Geometry of integrable hierarchies and their dispersionless limits
| dc.contributor.advisor | Ben-Zvi, David, 1974- | |
| dc.creator | Safronov, Pavel | en |
| dc.date.accessioned | 2014-06-25T16:21:22Z | en |
| dc.date.accessioned | 2017-05-11T23:10:34Z | |
| dc.date.available | 2017-05-11T23:10:34Z | |
| dc.date.issued | 2014-05 | en |
| dc.date.submitted | May 2014 | en |
| dc.date.updated | 2014-06-25T16:21:22Z | en |
| dc.description | text | en |
| dc.description.abstract | This thesis describes a geometric approach to integrable systems. In the first part we describe the geometry of Drinfeld--Sokolov integrable hierarchies including the corresponding tau-functions. Motivated by a relation between Drinfeld--Sokolov hierarchies and certain physical partition functions, we define a dispersionless limit of Drinfeld--Sokolov systems. We introduce a class of solutions which we call string solutions and prove that the tau-functions of string solutions satisfy Virasoro constraints generalizing those familiar from two-dimensional quantum gravity. In the second part we explain how procedures of Hamiltonian and quasi-Hamiltonian reductions in symplectic geometry arise naturally in the context of shifted symplectic structures. All constructions that appear in quasi-Hamiltonian reduction have a natural interpretation in terms of the classical Chern-Simons theory that we explain. As an application, we construct a prequantization of character stacks purely locally. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2152/24818 | en |
| dc.language.iso | en | en |
| dc.subject | Algebraic geometry | en |
| dc.subject | Integrable systems | en |
| dc.subject | Derived geometry | en |
| dc.subject | Topological field theories | en |
| dc.title | Geometry of integrable hierarchies and their dispersionless limits | en |
| dc.type | Thesis | en |