We meet Thursdays at 2:50–3:50 pm in WH-100E followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jonathan Williams.
Some seminar speakers will also give a colloquium talk at 4:30 pm on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.
Abstract: There are two basic questions in contact topology: Which manifolds admit tight contact structures, and on those that do, can we classify tight contact structures? There have been a lot of studies for many prime manifolds, especially for Seifert fibrations and toroidal manifolds. In this talk, we present such a classification on an infinite family of hyperbolic 3-manifolds. This is a joint work with James Conway.
Abstract: While producing subgroups of a group by specifying generators is easy, understanding the structure of such a subgroup is notoriously difficult problem. In the case of hyperbolic groups, Gitik utilized a local to global property for geodesics to produce an elegant condition which ensures a subgroup generated by two elements (or more generally generated by two subgroups) will split as an amalgamated free product over the intersection of the generators. We show that a large class of groups demonstrate a similar local to global property from which an analogy of Gitik's result can be obtained. This allows for a generalization of Gitik's theorem in many important classes of groups including CAT(0) groups, the mapping class groups of a surface, and 3-manifold groups. Joint work with Davide Spriano and Hung C. Tran.