Categorification In Geometry Topology And Physics
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Categorification in Geometry, Topology, and Physics
Author: Anna Beliakova
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-02-21
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.
Categorification in Geometry, Topology, and Physics
9.1. Uncolored trefoil-prime -- 9.2. Colored/iterated examples -- 9.3. Generalized twisting -- 9.4. Some examples -- 9.5. Toward the Skein -- Appendix A. Links and splice diagrams -- A.1. Links, cables and splices -- A.2. Splice diagrams -- A.3. Operations on links -- A.4. Equivalent diagrams -- A.5. Connection with DAHA -- References -- Back Cover
Higher Genus Curves in Mathematical Physics and Arithmetic Geometry
Author: Andreas Malmendier
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-04-03
This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington. Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics. The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic 3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.