Categorification in Geometry, Topology, and Physics
About this Title
Anna Beliakova, Universität Zürich, Zürich, Switzerland and Aaron D. Lauda, University of Southern California, Los Angeles, CA, Editors
Publication: Contemporary Mathematics
Publication Year: 2017; Volume 684
ISBNs: 978-1-4704-2821-1 (print); 978-1-4704-3691-9 (online)
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields.
This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology.
The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.
Graduate students and research mathematicians interested in categorification, link homology, and geometric representation theory.
Table of Contents
- Ben Webster – Geometry and categorification
- Yiqiang Li – A geometric realization of modified quantum algebras
- Tyler Lawson, Robert Lipshitz and Sucharit Sarkar – The cube and the Burnside category
- Sungbong Chun, Sergei Gukov and Daniel Roggenkamp – Junctions of surface operators and categorification of quantum groups
- Raphaël Rouquier – Khovanov-Rozansky homology and $2$-braid groups
- Ivan Cherednik and Ivan Danilenko – DAHA approach to iterated torus links