# 2014 Lafayette-Lehigh Geometry-Topology Seminar

The Lafayette-Lehigh Geometry-Topology Seminar will be held Saturday March 15, 2014 at Lafayette College. The Mathematics Department is located in Pardee Hall (building # 37 on the Campus Map). The Directions on the Lafayette Website direct you to the Visitor Parking Deck behind Markle Hall. You may be able to park near Pardee Hall—there are spots adjacent to the building, between Pardee and Watson Courts. Please refer to the the Campus Map.

The talks will be held in Pardee Hall 217. We will gather for coffee and bagels, etc., around 10:00 AM, across the hall in Pardee 218 (the Saalfrank Common Room). We will also have a light lunch there between the morning and afternoon talks.

** Schedule **

10:30-11:30: **Christine Breiner ** (Fordam University)

** Gluing constructions for constant mean curvature (hyper)surfaces **

* Abstract *: Constant mean curvature (CMC) surfaces are critical points of the area functional subject to an enclosed volume constraint. Classic examples include the round sphere, the cylinder, and a family of rotationally symmetric solutions discovered by Delaunay. More than 150 years later, Kapouleas determined a generalized gluing construction that produced infinitely many new examples of CMC surfaces. Building on and refining this work, we produce infinitely many new embedded CMC surfaces and hypersurfaces. In this talk I will outline the main steps of the gluing construction and explain some of the main difficulties involved in solving such a problem. This work is joint with N. Kapouleas.

11:45-12:45: **Christina Tønessen-Friedman ** (Union College)

** Sasaki join and admissible Kähler constructions **

*Abstract*: This talk is based on joint work in progress with Charles Boyer. Combining the Sasaki join construction for quasi-regular contact structures with the transverse admissible Kähler constructions (formalized by the joint work with Vestislav Apostolov, David Calderbank, and Paul Gauduchon) we have obtained irregular as well as quasi-regular constant scalar curvature (CSC) Sasaki metrics on a large family of manifolds in all dimensions. More specifically, I will show that for the join of a weighted 3-sphere with a regular CSC Sasaki manifold there exists a Reeb vector field in the Sasaki cone such that (up to isotopy) the corresponding ray of Sasakian structures has CSC.

1:00-2:00: Lunch Break: **Light lunch ** in Pardee 218.

2:00-3:00: **Jason Behrstock ** (CUNY-Lehman)

*Title: Geometry of right-angled Coxeter groups *

*Abstract*: In a metric space the divergence of a pair of rays is a way to measure how quickly they separate from each other. We will survey some of what is known about divergence, including the recent resolution of a question raised by Gromov and Gersten asking what divergence rates are possible in the presence of non-positive curvature. We will also consider the class of Coxeter groups and discuss what rates of divergence they can admit and some other interesting aspects of their geometry which was inspired by this question.

The seminar is co-sponsored by Lafayette College, Lehigh University, and LVAIC , the Lehigh Valley Association of Independent Colleges.

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