From kaul at iit.edu Mon May 5 16:43:45 2008 From: kaul at iit.edu (Hemanshu Kaul) Date: Mon, 05 May 2008 16:43:45 -0500 Subject: [Discrete-math-seminar] IIT Discrete Math Seminar: Wednesday 4pm In-Reply-To: References: Message-ID: Hello all, The last talk of this semester, in fact this academic year, will be given by Marcus Schaefer from Depaul University. He will talk about construction of intersecting simple curves on the torus that do not spiral or fold, using train tracks and word equations. The talk will be in our usual location - room 245, E1 building, at 4pm on Wednesday. The abstract is given below and is also available at http://www.iit.edu/csl/am/colloquia/abstracts/Schaefer_Marcus.shtml . I would like to take this opportunity to thank all of you for your support - as speakers or as attendees - for this seminar series. We will be back in Fall semester with more talks. Have a relaxing and productive summer break. Hemanshu Hemanshu Kaul Assistant Professor of Applied Mathematics Illinois Institute of Technology, Chicago http://www.math.iit.edu/~kaul/ ---------------------------------------------------------------- Marcus Schaefer, DePaul University Wednesday, 7 May, 2008 E1 245 4:00 pm We show that for every n there are two simple curves on the torus intersecting at least n times without the two curves folding or spiraling with respect to each other. On the other hand, two simple curves in the plane that intersect at least n times (without creating an empty bigon) must either form a spiral of depth d or a fold of width cn/d, where c only depends on the number of boundary components of the plane. The construction of the two curves on the torus uses train tracks and word equations. Joint work with Eric Sedgwick and Daniel Stefankovic. ----------------------------------------------------------------