This class gives an overview of both classical and modern results in Knot theory: the Kauffman bracket and the Jones polynomial; the Alexander polynomial; Khovanov homology; Seifert surfaces; examples...
Topics include the Whitney trick and its failure in 4 dimensions; its analogues in 3-dimensions: the Dehn lemma and the loop theorem; Milnor's invariants for classical links; various special 2...
The main goal of the class is to give an introduction to geometric and quantum topology in low (2, 3, 4) dimensions. Specific topics that will be discussed include the (colored) Jones polynomial of...
Topics include: manifolds, the Gauss map, parallel transport, curvature of curves and surfaces, the first and second fundamental forms, surface area and volume, geodesics, the exponential map, the...
Topics covered in this class include analytic functions, complex integration, Cauchy formulas, power series, residue theory, conformal mappings, and Laplace transforms.