Geometry graduate colloquium

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Spring Semester 2022

Date / Time

Speaker

Title

Location

3 March 2022
16:15-17:15

Waltraud Lederle
UC Louvain

Event Details

Geometry Graduate Colloquium

Title	Neretin's group: a great sandbox
Speaker, Affiliation	Waltraud Lederle, UC Louvain
Date, Time	3 March 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Neretin's group, also known as the almost automorphism group of a tree, was introduced by Neretin in the 90s as a p-adic analogue of the diffeomorphism group of the circle. Itself or its subgroups have been the "first known example of a group satisfying some properties but not some others" in several instances by now. I will explain what this group is, give some interesting subgroups and highlight what is interesting about it.

Neretin's group: a great sandboxread_more

HG E 22
Livestream

10 March 2022
16:15-17:15

Sami Fawaz
ETH Zurich

Event Details

Geometry Graduate Colloquium

Title	Hilbert's 3rd Problem
Speaker, Affiliation	Sami Fawaz, ETH Zurich
Date, Time	10 March 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Can a square be cut into finitely many pieces and rearranged into a regular triangle? Already in the early 19th century this question about so-called scissor congruence was answered affirmatively. In three dimensions the same question with a cube and a regular tetrahedron turns out to be more difficult and appeared as the third problem in Hilbert's famous list of problems in 1900. In this talk I will answer both of the above questions and present possible generalizations. Along with beautiful geometric proofs this leads to questions in homological algebra.

Hilbert's 3rd Problemread_more

HG E 22
Livestream

17 March 2022
16:15-17:15

Martina Joergensen
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	Geodesic spaces of low Nagata dimension
Speaker, Affiliation	Martina Joergensen, ETH Zurich, Switzerland
Date, Time	17 March 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	We discuss the notion of asymptotic and Nagata dimension, with emphasis on examples and applications. In particular, a relatively new result shows that all planar geodesic metric spaces have Nagata dimension at most two, hence asymptotic dimension at most two. We illustrate how this can be used to characterise all three-dimensional Hadamard manifolds as absolute Lipschitz retracts, and indicate the importance of this property.

Geodesic spaces of low Nagata dimensionread_more

HG E 22
Livestream

24 March 2022
16:15-17:15

Matthias Uschold
Universität Regensburg

Event Details

Geometry Graduate Colloquium

Title	Computability of L²-Betti numbers
Speaker, Affiliation	Matthias Uschold, Universität Regensburg
Date, Time	24 March 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	What can we learn from computability results about geometric invariants? We will see some examples and discuss what results we can hope for, in particular regarding real-valued invariants. This will be illustrated by the example of L²-Betti numbers, which can be viewed as a "stable" sibling of the ordinary Betti numbers.

Computability of L²-Betti numbersread_more

HG E 22
Livestream

31 March 2022
16:15-17:15

Jacques Audibert
Sorbonne University, France

Event Details

Geometry Graduate Colloquium

Title	Representations of surface groups in SL(3,R)
Speaker, Affiliation	Jacques Audibert, Sorbonne University, France
Date, Time	31 March 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Hyperbolic structures on a surface give rise to injective homomorphisms with discrete image from its fundamental group to SL(2,R). This is the object of study of classical Teichmüller Theory. In this talk, we will look for homomorphisms of the fundamental group of the surface to SL(3,R). To do so we will endow the space of such homomorphisms with a topology. It has three connected components; among them is the "Hitchin component" which has a nice geometric interpretation. We will particularly focus on injective homomorphisms with discrete image. This is the subject of Higher Teichmüller Theory.

Representations of surface groups in SL(3,R)read_more

HG E 22
Livestream

7 April 2022
16:15-17:15

Marta Magnani
Heidelberg University, Germany

Event Details

Geometry Graduate Colloquium

Title	Symmetric Spaces and Geometric Deep Learning
Speaker, Affiliation	Marta Magnani, Heidelberg University, Germany
Date, Time	7 April 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Symmetric spaces are Riemannian manifolds with rich symmetry groups. They have a compound geometry that contains Euclidean as well as hyperbolic or spherical subspaces. In the talk we will introduce symmetric spaces with particular attention to Siegel spaces. We will then illustrate how Siegel spaces form a versatile family to compute graph embeddings. This made them particularly interesting in the field of Geometric Deep Learning.

