TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, and Millersville University

Speakers 2018-19

  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 University
TGTS 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.

Next Talk

    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.

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