Sophomore Seminars

Mathematics of Knots, Braids, Links, and Tangles

MATH 87Q
Prerequisites: 
Mathematics 51.

In this seminar, students will investigate several questions involving knots, braids, and other similar objects. We will explore some interesting types of knots and learn how they can be distinguished from one another by means of numerical or polynomial invariants. All knots and links occur as boundaries of two-dimensional surfaces in space, so the seminar will include an introduction to the topology of surfaces. We will study both the geometry and algebra of braids, including their relationships to knots and links. Topics for further investigation might include applications of concepts from knot theory to biology, chemistry, and physics.

Meet the Instructor(s)

Wojciech Wieczorek

Wojciech Wieczorek received his Ph.D. at Michigan State University. He has taught at the University of Georgia, University of Wisconsin at Madison, and at Stanford since 2004. Earlier in his career, while working at University of Gdansk, he taught geometry at a high school there. His research interest is in three- and four-dimensional manifolds. Knots play a significant role in these areas.