# Trimester Seminar

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

**Organizers:** Alex Eskin, Ursula Hamenstädt, Maxim Kontsevich, Martin Möller, Jean-Christophe Yoccoz and Anton Zorich

## Tuesday, May 11

15:00 Vincent Delecroix and Samuel Lelièvre: Knowledge sharing - Demonstration of Sage, an open-source, free, collaborative computer algebra system

## Tuesday, May 18

15:00 Alex Wright: Knowledge sharing - Smillie's Theorem (translation surfaces whose orbit under SL_{2}(R) is closed are Veech surfaces)

16:30 Thierry Monteil: Knowledge sharing - Masur criterion (translation surfaces whose orbit under the geodesic flow is non-divergent have a uniquely ergodic vertical flow)

## Thursday, May 20

16:30 Anna Lenzhen: Shape of a ball in Teichmüller space

## Friday, May 21

14:00 Chris Judge: Introductory informal talk about Delaunay/Voronoi triangulation and tessellations

## Wednesday, May 26

14:00 Alex Eskin: Introductory informal talk about random walks on groups and random transformations

## Thursday, May 27

16:30 Chris Judge: Tessellations induced by quadratic differentials

## Friday, May 28

15:15 Samuel Lelievre: Knowledge sharing - Combinatorics of square-tiled surfaces and geometry of their Teichmüller curve

## Friday, June 4

14:15 Erwan Lanneau: Knowledge sharing - The Arnoux-Yoccoz surface

## Thursday, June 10

16:30 Gabriela Schmidthuesen: Veech groups of infinite staircases

## Friday, June 11

14:00 Pat Hooper: Knowledge sharing - Triangle groups as Veech groups

15:00 Alex Eskin: Semisimplicity of the Lyapunov spectrum

## Thursday, July 8

16:30 Nikita Selinger: Oberseminar Differential Geometry - On the Boundary Behaviour of Thurston's Pull-back Map

## Monday, July 12

11:00 Informal seminar on flows of SL(2,R)-type

## Tuesday, July 13

16:30 Corinna Ulcigrai: Informal seminar - IETs techniques for absence of mixing in area-preserving flows

## Thursday, July 15

11:00 Corentin Boissy: Two definitions of Rauzy Classes

16:30 Joshua Bowman: Oberseminar Differential Geometry - Singularities of non-compact translation surfaces

## Friday, July 16

14:00 Vincent Delecroix: The wind-tree model (dynamic in a billiard of infinite area)

## Tuesday, July 20

16:30 John Smillie: Compactification of strata

## Wednesday, July 21

16:30 Vincent Delecroix: Sage advertisement session (open source math software)

## Thursday, July 22

11:00 Inkang Kim: On character variety of free group representations in PSL(2,C)

Abstract: I want to discuss about geometrically infinite hyperbolic handlebodies which are primitive stable

## Tuesday, July 27

16:30 Ken'ichi Ohshika: Algebraic limits viewed through geometric limits

Abstract: We consider a sequence of quasi-Fuchsian groups G_{i}. In general, it was not easy to determine its algebraic limit even when we know it converges. We shall show how we can determine the algebraic limit from the conformal structures at infinity of G_{i}.

## Thursday, August 10

16:30 Ken'ichi Ohshika: Necessary sufficient conditions for primitive stability

Abstract: We shall give necessary sufficient conditions for Kleinian groups on the boundary of Schottky spaces to be primitive stable in the sense of Minsky.

## Thursday, August 17

16:30 Ara Basmajian: Universal Length bounds for self-intersecting closed geodesics

Abstract: We investigate the relationship, in various contexts, between a closed geodesic with self-intersection number k (for brevity, called a k-geodesic) and its length. The length of a k-geodesic on any hyperbolic surface is known to be bounded from below by a constant that goes to infinity with k. We show that the optimal constants grow like log k. Moreover, we show that for each natural number k, there exists a hyperbolic surface where the optimal constant is realized as the length of a k-geodesic. This was previously known for k=1, where the optimal constant is realized by the length of the figure eight on the thrice punctured sphere.

## Thursday, August 24

16:30 Shinpei Baba: 2π-graftings on complex projective structures

Abstract: A complex projective structure is a certain geometric structure on a surface, which is a generalization of a hyperbolic structure. A complex projective structure comes with a holonomy representation of the surface group into PSL(2,C). On the other hand, such a fixed representation may correspond to infinitely many different projective structures. We show that 2π-graftings, a certain surgery operation, generate this class of projective structures, under the assumption that the fixed representation is generic one in the character variety.