Departement Mathematik

Geometry graduate colloquium

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Frühjahrssemester 2021

Datum / Zeit Referent:in Titel Ort
4. März 2021
16:00-17:00 		Sam Hughes
University of Southhampton, UK
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Geometry Graduate Colloquium

Titel Lattices in non-positive curvature
Referent:in, Affiliation Sam Hughes, University of Southhampton, UK
Datum, Zeit 4. März 2021, 16:00-17:00
Ort 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. März 2021
16:00-17:00 		Dr. Claire Burrin
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Titel Automorphic forms and winding numbers
Referent:in, Affiliation Dr. Claire Burrin, ETH Zurich, Switzerland
Datum, Zeit 11. März 2021, 16:00-17:00
Ort 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. März 2021
16:00-17:00 		Damian Iltgen
Universität Regensburg
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Geometry Graduate Colloquium

Titel Khovanov Homology and the Lee Spectral Sequence
Referent:in, Affiliation Damian Iltgen, Universität Regensburg
Datum, Zeit 18. März 2021, 16:00-17:00
Ort 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. März 2021
16:00-17:00 		Alon Dogon
Hebrew University of Jerusalem, Israel
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Geometry Graduate Colloquium

Titel Hilbert Schmidt stability of groups and C*-algebras
Referent:in, Affiliation Alon Dogon, Hebrew University of Jerusalem, Israel
Datum, Zeit 25. März 2021, 16:00-17:00
Ort 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

Titel Learning graph representations in constant curvature spaces
Referent:in, Affiliation Gregor Bachmann, ETH Zürich, Switzerland
Datum, Zeit 1. April 2021, 16:00-17:00
Ort 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

Titel The cotangent bundle of a circle and its symplectic geometry
Referent:in, Affiliation Valentin Bosshard, ETH Zurich, Switzerland
Datum, Zeit 15. April 2021, 16:00-17:00
Ort 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

Titel Slicing knots using topological Surgery Theory
Referent:in, Affiliation Dr. Patrick Orson, ETH Zurich, Switzerland
Datum, Zeit 22. April 2021, 16:00-17:00
Ort 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

Titel Bounded cohomology of the free group
Referent:in, Affiliation Sofia Amontova, University of Geneva, Switzerland
Datum, Zeit 29. April 2021, 16:00-17:00
Ort 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. Mai 2021
16:00-17:00 		Daniel Bertschinger
ETH Zürich, Switzerland
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Geometry Graduate Colloquium

Titel Highlights from discrete geometry
Referent:in, Affiliation Daniel Bertschinger, ETH Zürich, Switzerland
Datum, Zeit 6. Mai 2021, 16:00-17:00
Ort 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. Mai 2021
16:00-17:00 		Emilio Corso
ETH Zurich, Switzerland
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Geometry Graduate Colloquium

Titel Statistical properties of geodesic and horocycle orbits on negatively-curved surfaces
Referent:in, Affiliation Emilio Corso, ETH Zurich, Switzerland
Datum, Zeit 20. Mai 2021, 16:00-17:00
Ort 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. Juni 2021
17:00-18:00 		Catherine Babecki
University of Washington, USA
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Geometry Graduate Colloquium

Titel Cubes, Codes, and Graphical Designs
Referent:in, Affiliation Catherine Babecki, University of Washington, USA
Datum, Zeit 3. Juni 2021, 17:00-18:00
Ort 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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Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen.

Organisatoren:innen: Xenia Lorena Flamm, Yannick Krifka, Paula Truöl

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 HS 18 FS 18

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