This book is a collection of expository articles based on four lecture series presented during the 2012 Notre Dame Summer School in Topology and Field Theories. The four topics covered in this volume are: Construction of a local conformal field theory associated to a compact Lie group, a level and a Frobenius object in the corresponding fusion category; Field theory interpretation of certain polynomial invariants associated to knots and links; Homotopy theoretic construction of far-reaching generalizations of the topological field theories that Dijkgraf and Witten associated to finite groups; and a discussion of the action of the orthogonal group \(O(n)\) on the full subcategory of an \(n\)-category consisting of the fully dualizable objects. The expository style of the articles enables non-experts to understand the basic ideas of this wide range of important topics. Readership Graduate students and research mathematicians interested in field theories from an algebraic topology and higher category perspective. |