Department of Mathematics

Search

Geometry seminar

×

Modal title

Modal content

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

Autumn Semester 2024

Date / Time Speaker Title Location
* 2 October 2024
15:30-16:30 		Prof. Dr. Sobhan Seyfaddini
ETH Zurich, Switzerland
Details

Geometry Seminar

Title On the algebraic structure of area preserving homeomorphisms of the sphere
Speaker, Affiliation Prof. Dr. Sobhan Seyfaddini, ETH Zurich, Switzerland
Date, Time 2 October 2024, 15:30-16:30
Location HG G 19.1
On the algebraic structure of area preserving homeomorphisms of the sphere
HG G 19.1
9 October 2024
15:30-16:30 		Alexander Dranishnikov
University of Florida
Details

Geometry Seminar

Title On Gromov's Positive Scalar Curvature Conjecture for RAAGs
Speaker, Affiliation Alexander Dranishnikov, University of Florida
Date, Time 9 October 2024, 15:30-16:30
Location HG G 43
Abstract Gromov's PSC conjecture for a discrete group G states that the universal cover of a closed PSC n-manifold with the fundamental group G has the macroscopic dimension less than or equal to n-2. We prove Gromov's conjecture for right-angled Artin groups (RAAGs).
On Gromov's Positive Scalar Curvature Conjecture for RAAGsread_more
HG G 43
16 October 2024
15:30-16:30 		Prof. Dr. Thomas Mettler
UniDistance Suisse
Details

Geometry Seminar

Title Flat extensions of principal connections and the Chern—Simons 3-form
Speaker, Affiliation Prof. Dr. Thomas Mettler, UniDistance Suisse
Date, Time 16 October 2024, 15:30-16:30
Location HG G 43
Abstract I will introduce the notion of a flat extension of a connection on a principal bundle. Roughly speaking, a connection admits a flat extension if it arises as the pull-back of a component of a Maurer–Cartan form. For trivial bundles over closed oriented 3-manifolds, I will relate the existence of certain flat extensions to the vanishing of the Chern–Simons invariant associated to the connection. Joint work with Andreas Cap & Keegan Flood.
Flat extensions of principal connections and the Chern—Simons 3-formread_more
HG G 43
23 October 2024
15:30-16:30 		Francesco Fournier-Facio
University of Cambridge
Details

Geometry Seminar

Title Bounded cohomology of transformation groups of R^n
Speaker, Affiliation Francesco Fournier-Facio, University of Cambridge
Date, Time 23 October 2024, 15:30-16:30
Location HG G 43
Abstract Bounded cohomology is a functional analytic analogue of group cohomology, with many applications in rigidity theory, geometric group theory, and geometric topology. A major drawback is the lack of excision, and because of this some basic computations are currently out of reach; in particular the bounded cohomology of some “small” groups, such as the free group, is still mysterious. On the other hand, in the past few years full computations have been carried out for some “big” groups, most notably transformation groups of R^n, where the ordinary cohomology is not yet completely understood. I will report on this recent progress, which will include joint work with Caterina Campagnolo, Yash Lodha and Marco Moraschini, and joint work with Nicolas Monod, Sam Nariman and Sander Kupers.
Bounded cohomology of transformation groups of R^nread_more
HG G 43
13 November 2024
15:30-16:30 		John Baldwin
Boston College
Details

Geometry Seminar

Title Characterizing traces for knots
Speaker, Affiliation John Baldwin, Boston College
Date, Time 13 November 2024, 15:30-16:30
Location HG G 43
Abstract There has been a lot of interest in understanding which knots are characterized by which Dehn surgeries. In this talk, I'll propose studying a 4-dimensional version of this question: which knots are determined by the orientation-preserving diffeomorphism types of which traces? I'll discuss several results that are in stark contrast with what is known about characterizing slopes; for example, that every algebraic knot is determined by its 0-trace. Moreover, every positive torus knot is determined by its n-trace for any n <= 0, whereas no non-positive integer is known to be a characterizing slope for any positive torus knot besides the right-handed trefoil. Our proofs use tools from Heegaard Floer homology and results about surface homeomorphisms.
Characterizing traces for knotsread_more
HG G 43
20 November 2024
15:30-16:30 		Ben Lowe
University of Chicago
Details

Geometry Seminar

Title Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature
Speaker, Affiliation Ben Lowe, University of Chicago
Date, Time 20 November 2024, 15:30-16:30
Location HG G 43
Abstract There is a broad body of work devoted to proving theorems of the following form: spaces with infinitely many special sub-spaces are either nonexistent or rare. Such finiteness statements are important in algebraic geometry, number theory, and the theory of moduli space and locally symmetric spaces. I will talk about joint work with Simion Filip and David Fisher proving a finiteness statement of this kind in a differential geometry setting. Our main theorem is that a closed negatively curved analytic Riemannian manifold with infinitely many closed totally geodesic hypersurfaces must be isometric to an arithmetic hyperbolic manifold. The talk will be more focused on providing background and context than details of proofs and should be accessible to a general audience.
Finiteness of Totally Geodesic Hypersurfaces in Negative Curvatureread_more
HG G 43
27 November 2024
15:30-16:30 		Michelle Bucher
Université de Genève
Details

