For the time being, the seminar this semester will continue meeting online using Zoom. The Zoom doors will open 10 minutes before the seminar at 9:50am (EST) for chatter and self provided coffee, tea, beer, wine, cocktail, aperitif, digestif, cheese, and snacks depending on your time zone and predilection. If you would like to be put on the email list contact Ara Basmajian (abasmajian@gc.cuny.edu). The zoom link for the upcoming seminar will be included in the weekly mailing to the email list.
Tuesdays 10am–11am (Talks are 50 minutes long). ***Note the new time. This change is for Fall 2022 only.
Ara Basmajian (CUNY, Graduate Center and Hunter College)
Email: abasmajian@gc.cuny.edu
Dragomir Saric (CUNY, Graduate Center and Queens College)
Email: dragomir.saric@qc.cuny.edu
Nick Vlamis (CUNY, Graduate Center and Queens College)
Email: nvlamis@gc.cuny.edu
Title: Bi-Lipschitz and quasiconformal classification of certain spirals
Abstract: Classifying sets up to bi-Lipschitz and quasiconformal maps has been a long-standing effort with applications to many different areas. This talk will focus on said classification of polynomial spirals of the form $S_a:= \{ x^{-a} e^{ix} : x\in (1, \infty ) \}$, $a>0$, using the geometric information encoded within certain types of dimensions. At the start of the talk, the notions of box and Assouad dimension and spectra will be introduced. Furthermore, the distortion under quasiconformal maps of the box dimension (by Kaufman) and Assouad spectra (by C-G, Tyson) will be discussed. In conclusion, it will be shown how these results, along with the formulas for the spirals' dimensions (by Fraser), can be combined to completely classify these spirals up to bi-Lipischitz and quasiconformal equivalence.
Title: Topological stability of hyperbolic group actions on their boundaries
Abstract: Any word-hyperbolic group acts by homeomorphisms on its boundary at infinity, and the dynamics of the action often encode detailed geometric information about the group. Classical work of Sullivan shows that any small Lipschitz perturbation of this action is conjugate to the standard action. In this talk, we discuss joint work with Kathryn Mann and Jason Manning which shows that any small perturbation of the boundary action is semi-conjugate to the standard action.
Title: Geometry of some infinite-type hyperbolic 3-manifolds
Abstract: In this talk I will give some purely topological construction for hyperbolic 3-manifolds with infinitely generated fundamental group, this will let us construct many infinite-type hyperbolic 3-manifolds. Then, I will say something about the set of hyperbolic structures that they can admit.
Title: Trinity of geodesic currents
Abstract: Geodesic currents are a suitable closure of the space of curves on a hyperbolic surface introduced by Bonahon in 1986. Notions such as the geometric intersection number of curves extend to geodesic currents. In this talk, I will discuss two equivalent viewpoints on geodesic currents: dual curve functionals and dual spaces. On the one hand, a geodesic current induces a functional on the space of curves on the surface via intersection number with the current. We say that such a curve functional is ``dual to the current''. In this talk, we will give sufficient and necessary conditions for curve functionals to be dual to geodesic currents. On the other hand, a geodesic current induces a Gromov hyperbolic space, that we call the ``dual space of the current''. In the talk, I will describe such spaces. The first part is joint work with Dylan Thurston and the second, with Luca De Rosa.