Symmetric Spaces and Geometric Deep Learningread_more

HG E 22
Livestream

14 April 2022
16:15-17:15

Matthew Cordes
ETH Zurich

Event Details

Geometry Graduate Colloquium

Title	Gromov boundaries of hyperbolic spaces
Speaker, Affiliation	Matthew Cordes, ETH Zurich
Date, Time	14 April 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Using the "boundary at infinity" of the hyperbolic plane, one can learn a lot about the algebraic properties of discrete subgroups of the isometry group of the hyperbolic plane, PSL(2,R). In the 1980's Gromov introduced a large class of groups, now called Gromov hyperbolic groups, and showed that all the groups in this class have a boundary, called the Gromov boundary, which shares many of the same properties as the boundary of the hyperbolic plane. In this talk I will introduce hyperbolic groups and Gromov boundaries and touch on some of their interesting properties.

Gromov boundaries of hyperbolic spacesread_more

HG E 22
Livestream

28 April 2022
16:15-17:15

Lisa Ricci
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	Higher Teichmüller spaces
Speaker, Affiliation	Lisa Ricci, ETH Zurich, Switzerland
Date, Time	28 April 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Higher Teichmüller spaces are special components of the space of representations of surface groups into simple real Lie groups of higher rank. They generalise classical Teichmüller space and have nice geometrical and dynamical behaviours. We will see the two main examples of such spaces, their shared features and how these lead to further examples and generalisations.

Higher Teichmüller spacesread_more

HG E 22
Livestream

5 May 2022
16:15-17:15

Gonzalo Emiliano Ruiz Stolowicz
EPFL (Lausanne)

Event Details

Geometry Graduate Colloquium

Title	Group actions in hyperbolic spaces
Speaker, Affiliation	Gonzalo Emiliano Ruiz Stolowicz, EPFL (Lausanne)
Date, Time	5 May 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	A brief exposition on the study of isometric group representations in (infinite-dimensional) hyperbolic spaces from a Gelfand-Naimark-Segal perspective.

Group actions in hyperbolic spacesread_more

HG E 22
Livestream

* 12 May 2022
14:15-15:15

Giada Franz
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	Heegaard splittings of three-manifolds
Speaker, Affiliation	Giada Franz, ETH Zurich, Switzerland
Date, Time	12 May 2022, 14:15-15:15
Location	HG E 22
Abstract	A Heegaard splitting of a three-dimensional manifold is a decomposition in two handlebodies glued along their boundary, which turns out to be a convenient description in many applications. We will introduce this notion and review some basic properties. Then, we will focus on the connection between Heegaard splittings and minimal surfaces and see how this relation can be helpful in studying both themes.

Heegaard splittings of three-manifoldsread_more

HG E 22

19 May 2022
16:15-17:15

Anna Bot
University of Basel

Event Details

Geometry Graduate Colloquium

Title	Dynamics in birational geometry
Speaker, Affiliation	Anna Bot, University of Basel
Date, Time	19 May 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Birational geometry, which is the study of birational maps of algebraic varieties, lends itself to be studied in the context of dynamics. We will focus on projective surfaces – and in particular the projective plane – and introduce the bubble space with which we can define the Picard-Manin space and the hyperbolic space associated to the surface. Within this framework, we can then discuss the dynamical degree of a birational map of $\mathbb{P}^2$.

Dynamics in birational geometryread_more

HG E 22
Livestream

2 June 2022
16:15-17:15

Dr. Maria Yakerson
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	How homotopy theory helps to classify algebraic vector bundles
Speaker, Affiliation	Dr. Maria Yakerson, ETH Zurich, Switzerland
Date, Time	2 June 2022, 16:15-17:15
Location	HG E 22 Livestream
Abstract	Classically, topological vector bundles are classified by homotopy classes of maps into infinite Grassmannians. This allows us to study topological vector bundles using obstruction theory: we can detect whether a vector bundle has a trivial subbundle by means of cohomological invariants. In the context of algebraic geometry, one can ask whether algebraic vector bundles over smooth affine varieties can be classified in a similar way. Recent advances in motivic homotopy theory give a positive answer, at least over an algebraically closed base field. Moreover, the behaviour of vector bundles over general base fields has surprising connections with the theory of quadratic forms.

How homotopy theory helps to classify algebraic vector bundlesread_more

HG E 22
Livestream

Note: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organizers: Raphael Appenzeller, Emilio Corso, Francesco Fournier Facio, Paula Truöl

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