Geometry graduate colloquium

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Spring Semester 2023

Date / Time

Speaker

Title

Location

2 March 2023
15:00-16:00

Mireille Soergel
Université de Bourgogne, ETH Zürich

Event Details

Geometry Graduate Colloquium

Title	Simplicial non-positive curvature
Speaker, Affiliation	Mireille Soergel, Université de Bourgogne, ETH Zürich
Date, Time	2 March 2023, 15:00-16:00
Location	HG G 19.1
Abstract	A classical notion of curvature is the sectional curvature of a Riemannian manifold. Alexandrov and Gromov generalized the Riemannian curvature notion to metric spaces. In 2006 Januszkiewicz and Świątkowski introduced systolicity as a non-positive curvature criterion for simplicial complexes. I will define systolic complexes and give some examples. I will also mention some properties of these spaces and of groups acting on them. We will also see how this notion compares to other notions on non-positive curvature.

Simplicial non-positive curvatureread_more

HG G 19.1

9 March 2023
14:30-15:30

Anna Michael
Otto von Guericke Universität Magdeburg

Event Details

Geometry Graduate Colloquium

Title	Coxeter shadows - unfolding the beauty of folded galleries
Speaker, Affiliation	Anna Michael, Otto von Guericke Universität Magdeburg
Date, Time	9 March 2023, 14:30-15:30
Location	HG G 19.1
Abstract	In 2018 Marius Graber and Petra Schwer introduced the notion of Coxeter Shadows, being a subset of the Coxeter group elements combinatorially defined via foldings of galleries in the Coxeter complex. These shadows have shown to have versatile applications in algebra and geometry, making them an object of interest for current research. In this talk we will retrace the roots of their invention to the early 20th century, and by examining vivid examples discover the beauty of folded galleries.

Coxeter shadows - unfolding the beauty of folded galleriesread_more

HG G 19.1

16 March 2023
14:30-15:30

Alexis Marchand
University of Cambridge

Event Details

Geometry Graduate Colloquium

Title	Stable commutator length and rationality theorems
Speaker, Affiliation	Alexis Marchand, University of Cambridge
Date, Time	16 March 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Stable commutator length (scl) is a measure of homological complexity in groups that has many surprising connections with various topics in geometric topology and group theory. We will introduce scl as well as some of those connections, and discuss the (hard) problem of computing scl. Time permitting, we will explain some of the ideas behind rationality theorems, which provide algorithms to compute scl in free groups and some generalisations.

Stable commutator length and rationality theoremsread_more

HG G 19.1

23 March 2023
14:30-15:30

Victor Jaeck
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	Non-Archimedean Geometry and Berkovich Analytification
Speaker, Affiliation	Victor Jaeck, ETH Zurich, Switzerland
Date, Time	23 March 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Let us consider metric spaces in which the triangular inequality is strengthened to d(x,z) ≤ max{d(x,y), d(y,z)}, that is, ultrametric spaces. These spaces, interesting in themselves, play an important role in the study of the geometry at infinity of various mathematical objects. The topological properties induced by the strengthened triangle inequality do not facilitate the study of the analytic properties of these spaces. The aim of this colloquium is to give an introduction to Berkovich's analytification, which provides a way to study the geometric properties of ultrametric spaces by analytical means.

Non-Archimedean Geometry and Berkovich Analytificationread_more

HG G 19.1

30 March 2023
14:30-15:30

Lukas Böke
Ludwig-Maximilians-Universität München

Event Details

Geometry Graduate Colloquium

Title	Uniform perfectness of groups of diffeomorphisms
Speaker, Affiliation	Lukas Böke, Ludwig-Maximilians-Universität München
Date, Time	30 March 2023, 14:30-15:30
Location	HG G 19.1
Abstract	The component of the identity of the diffeomorphism group of a compact manifold has been known to be perfect, i.e. we can factor every group element into simple commutators. This is due to work of Mather and Thurston in the 1970s. More recently, Burago-Ivanov-Polterovich and Tsuboi have shown that other than in dimensions 2 and 4, one can find a uniform bound on the number of commutators needed when factoring a group element into simple commutators. The situation in dimension 2 is drastically different. We will look at the tools involved for proving both boundedness and unboundedness of the commutator length on these groups.

Uniform perfectness of groups of diffeomorphismsread_more

HG G 19.1

6 April 2023
14:30-15:30

Naomi Bredon
Université de Fribourg

Event Details

Geometry Graduate Colloquium

Title	Coxeter polyhedra and reflection groups
Speaker, Affiliation	Naomi Bredon, Université de Fribourg
Date, Time	6 April 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Coxeter polyhedra are convex polyhedra whose dihedral angles are integer submultiples of π. They are intimately related with regular polyhedra tessellating the space and enjoy nice extremal properties. Due to the work of H.S.M Coxeter, spherical and Euclidean Coxeter polyhedra are fully classified. However, in the hyperbolic case, such a classification is far from being complete. In this talk, we go into classification results in small dimensions, providing various examples, and discuss the properties of their associated reflection groups in terms of co-volumes and growth rates.

