Title:  Handling Knottiness

Time:  friday,  7:30 pM - 8:30 PM

Abstract: The floppiness of knots makes them hard to study mathematically. For instance, the nicest picture of a knot may not be the best way to witness its topological properties. Knot theorists address the challenge by imposing additional structures on knots. One especially useful type of structure arises from handle decompositions. In this talk, I'll look at some of the ways we can use handles to handle knots, with the particular goal of better understanding  how different sorts of knot invariants (quantities or algebraic structures) behave when we add knots together. Using handle decompositions involves an intricate interplay of one, two, and three-dimensional spaces. Along the way, I'll reflect on how my experience of working in this area has given me a broader understanding of ``applications of mathematics'' and new ways to articulate the value of a mathematical education.

Bio:  Scott Taylor is a professor of mathematics at Colby College in Waterville, Maine working in low-dimensional topology. He is the author or co-author of 26 research papers and several expository articles. His textbook for intro to-proofs courses Introduction to Mathematics: Number, Space, and Structure is published by the American Mathematical  Society. He is active in mathematics outreach and is the producer for Sum Camp, a summer day camp for public  elementary school students that uses music, art, theatre and math games to build number sense.