Geometry graduate colloquium

Modal title

Modal content

Please subscribe here if you would you like to be notified about these presentations via e-mail. Moreover you can subscribe to the iCal/ics Calender.

Autumn Semester 2022

Date / Time

Speaker

Title

Location

22 September 2022
16:15-17:15

Pietro Capovilla
Scuola Normale Superiore, Italy

Event 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

Event Details

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

Event Details

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

Event 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

Event Details

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

Event 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

Event 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

Event 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

Event 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

Event 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

Event 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

Event 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

Event 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

Organizers: Raphael Appenzeller, Martina Joergensen, 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