Meetings
The seminar usually takes place on Monday, 45pm in Room S6A (MNO)
Organizers
Next seminar

December 9th, 2019  Room S6AJohn Parker (Durham University), "Nonarithmetic lattices"Abstract: A lattice in a semisimple Lie group is a discrete subgroup with finite covolume. An arithmetic group is a subgroup of a linear algebraic group corresponding to integral points. By fundamental work of Borel and HarishChandra, all arithmetic groups are lattices. By work of Margulis, Corlette, Gromov and Schoen any lattice that is not arithmetic is (up to commensurability) contained in SO(n,1) or SU(n,1). Gromov and PiatetskiShapiro constructed examples of nonarithmetic lattices in SO(n,1) for all n at least 2. In this talk I will survey what is known about SU(n,1): There are many lattices in SU(1,1); nothing is known about SU(n,1) for n at least 4; a few examples are known for n=2 and n=3. These examples may be described from several rather different points of view.
Upcoming sessions

December 16th, 2019  Room S6AHongming Nie (Hebrew University of Jerusalem), "TBA"

December 18th, 2019  Room S6AIndira Chatterji (Université de Nice), "TBA"
Previous seminars

November 27th, 2019  Room S6A
CAUTION: Seminar on Wednesday at 2pmAndrés Sambarino (Sorbonne Université, IMJPRG), "Pressure forms on pure imaginary directions"Abstract: Anosov groups are a class of discrete subgroups of semisimple algebraic groups analogue to what is known as convexcocompact groups in negative curvature. Thermodynamical constructions equip the (regular points of the) moduli space of Anosov representations from $\Gamma$ to $G$ with natural positive semidefinite bilinear forms, known as pressure forms. Determining whether such a pressure form is Riemannian requires nontrivial work. The purpose of the lecture is to explain some geometrical meaning of these forms, via a higher rank version of a celebrated result for quasiFuchsian space by BridgemanTaylor and McMullen on the Hessian of Hausdorff dimension on pure bending directions. This is work in collaboration with M. Bridgeman, B. Pozzetti and A. Wienhard. 
November 25th, 2019  Room S6AJavier Aramayona (Instituto de Ciencias Matemáticas), "The first cohomology group of pure mapping class groups"Abstract: We will start by recalling the proof of a classical result of Powell, which asserts that mapping class groups of finitetype surfaces of genus at least three have trivial abelianization. In stark contrast, we will show that this is no longer the case if the surface is allowed to have infinite type; more concretely, we will explain how to construct nontrivial integervalued homomorphisms from mapping class groups of infinitegenus surfaces. Further, we will give a description the first integral cohomology group of pure mapping class groups in terms of the first homology of the underlying surface. This is joint work with Priyam Patel and Nick Vlamis.

November 18th, 2019  Room S6AWai Yeung Lam (Internal seminar), "Holomorphic quadratic differentials on graphs"Abstract: In the classical theory, holomorphic quadratic differentials are tied to a wide range of objects, e.g. harmonic functions, minimal surfaces and Teichmüller space. We present a discretization of holomorphic quadratic differentials that preserves such a rich theory. We introduce discrete holomorphic quadratic differentials and discuss their connections to the surface theory and Teichmüller theory. On one hand, holomorphic quadratic differentials are related to discrete minimal surfaces via a Weierstrass representation. On the other hand, they arise from deformations of circle packings on surfaces with complex projective structures.

November 11th, 2019  Room S6AVincent Pecastaing (Internal seminar), "Actions of higherrank lattices on conformal and projective structures"Abstract: The main idea of Zimmer's program is that in realrank at least 2, the rigidity of lattices of semisimple Lie groups makes that their actions on closed manifolds are understandable. After a short survey giving a more precise idea of Zimmer's conjectures and their context, I will give recent results about conformal and projective actions of cocompact lattices. The fact that these geometric structures do not carry a natural invariant volume is a major motivation. We will see that the realrank is bounded above like when the ambient Lie group is acting, and that at the critical value, the manifold is globally isomorphic to a model homogeneous space. The proofs rely in part on an "invariance principle" recently introduced by Brown, RodriguezHertz and Wang, which guarantees the existence of finite invariant measures in some dynamical context.

November 4th, 2019  Room S6ASourav Ghosh (Internal seminar), "Affine Anosov representations"Abstract: In this talk I will define affine Anosov representations and explain their relation to proper affine actions of a word hyperbolic group. Moreover, I will also explain how affine Anosov representations capture infinitesimal versions of certain special Anosov representations.

October 21st, 2019  Room S6AChristian 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.

October 14th, 2019  Room S6AMartin Leguil (Université ParisSud), "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 noneclipse condition. The restriction of the dynamics to the set of nonescaping 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 2periodic 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 S6AFunda Gültepe (University of Toledo), "Space filling curves, CannonThurston maps and boundaries of curve complexes"Abstract: Given a hyperbolic 3manifold 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 spacefilling Peano curve. Such continuous extension of a map, in particular extension to a map between corresponding boundaries is called a 'CannonThurston map' . In this talk we will discuss existence of CannonThurston maps in different settings. In particular, we will explain how to construct a CannonThurston map for the boundary of 'surviving' curve complex of a surface with punctures. Joint work with Christopher Leininger.

September 23rd, 2019  Room S6ANariya 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 S6ATian Yang (Texas A&M University), "Recent progress on the volume conjecture for the TuraevViro 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 TuraevViro and the ReshetikhinTuraev invariants of a hyperbolic 3manifold 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 3manifolds, the fundamental shadow links complement, for which the conjecture is true.

September 9th, 2019  Room S6AMasashi Yasumoto (Osaka City University), "Discrete Weierstrasstype representations"Abstract: In this talk we consider discrete surfaces with Weierstrasstype representations. In the smooth case, these representations for surfaces are powerful tools for constructing surfaces and analyzing their global behaviors. By the same reason, Weierstrasstype 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).