Coxeter polyhedra and reflection groupsread_more

HG G 19.1

20 April 2023
14:30-15:30

Hermès Lajoinie
Université de Montpellier

Event Details

Geometry Graduate Colloquium

Title	Strong property (T) and hyperbolicity
Speaker, Affiliation	Hermès Lajoinie, Université de Montpellier
Date, Time	20 April 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Hyperbolic groups were introduced in the 80's by M.Gromov as a generalization of fundamental groups of Riemannian manifold with non-positive curvature. These groups form a large class of finitely generated groups with lots of good combinatorial properties. Property (T) was introduced in the 60's by D.Kahzdan to prove that a large class of lattices are finitely generated. This is a rigidity property, this means that if a group has this property, actions on some particular metric spaces have to be trivial. For example, actions on trees have a fixed point. I will discuss these two notions and links between them. Time permitting, I will talk about a strengthening of Property (T) called Strong Property (T).

Strong property (T) and hyperbolicityread_more

HG G 19.1

27 April 2023
14:30-15:30

Diego Santoro
Scuola Normale Superiore di Pisa

Event Details

Geometry Graduate Colloquium

Title	Taut foliations and the Property R conjecture
Speaker, Affiliation	Diego Santoro, Scuola Normale Superiore di Pisa
Date, Time	27 April 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Taut foliations are an important research topic in low-dimensional topology that has been widely used in the study of 3-manifolds. In this talk I will introduce the operation of Dehn surgery on a knot and state the Property R conjecture. Then I will give a rough outline of how taut foliations were used by Gabai to prove this conjecture.

Taut foliations and the Property R conjectureread_more

HG G 19.1

4 May 2023
14:30-15:30

Giuseppe Bargagnati
Università di Pisa

Event Details

Geometry Graduate Colloquium

Title	Contractible 3-manifolds and simplicial volume
Speaker, Affiliation	Giuseppe Bargagnati, Università di Pisa
Date, Time	4 May 2023, 14:30-15:30
Location	HG G 19.1
Abstract	In 1934, in what he thought to be a proof of the Poincaré Conjecture, the american mathematician J.H.C. Whitehead claimed that an open contractible 3-manifold has to be homeomorphic to R³. In 1935 Whitehead corrected his claim and discovered the first known example of contractible open 3-manifold not homeomorphic to the Euclidean space, which now carries his name. It turned out that there are plenty of open 3 manifolds with this property (in fact, continuum infinitely many of them). In 1982, Gromov introduced an invariant of manifolds called simplicial volume. In this seminar we will define this invariant, show some of its basic properties, and explore the wild world of contractible 3-manifolds. In the end, we will see how the simplicial volume can distinguish R³ from the other contractible 3-manifolds.

Contractible 3-manifolds and simplicial volumeread_more

HG G 19.1

11 May 2023
14:30-15:30

Fernando Camacho Cadena
Ruprecht-Karls-Universität Heidelberg

Event Details

Geometry Graduate Colloquium

Title	Deforming geometric structures through Hamiltonian flows
Speaker, Affiliation	Fernando Camacho Cadena, Ruprecht-Karls-Universität Heidelberg
Date, Time	11 May 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Intuitively, a geometric structure on a manifold is a way to locally model it on a specific geometry. A rich class of examples are hyperbolic and convex projective structures on surfaces. It turns out that these geometric structures can be deformed. Moreover, spaces parameterizing such geometric structures (some of which are (higher) Teichmüller spaces) also carry a natural symplectic form. With this tool at hand, it is possible to study deformations through Hamiltonian flows. The goal of this talk is to explain how to deform hyperbolic structures by “twisting and earthquaking”, their generalizations to convex projective structures, and finally how they can be interpreted as Hamiltonian flows. If time permits, I will briefly explain the more recent work of Wienhard-Zhang on eruption flows, which are newly discovered types of deformations.

Deforming geometric structures through Hamiltonian flowsread_more

HG G 19.1

25 May 2023
14:30-15:30

Younghan Bae
ETH Zurich, Switzerland

Event Details

Geometry Graduate Colloquium

Title	Moduli spaces of algebraic curves and line bundles
Speaker, Affiliation	Younghan Bae, ETH Zurich, Switzerland
Date, Time	25 May 2023, 14:30-15:30
Location	HG G 19.1
Abstract	Let C be a Riemann surface of genus g and let p₁, ..., p_n be n distinct points on C. For an n-tuple of integers (a₁, ..., a_n) which sum up to zero, one can ask when the holomorphic line bundle O_C(a₁.p₁ + ... + a_n.p_n) is trivial. The complete answer to this question was given by Abel in 19th century. Now one can ask a similar question over the moduli space of marked Riemann surfaces or its Deligne-Mumford compactification. How can we compactify this locus and can we compute the homology class of this locus systematically? We will see a quantitative answer to this question and its generalisation.

Moduli spaces of algebraic curves and line bundlesread_more

HG G 19.1

Organizers: Konstantin Andritsch, Raphael Appenzeller, Francesco Fournier Facio, Martina Joergensen, Lauro Silini, 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