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Josh Sabloff, assistant professor of mathematics at Haverford College, will speak on “Invariants of Legendrian Knots” 4:10-5 p.m. Tuesday in Pardee Hall room 217 for the Lafayette/Lehigh Geometry and Topology Seminar.
Sabloff is teaching Differential Geometry and Advanced Calculus courses at Haverford this semester. He earned a Ph.D. at Stanford, a Certificate of Advanced Studies with Distinction from Cambridge, and an A.B. summa cum laude from Harvard.
“The art of good teaching is complex: It is a nontrivial task to position concepts relative to procedures and coherently entwine them using appropriate pedagogical techniques,” he says. “I want my students to gain a conceptual understanding of the mathematics I teach and to grasp the interaction between concept and computation; I want them to improve their problem-solving skills; and I want them to be able to express their understanding clearly. I endeavor to help my students achieve these goals through the practice of questioning.”
His summary of the talk: “I will introduce a special type of 2-plane field on R3 called the standard contact structure. A Legendrian knot is a closed curve that is everywhere tangent to the contact structure. Similarly to topological knot theory, a fundamental problem in Legendrian knot theory is to determine when it is possible — or impossible — to deform one Legendrian knot into another through Legendrian knots. I will introduce two ‘classical’ invariants of Legendrian knots, and then show, using some newer, ‘non-classical’ invariants, that the classical invariants do not tell the whole story.