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Autumn Semester 2022

Date / Time Speaker Title Location
22 September 2022
16:15-17:15 		Pietro Capovilla
Scuola Normale Superiore, Italy
Details

Geometry Graduate Colloquium

Title Amenable covers and simplicial volume
Speaker, Affiliation Pietro Capovilla, Scuola Normale Superiore, Italy
Date, Time 22 September 2022, 16:15-17:15
Location CAB G 52
Abstract A key problem in topology is to relate the volume of a manifold to some other notions of complexity. On one hand, we focus on the simplicial volume of the manifold, a homotopy invariant encoding non-trivial information about the Riemmanian volume. On the other, to describe the complexity of a space, we use integer-valued invariants associated with covers, the so-called categorical invariants. In particular, since amenable groups are small in the context of large-scale geometry, we will see how amenable open covers are the right approximating tool for simplicial volume.
Amenable covers and simplicial volumeread_more
CAB G 52
29 September 2022
16:15-17:15 		Damaris Meier
University of Fribourg, Switzerland
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Geometry Graduate Colloquium

Title Uniformization of metric surfaces
Speaker, Affiliation Damaris Meier, University of Fribourg, Switzerland
Date, Time 29 September 2022, 16:15-17:15
Location CAB G 52
Abstract The classical uniformization theorem states that every simply connected Riemann surface is conformally diffeomorphic to the unit disk, the complex plane or the 2-sphere. The uniformization problem for metric surfaces now asks to generalize this to a non-smooth setting. After motivating this problem with an example arising from geometric group theory, I will introduce the necessary notions and present the main results on uniformization in metric spaces.
Uniformization of metric surfacesread_more
CAB G 52
6 October 2022
16:15-17:15 		Philip Möller
Universität Münster
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Geometry Graduate Colloquium

Title Automatic continuity for groups from geometric group theory
Speaker, Affiliation Philip Möller, Universität Münster
Date, Time 6 October 2022, 16:15-17:15
Location CAB G 52
Abstract The automatic continuity problem asks the following question: Given two topological groups G and H and an algebraic homomorphism φ : G -> H, can we find conditions on G, H and φ ensuring that φ is continuous. The first result in this direction was proved by Dudley in the 1960s and says that any abstract homomorphism from a locally compact Hausdorff group to a free (abelian) group is continuous. In this talk I want to motivate related questions for groups originating from geometric group theory and talk about recent developments.
Automatic continuity for groups from geometric group theoryread_more
CAB G 52
13 October 2022
16:15-17:15 		Alessandro Lägeler
ETH Zurich, Switzerland
Details

Geometry Graduate Colloquium

Title Lattice Points in Triangles
Speaker, Affiliation Alessandro Lägeler, ETH Zurich, Switzerland
Date, Time 13 October 2022, 16:15-17:15
Location CAB G 52
Abstract Counting points with integer coordinates in geometric objects are challenging and well-studied problems in mathematics and use methods from both number theory and geometry. These problems are typically very hard. In this talk, I will present the problem of counting lattice points in the triangle bounded by the coordinate axes and a line L in the plane. Albeit being a geometric question, certain arithmetic conditions on the slope of L determine the solution to the problem. We will see explicit formulae for rational slope and asymptotic formulae for irrational slope (which behave differently if, e.g., the slope is algebraic). No prior knowledge of number theory is required.
Lattice Points in Trianglesread_more
CAB G 52
20 October 2022
16:15-17:15 		Eric Stenhede
Universität Wien
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Geometry Graduate Colloquium

Title A contact geometric proof of the Whitney-Graustein Theorem
Speaker, Affiliation Eric Stenhede, Universität Wien
Date, Time 20 October 2022, 16:15-17:15
Location CAB G 52
Abstract In this talk we will see a proof of the Whitney–Graustein theorem, which states that regular immersions of the circle in the plane are classified by their rotation number. This classical result first appeared in 1937 in a paper of Whitney although he attributes the statement and the proof to Graustein. The original proof is quite involved, so I will present a more modern proof by Geiges in 2007 that uses contact topology. Only very basic knowledge of differential geometry is needed, and in particular I will not assume any familiarity with contact topology.
A contact geometric proof of the Whitney-Graustein Theoremread_more
CAB G 52
27 October 2022
16:15-17:15 		Marco Lotz
Otto von Guericke Universität Magdeburg
Details

Geometry Graduate Colloquium

Title Reflection length in non-affine Coxeter groups
Speaker, Affiliation Marco Lotz, Otto von Guericke Universität Magdeburg
Date, Time 27 October 2022, 16:15-17:15
Location CAB G 52
Abstract Coxeter groups are finitely generated reflection groups, classified roughly by the type of space they act on. This talk illustrates the geometric nature of Coxeter groups by means of the reflection length. Besides introductory definitions and results, we look at some hyperbolic pictures.
Reflection length in non-affine Coxeter groupsread_more
CAB G 52
3 November 2022
16:15-17:15 		Laura Marino
Université de Paris
Details

