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Spring Semester 2021

Date / Time Speaker Title Location
4 March 2021
16:00-17:00 		Sam Hughes
University of Southhampton, UK
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Geometry Graduate Colloquium

Title Lattices in non-positive curvature
Speaker, Affiliation Sam Hughes, University of Southhampton, UK
Date, Time 4 March 2021, 16:00-17:00
Location Zoom
Abstract In this talk I will introduce the study of lattices in locally compact groups through their actions on non-positively curved or CAT(0) spaces. This is an extremely rich class of groups including S-arithmetic groups acting on products of symmetric spaces and buildings, right angled Artin and Coxeter groups acting on polyhedral complexes, Burger-Mozes simple groups acting on products of trees, and the recent CAT(0) but non biautomatic groups of Leary and Minasyan. The goals of the talk are to motivate the study of these lattices and to draw attention to a number of questions related to my research.
Lattices in non-positive curvatureread_more
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11 March 2021
16:00-17:00 		Dr. Claire Burrin
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Automorphic forms and winding numbers
Speaker, Affiliation Dr. Claire Burrin, ETH Zurich, Switzerland
Date, Time 11 March 2021, 16:00-17:00
Location Zoom
Abstract I will discuss an attempt to construct quasimorphisms on Fuchsian groups that represent the bounded Euler class. The approach builds on the theory of automorphic forms, and pays off grandly — in certain situations — with (1) a winding number function for closed geodesics that wrapping around a cusp of the corresponding surface and (2) precise statistics on the number of closed geodesics with any prescribed winding number.
Automorphic forms and winding numbersread_more
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18 March 2021
16:00-17:00 		Damian Iltgen
Universität Regensburg
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Geometry Graduate Colloquium

Title Khovanov Homology and the Lee Spectral Sequence
Speaker, Affiliation Damian Iltgen, Universität Regensburg
Date, Time 18 March 2021, 16:00-17:00
Location Zoom
Abstract In 1999, Khovanov defined a link invariant which takes the form of a bigraded homology theory and categorifies the Jones polynomial. This link invariant is now known as Khovanov homology and has been a popular object of study in knot theory ever since. In 2003, Lee used a deformation of Khovanov homology to obtain a new theory known as Lee homology. This theory is related to Khovanov homology by means of a spectral sequence, which carries an astonishing amount of information. For example, there is the Rasmussen s-invariant which reveals properties of the 4-dimensional geometry of the knot, or the recent work of Alishahi and Dowlin which provides a bound on the unknotting number, all derived from the Lee spectral sequence. The aim of this talk is to give an introduction to these topics and present further developments in this theory.
Khovanov Homology and the Lee Spectral Sequenceread_more
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25 March 2021
16:00-17:00 		Alon Dogon
Hebrew University of Jerusalem, Israel
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Geometry Graduate Colloquium

Title Hilbert Schmidt stability of groups and C*-algebras
Speaker, Affiliation Alon Dogon, Hebrew University of Jerusalem, Israel
Date, Time 25 March 2021, 16:00-17:00
Location Zoom
Abstract Consider the following classical question: Given two almost commuting matrices, are they necessarily close to a pair of commuting matrices? The first goal of this lecture is to recast this question in terms of a lifting property for groups and C*-algebras, called stability. We will introduce this notion which has gained interest in recent years, and use it to give a positive answer to the above question in the setting of the normalized Hilbert Schmidt distance. No prior knowledge on C*-algebras will be assumed.
Hilbert Schmidt stability of groups and C*-algebrasread_more
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1 April 2021
16:00-17:00 		Gregor Bachmann
ETH Zürich, Switzerland
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Geometry Graduate Colloquium