Geometry Seminar

Title Continuous cocycles on the Furstenberg boundary and applications to bounded cohomology
Speaker, Affiliation Michelle Bucher, Université de Genève
Date, Time 27 November 2024, 15:30-16:30
Location HG G 43
Abstract Group cohomology comes in many variations. The standard Eilenberg-MacLane group cohomology is the cohomology of the cocomplex {f:Gq+1→ ℝ | f is G-invariant} endowed with its natural homogeneous coboundary operator. Now whenever a property P of such cochains is preserved under the coboundary one can obtain the corresponding P-group cohomology. P could be: continuous, measurable, L0, bounded, alternating, etc. Sometimes these various cohomology groups are known to differ (eg P=empty and P=continuous for most topological groups), in other cases they are isomorphic (eg P=empty and P=alternating (easy), P=continuous and P=L0 (a highly nontrivial result by Austin and Moore valid for locally compact second countable groups)). In 2006, Monod conjectured that for semisimple connected, finite center, Lie groups of noncompact type, the natural forgetful functor induces an isomorphism between continuous bounded cohomology and continuous cohomology (which is typically very wrong for discrete groups). I will focus here on the injectivity and show its validity in several new cases including isometry groups of hyperbolic n-spaces in degree 4, known previously only for n=2 by a tour de force due to Hartnick and Ott. Monod recently proved that all such continuous (bounded) cohomology classes can be represented by measurable (bounded) cocycles on the Furstenberg boundary. Our main result is that these cocycles can be chosen to be continuous on a subset of full measure. In the real hyperbolic case, this subset of full measure is the set of distinct tuples of points, easily leading to the injectivity in degree 4. This is joint work with Alessio Savini.
Continuous cocycles on the Furstenberg boundary and applications to bounded cohomologyread_more
HG G 43
4 December 2024
15:30-16:30 		Xenia Flamm
MPI Leipzig
Details

Geometry Seminar

Title Hilbert geometry over non-archimedean ordered valued fields
Speaker, Affiliation Xenia Flamm, MPI Leipzig
Date, Time 4 December 2024, 15:30-16:30
Location HG G 43
Abstract The Hilbert metric is a distance defined on properly convex subsets of real projective space. It generalizes the hyperbolic metric in Klein's model of hyperbolic space, where the convex set is the unit ball. The study of degenerations in Hilbert geometry leads to replacing the reals by a non-archimedean ordered valued field. The aim of this talk is to introduce convex sets over such fields, describe their Hilbert metrics through several examples and view how they arise as limits of classical Hilbert geometries. This is joint work with Anne Parreau.
Hilbert geometry over non-archimedean ordered valued fieldsread_more
HG G 43
11 December 2024
15:30-16:30 		Mikolaj Fraczyk
Jagiellonian University, Krakow
Details

Geometry Seminar

Title On the number of generators of higher rank lattices
Speaker, Affiliation Mikolaj Fraczyk, Jagiellonian University, Krakow
Date, Time 11 December 2024, 15:30-16:30
Location HG G 43
Abstract In my talk I will explain how to use probabilistic methods to show that the number of generators of a higher rank lattice is sublinear in the covolume. We will look at the properties of Voronoi tessellations of symmetric spaces with seeds at a very sparse Poisson point process. In higher rank, one can use dynamics to prove that the Voronoi cells have very elongated walls. This phenomenon is missing in the rank one cases and is the key ingredient for the upper bound on the number of generators. Based on a joint work with Sam Mellick and Amanda Wilkens.
On the number of generators of higher rank latticesread_more
HG G 43
18 December 2024
15:30-16:30 		Andrew Lobb
Durham University, UK
Details

Geometry Seminar

Title Symplectic geometry and peg problems
Speaker, Affiliation Andrew Lobb, Durham University, UK
Date, Time 18 December 2024, 15:30-16:30
Location HG G 43
Abstract The Square Peg Problem (SPP), formulated by Toeplitz in 1911 and still unsolved, asks whether every Jordan curve contains four points at the vertices of a square. We shall discuss how, when the Jordan curve is smooth, SPP and related peg problems can be interpreted as questions in symplectic geometry, and deduce some consequences both for smooth curves and for other classes. Joint work with Josh Greene.
Symplectic geometry and peg problemsread_more
HG G 43

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

Organisers: Marc Burger, Manfred Einsiedler, Urs Lang, Lukas Lewark, Christian Urech

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

JavaScript has been disabled in your browser