees are spaces that can be thought of as lying somewhere between trees and hyperbolic spaces. They retain many of the strong geometric properties of trees, while at the same time admitting many interesting group actions, most notably by acylindrically hyperbolic groups. The aim of this talk will be to illustrate quite how "tree-like" quasi-trees are, as well as to give some idea of their importance in geometric group theory.
Tree approximation in quasi-treesread_more
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26 November 2020
13:00-14:00 		Andrea Thevis
Universität des Saarlandes, Germany
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Geometry Graduate Colloquium

Title Square-tiled surfaces: A class of extraordinary translation surfaces
Speaker, Affiliation Andrea Thevis, Universität des Saarlandes, Germany
Date, Time 26 November 2020, 13:00-14:00
Location Zoom
Abstract A translation surface is obtained by taking finitely many polygons in the Euclidean plane and gluing them along their edges by translations. If we restrict to gluing squares of the same size, we obtain a square-tiled surface, also known as origami. In the first part of the talk, I explain some motivations for studying translation surfaces. I especially aim to point out why it is natural to study square-tiled surfaces in some of these contexts. In the second part of the talk, we consider square-tiled surfaces in more detail. More precisely, we examine their Veech groups and explore extraordinary properties of a famous surface called the Eierlegende Wollmilchsau. This surface motivates studying the class of normal or regular square-tiled surfaces, i.e., square-tiled surfaces which are normal torus covers.
Square-tiled surfaces: A class of extraordinary translation surfacesread_more
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3 December 2020
13:00-14:00 		Adélie Garin
EPFL, Switzerland
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Geometry Graduate Colloquium

Title From trees to barcodes and back again: at the melding point of topology, geometry, group theory and probability
Speaker, Affiliation Adélie Garin, EPFL, Switzerland
Date, Time 3 December 2020, 13:00-14:00
Location Zoom
Abstract Methods of topological data analysis (TDA) have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this talk I will first give an overview of TDA, and then discuss in particular the Topological Morphology Descriptor (TMD), an algorithm to build a topological summary, called barcode, from a tree, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm. I will provide an overview of the TMD and the TNS and describe to what extent the TNS provides an inverse to the TMD. On the way, I will show an approach to classify barcodes using symmetric groups, illustrating the ability of TDA to merge several mathematical fields in one. No prerequisites are required.
From trees to barcodes and back again: at the melding point of topology, geometry, group theory and probabilityread_more
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10 December 2020
13:00-14:00 		Nick Bell
University of Bristol, UK
Details

Geometry Graduate Colloquium

Title Counting curves and arcs on surfaces
Speaker, Affiliation Nick Bell, University of Bristol, UK
Date, Time 10 December 2020, 13:00-14:00
Location Zoom
Abstract Curves and arcs are natural objects on surfaces, and one might wish to know how many there are on a given surface, up to homotopy. As there are infinitely many curves (or arcs) on any (complex enough) surface, this becomes a question of how quickly does the number of curves (or arcs) of bounded length grow, in terms of the length. One might also wonder how this number grows when only considering a particular mapping class group orbit of curves (or arcs). We will discuss the history of these questions, and some recent developments.
Counting curves and arcs on surfacesread_more
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Organisers: Luca De Rosa, Xenia Lorena Flamm, Yannick Krifka, Paula Truöl

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 AS 18 SS 18

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