Starting in Spring 2023 the seminar will go back to in-person talks. We will also attempt to run the seminar as hybrid using zoom. Zoom doors will open a few minutes before the seminar 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 2:45pm–3:45pm, room 6495.
Organizers
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
September 10: Hanh Vo (Arizona State U.)
Title: Curves with self-intersections on hyperbolic surfaces
Abstract: In this talk, I will discuss curves with self-intersections on hyperbolic surfaces. In the first part, I will speak about the k-systoles (where k is a natural number) of hyperbolic surfaces, which are the shortest closed geodesics with at least k self-intersections. In the second part, I will discuss how results regarding self-intersections of closed curves can be extended to arcs. This talk is based on joint work with A. Basmajian, M. Doan, H. Parlier, and B. Xu.
September 17: Nathaniel Sagman (U. of Luxembourg)
Title: Labourie's Conjecture and high energy harmonic maps
Abstract: For S a closed surface of genus at least 2, Labourie proved that every Hitchin representation of pi_1(S) into PSL(n,R) gives rise to an equivariant minimal surface in the corresponding symmetric space, and conjectured that uniqueness holds as well (this was known for n=2,3). After giving the relevant background, we will explain how we used the theory of high energy harmonic maps to give counterexamples to Labourie’s conjecture. We will then discuss more recent work on high energy harmonic maps, and relations to Thurston's compactification of Teichmuller space. This is all joint with Peter Smillie.
September 24: Tommaso Cremaschi (Trinity College Dublin)
Title: Big and small surfaces and Nielsen-Thurston Classification
Abstract: We will give a short overview of the Nielsen-Thurston Classification problem (classifying the homeomorphism type of surfaces) on finite-type surfaces and then move to infinite-type surface mentioning what is known and pointing out some difficulties. We will then discuss how to approximate, in the compact-open topology, a general self-homeomorphism of an infinite-type surface (joint with Y.Chandran) and potential definitions of pseudo-anosov mapping classes in the infinite-type setting (joint with F.Valdez).
October 1: (No seminar)
October 8: Kasra Rafi (U. of Toronto)
Title: Lengths of saddle connections on random translation surfaces of large genus
Abstract: We prove that the distribution of the number of short saddle connections in a random translation surface of genus g in the principle stratum of abelian differentials limits to the Poisson distribution as g goes to infinity. The result is a.direct analogue of the work of Mirzakhani-Petri regarding the distribution of the number of short simple closed curves in a random hyperbolic surface of large genus. This is a joint work with Anja Randecker and Howard Masur.
October 15: (No seminar, CUNY on Monday schedule)
October 22: (No Seminar: GC Colloquium 2-3pm)
October 29: (No seminar)
November 5: Ken Bromberg (U. of Utah)
Title: Disintegrating the curve graph
Abstract: : On a surface, the curve graph, defined by Harvey, is a 1-complex whose vertices are isotopy class of simple closed curves and edges correspond to disjointness. Masur and Minsky famously proved that this graph is Gromov hyperbolic. Here we will examine a family of similar graphs, defined by Hamenstädt, where edges are determined by a complexity condition on the two curves. More precisely rather than just asking if the two curves intersect we want to measure the complexity of the intersection. When the two curves ``fill’’ the surface (every curve intersects one of the two) then complementary regions will be a collection of even sided polygons. The complexity is highest when these complementary polygons are all hexagons and quadrilaterals and in the principal curve graph there is an edge between two curves whenever the two curves intersection is not of this maximal complexity. By changing the complexity threshold we get a sequence of graphs (and maps) that interpolate between the original curve graph and the principal graph. We show that principal curve graph is a quasi-tree (a strong hyperbolicity condition) and, more generally, for any of the graphs in the sequence the pre-image of a bounded set in one graph is a quasi-tree in the graph one level up. This is joint work with Mladen Bestvina and Alex Rasmussen.
November 12: Matt Stover (Temple University)
Title: One-cusped negatively curved manifolds
Abstract: One-cusped hyperbolic 2- and 3-manifolds of finite volume are quite easy to build, thanks to the uniformization theorem and work of Thurston, respectively. A one-cusped hyperbolic 4-manifold wasn't known until work of Kolpakov and Martelli about a decade ago, and it is unknown if one-cusped hyperbolic manifolds - or more generally negatively curved locally symmetric manifolds - exist in higher dimensions. The other 4-D negatively curved locally symmetric space is complex hyperbolic 2-space, which has constant holomorphic curvature -1. Martin Deraux recently found the first one-cusped complex hyperbolic 2-manifolds using computer experiment. I will describe more recent work where Deraux and I give an explicit topological construction using finite groups acting on products of Riemann surfaces and a uniformization hammer due to Tian and Yau.
November 19: (No Seminar)
November 26: (No Seminar, Thanksgiving week)
December 3: (No Seminar: GC Colloquium)
History of the hyperbolic geometry seminar