Title Learning graph representations in constant curvature spaces
Speaker, Affiliation Gregor Bachmann, ETH Zürich, Switzerland
Date, Time 1 April 2021, 16:00-17:00
Location Zoom
Abstract One of the main goals in machine learning is to provide representative embeddings of data into a suitable space that allows to perform computations and to extract important information. Euclidean space has so far been the dominant domain to this end, due to its very natural interpretation and efficient arithmetic formulae. On the other hand, Euclidean space is not always the optimal choice. For certain data such as graphs, the geometric structure can be more accurately captured by resorting to embeddings in hyperbolic or spherical space. The lack of a vector space structure to perform computations can be overcome by leveraging the gyrovector space framework introduced by A. Ungar. By extending this notion to spherical geometry, we obtain a unified computational model for constant curvature manifolds that interpolates smoothly between all geometries. We employ these results to extend the very popular (euclidean) graph neural networks to spaces of constant curvature.
Learning graph representations in constant curvature spacesread_more
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15 April 2021
16:00-17:00 		Valentin Bosshard
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title The cotangent bundle of a circle and its symplectic geometry
Speaker, Affiliation Valentin Bosshard, ETH Zurich, Switzerland
Date, Time 15 April 2021, 16:00-17:00
Location Zoom
Abstract We discuss symplectic phenomena on the cotangent bundle of a circle to motivate phenomena and expectations in higher dimensional symplectic geometry. For example classifying or generating Lagrangian manifolds (The Nearby Lagrangian Conjecture, Generation of the Wrapped Fukaya Category) and some Lagrangian intersection theory (The Lagrangian Arnold Conjecture).
The cotangent bundle of a circle and its symplectic geometryread_more
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22 April 2021
16:00-17:00 		Dr. Patrick Orson
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Slicing knots using topological Surgery Theory
Speaker, Affiliation Dr. Patrick Orson, ETH Zurich, Switzerland
Date, Time 22 April 2021, 16:00-17:00
Location Zoom
Abstract A knotted circle in the 3-sphere is called slice if it bounds a 2-disc in the 4-ball. Most techniques for constructing such slicing 2-discs are very hands-on, involving actually drawing or seeing the disc. I will discuss these methods, and then a famous exception to this: Freedman's theorem that Alexander polynomial 1 knots are (topologically) slice.
Slicing knots using topological Surgery Theory read_more
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29 April 2021
16:00-17:00 		Sofia Amontova
University of Geneva, Switzerland
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Geometry Graduate Colloquium

Title Bounded cohomology of the free group
Speaker, Affiliation Sofia Amontova, University of Geneva, Switzerland
Date, Time 29 April 2021, 16:00-17:00
Location Zoom
Abstract Despite its wide range of uses in geometric group theory as well as in the geometry and topology of manifolds, bounded cohomology turns out to be hard to compute in general. In this talk we outline some applications of this theory and then discuss methods to understand the bounded cohomology of the free group.
Bounded cohomology of the free groupread_more
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6 May 2021
16:00-17:00 		Daniel Bertschinger
ETH Zürich, Switzerland
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Geometry Graduate Colloquium

Title Highlights from discrete geometry
Speaker, Affiliation Daniel Bertschinger, ETH Zürich, Switzerland
Date, Time 6 May 2021, 16:00-17:00
Location Zoom
Abstract As the name already suggests, Discrete Geometry studies properties of discrete geometric objects. Most questions involve finite sets of basic geometric objects (in euclidean space) including points, lines, planes and hyperplanes; circles and spheres; polygons and polyhedra and how we can arrange or pack them and how they can intersect. In this talk I'm trying to give you a short overview over the wide field of discrete geometry. We will take a closer look at famous results of the field, see some intuitive arguments for working with them and encounter some (surprisingly) open problems.
Highlights from discrete geometryread_more
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20 May 2021
16:00-17:00 		Emilio Corso
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Title Statistical properties of geodesic and horocycle orbits on negatively-curved surfaces
Speaker, Affiliation Emilio Corso, ETH Zurich, Switzerland
Date, Time 20 May 2021, 16:00-17:00
Location Zoom
Abstract One of the most informative approaches to understand the geometry of a Riemannian manifold is to examine the large-scale behaviour of its geodesics. As it was already observed at the beginning of the last century, a striking dichotomy emerges, in this respect, between positively and negatively curved manifolds: while geodesic trajectories in positive curvature are easily predictable, a considerable amount of randomness appears in the presence of hyperbolicity. Taking advantage of the well-established ergodic theory of flows, the talk aims to survey several manifestations of such randomness in the context of finite-volume hyperbolic surfaces, emphasising the analogies as well as the subtle differences with the properties of the closely related horocycle flow. Featured topics include ergodicity, equidistribution, mixing and distributional limit theorems.
Statistical properties of geodesic and horocycle orbits on negatively-curved surfacesread_more
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* 3 June 2021
17:00-18:00 		Catherine Babecki
University of Washington, USA
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Geometry Graduate Colloquium

Title Cubes, Codes, and Graphical Designs
Speaker, Affiliation Catherine Babecki, University of Washington, USA
Date, Time 3 June 2021, 17:00-18:00
Location Zoom
Abstract Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that even in highly structured graphs, graphical designs are distinct from the related concepts of extremal designs, maximum stable sets in distance graphs, and $t$-designs on association schemes.
Cubes, Codes, and Graphical Designsread_more
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Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: 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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