This is the webpage of the seminar of the Research Cluster in Geometry at the Mathematics Department of the University of Luxembourg.

Meetings

The seminar usually takes place on Monday, 4-5pm in Room S-6A (MNO)

Next seminar

• October 21st, 2019 -- Room S6A
Christian El Emam (Università di Pavia), "On immersions of surfaces into $PSL(2, \mathbb C)$ and on a tool for constructing holomorphic maps into its character variety."
Abstract: We will discuss immersions of surfaces into $PSL(2, \mathbb C)$ equipped with its complex killing form: in a sense, the formalism provided by the study of such immersions is able to unify the theories about immersions of surfaces into $\mathbb H^3$, $AdS^3$, $\mathbb S^3$ and $dS^3$. We will also show that a holomorphic variation of the immersion data into $PSL(2, \mathbb C)$ provides a holomorphic variation of the holonomy. Time permitting, we will provide an example of this result concerning landslide flow and smooth grafting. This is joint work with Francesco Bonsante.

Upcoming sessions

• November 4th, 2019 -- Room S6A
Wai Yeung Lam (Internal seminar), "TBA"

• November 11th, 2019 -- Room S6A
Sourav Ghosh (Internal seminar), "TBA"

• November 25th, 2019 -- Room S6A
Javier Aramayona (Instituto de Ciencias Matemáticas), "TBA"

Previous seminars

• October 14th, 2019 -- Room S6A
Martin Leguil (Université Paris-Sud), "Spectral determination of open dispersing billiards"
Abstract: In an ongoing project with P. Bálint, J. De Simoi and V. Kaloshin, we have been studying the inverse problem for a class of open dispersing billiards obtained by removing from the plane a finite number of smooth strictly convex scatterers satisfying a non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift of finite type that provides a natural labeling of all periodic orbits. We show that the Marked Length Spectrum determines the curvatures of the scatterers at the base points of 2-periodic orbits, and the Lyapunov exponents of each periodic orbit. Besides, we show that it is generically possible, in the analytic category and for billiard tables with two (partial) axial symmetries, to determine completely the geometry of those billiards from the purely dynamical data encoded in their Marked Length Spectrum.
• September 30th, 2019 -- Room S6A
Funda Gültepe (University of Toledo), "Space filling curves, Cannon-Thurston maps and boundaries of curve complexes"
Abstract: Given a hyperbolic 3-manifold which fibers over the circle with hyperbolic surface fiber, the inclusion map between the fiber and the manifold can be extended continuously to a map, resulting in a space-filling Peano curve. Such continuous extension of a map, in particular extension to a map between corresponding boundaries is called a 'Cannon-Thurston map' . In this talk we will discuss existence of Cannon-Thurston maps in different settings. In particular, we will explain how to construct a Cannon-Thurston map for the boundary of 'surviving' curve complex of a surface with punctures. Joint work with Christopher Leininger.
• September 23rd, 2019 -- Room S6A
Nariya Kawazumi (University of Tokyo), "Gate double derivatives"
Abstract: Recently Turaev introduced the notion of a gate derivative on the group ring of the fundamental group of an oriented surface. Its double version gives a topological interpretation of a double divergence, which connects the homotopy intersection form and the Turaev cobracket. We will explain the definition of a gate double derivative and some of its properties including a topological proof of the formula connecting the double divergence and the Turaev cobracket. This is a joint work with Anton Alekseev, Yusuke Kuno and Florian Naef.
• September 16th, 2019 -- Room S6A
Tian Yang (Texas A&M University), "Recent progress on the volume conjecture for the Turaev-Viro invariants"
Abstract: In 2015, Qingtao Chen and I conjectured that at the root of unity $\exp(2\pi \sqrt{-1}/r)$ instead of the usually considered root $\exp(\pi \sqrt{-1}/r)$, the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic 3-manifold grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold. In this talk, I will recall known results about this conjecture and present a recent joint work with Giulio Belletti, Renaud Detcherry and Effie Kalfagianni on an infinite family of cusped hyperbolic 3-manifolds, the fundamental shadow links complement, for which the conjecture is true.
• September 9th, 2019 -- Room S6A
Masashi Yasumoto (Osaka City University), "Discrete Weierstrass-type representations"
Abstract: In this talk we consider discrete surfaces with Weierstrass-type representations. In the smooth case, these representations for surfaces are powerful tools for constructing surfaces and analyzing their global behaviors. By the same reason, Weierstrass-type representations for discrete surfaces are important both for investigating the theory itself and for expanding our knowledge of global behaviors. We introduce how to derive the formulae in terms of transformation theory for discrete Omega surfaces, and introduce how these are related to a discrete version of holomorphic functions. This talk is partly based on joint work with Mason Pember and Denis Polly (TU Wien).