Sponsored by Elizabethtown College, Franklin and Marshall College, Lebanon Valley College, and Millersville University
14 September: Linda Chen, Swarthmore College 5 October: Edgar A. Bering, Temple University 2 November: Irina Bobkova, IAS Princeton 1 February: Vince Coll, Lehigh University 1 March: Zhigang Han, Millersville University 5 April: Ping Xu, Pennsylvania State UniversityTGTS is a regional mathematics seminar/colloquium. We meet at 4:30 p.m. on the first Friday of each month during the academic year (with some exceptions, as noted in the schedule above). The public is cordially invited to attend.
Date: 5 October 2018 Location: Hempfield High School, Room 213 Speaker: Edgar A. Bering, Temple University Title: Uniform twisting in mapping class groups and outer automorphisms of free groups Abstract: There is a long running analogy between the mapping class group of a surface and the outer automorphism group of a free group. In both settings there is a notion of Dehn twist. It is well-known that in a mapping class group, two Dehn multi-twists about intersecting curve systems have powers that generate a free group. A recent line of work in this area is focused on quantitative theorems. Hamidi-Tehrani showed that fourth powers suffice to guarantee a free group; Leininger and Margalit conjecture that taking squares should suffice. In this talk I will present Hamidi-Tehrani's result, and then my analogous theorem for Dehn twists of a free group. The situation for free groups is complicated by a lack of geometry; this is compensated for with combinatorics. To prevent the talk from being overly technical, all of the results will be presented only in the case of simple twists, though they hold in greater generality.