Geometry Graduate Colloquium

Title Topological quantum field theories and applications
Speaker, Affiliation Laura Marino, Université de Paris
Date, Time 3 November 2022, 16:15-17:15
Location CAB G 52
Abstract Topological quantum field theories are a rich field of study, at the crossroads of many areas of mathematics and physics. Informally, a TQFT is a map that translates a geometric structure into an algebraic setting. More precisely, it is a symmetric monoidal functor from a category of cobordisms to a category of vector spaces. In this talk, we will introduce 1- and 2-dimensional TQFTs and see how they can be used to define some important invariants of knots, links and 3-manifolds.
Topological quantum field theories and applicationsread_more
CAB G 52
10 November 2022
16:15-17:15 		Alice Merz
Università di Pisa
Details

Geometry Graduate Colloquium

Title Strongly invertible knots and equivariant 4-genus
Speaker, Affiliation Alice Merz, Università di Pisa
Date, Time 10 November 2022, 16:15-17:15
Location CAB G 52
Abstract A classical object of study in low dimensional topology, and specifically knot theory, is the knot concordance group. The study and understanding of this group has a strong relation with the 4-dimensional topology of the knot, like for example its 4-genus. After an introduction on classical knot concordance, we will see an analogue construction of this group for strongly invertible knots (i.e. knots with a special symmetry), called the equivariant concordance group. We will also see some differences in the study of the 4-genus in the classical and equivariant context.
Strongly invertible knots and equivariant 4-genusread_more
CAB G 52
17 November 2022
16:15-17:15 		Arno Wildi
Universität Zürich
Details

Geometry Graduate Colloquium

Title Categorification, a very general idea in mathematics
Speaker, Affiliation Arno Wildi, Universität Zürich
Date, Time 17 November 2022, 16:15-17:15
Location CAB G 52
Abstract We will introduce in a understandable-for-everyone-way the concept of categorification. Say, you want to study some object which seems to carry too little structure to prove certain theorems. It can be worth looking at your object as a shadow of something bigger where you may have more tools to work with. This process is called categorification and we will discuss it with the help of various examples, most of them you will know.
Categorification, a very general idea in mathematicsread_more
CAB G 52
24 November 2022
16:15-17:15 		Lara Beßmann
Universität Münster
Details

Geometry Graduate Colloquium

Title Universal groups for right-angled buildings
Speaker, Affiliation Lara Beßmann, Universität Münster
Date, Time 24 November 2022, 16:15-17:15
Location CAB G 52
Abstract Universal groups have been introduced by Burger and Mozes in 2000 as subgroups of the automorphism group of a regular tree satisfying some local data. In 2018 this construction has been generalized to right-angled buildings by De Medts, Silva, and Struyve. I will introduce universal groups and right-angled buildings and then present the construction of universal groups for right-angled buildings. Further, we will discuss some of the properties of these groups.
Universal groups for right-angled buildingsread_more
CAB G 52
1 December 2022
16:15-17:15 		Benjamin Ruppik
Heinrich-Heine Universität Düsseldorf
Details

Geometry Graduate Colloquium

Title Topological Data Analysis in Word Embedding Spaces
Speaker, Affiliation Benjamin Ruppik, Heinrich-Heine Universität Düsseldorf
Date, Time 1 December 2022, 16:15-17:15
Location CAB G 52
Abstract Word embeddings are a popular method from deep learning used to represent natural language as point clouds in a high dimensional space: If two words (such as “color” and “paint”) have similar meaning, their associated points are close in the metric of the embedding space. Topological Data Analysis, with tools such as Persistent Homology, can be used to probe the geometry of word spaces at different scales. For instance, we demonstrate the existence of singularities in static word embeddings, which is in stark contrast to the common “manifold hypothesis” in data analysis.
Topological Data Analysis in Word Embedding Spacesread_more
CAB G 52
8 December 2022
16:15-17:15 		Lars Munser
Universität Regensburg
Details

Geometry Graduate Colloquium

Title Knot concordances, twisted homology and Kirk-Lesch invariants
Speaker, Affiliation Lars Munser, Universität Regensburg
Date, Time 8 December 2022, 16:15-17:15
Location CAB G 52
Abstract Atiyah, Patodi and Singer defined a real-valued invariant for closed odd dimensional manifolds, which might be seen as an equivalent of the (twisted) signature for even dimensional manifolds. Later, Kirk and Lesch generalized the invariant to manifolds with boundary, which lets us study these invariants for the exteriors of knots and links. In this talk I will give a brief introduction to these invariants. The overall goal is to see when these are link concordance invariants.
Knot concordances, twisted homology and Kirk-Lesch invariantsread_more
CAB G 52
15 December 2022
16:15-17:15 		William Sarem
ETHZ / ENS de Lyon
Details

Geometry Graduate Colloquium

Title Harmonic forms and cohomology in smooth (complex) manifolds
Speaker, Affiliation William Sarem, ETHZ / ENS de Lyon
Date, Time 15 December 2022, 16:15-17:15
Location CAB G 52
Abstract This talk aims at being a gentle introduction to Hodge theory and its application to the cohomology of real and complex closed manifolds. If time permits, I will explain some vanishing theorems and introduce the idea of L²-estimates. Basic notions of differential and complex geometry will be recalled.
Harmonic forms and cohomology in smooth (complex) manifoldsread_more
CAB G 52

Organisers: Raphael Appenzeller, Martina Joergensen, 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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