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123,50 ۥ Geometry and categorification12
• A geometric realization of modified quantum algebras34
• The cube and the Burnside category74
• Junctions of surface operators and categorification of quantum groups98
• Khovanov-Rozansky homology and 2-braid groups158
• DAHA approach to iterated torus links170
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.
Authors
• Anna Beliakova: Universität Zürich, Zürich, Switzerland,
• Aaron D. Lauda: University of Southern California, Los Angeles, CA
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