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Mathematics of Knots, Braids, Links, and Tangles
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.