Power operations and central maps in representation theory
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2018
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| Online Access: | http://hdl.handle.net/1721.1/117873 |
| _version_ | 1826196531701612544 |
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| author | Lonergan, Gus (Gus C.) |
| author2 | Roman Bezrukavnikov. |
| author_facet | Roman Bezrukavnikov. Lonergan, Gus (Gus C.) |
| author_sort | Lonergan, Gus (Gus C.) |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. |
| first_indexed | 2024-09-23T10:28:49Z |
| format | Thesis |
| id | mit-1721.1/117873 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:28:49Z |
| publishDate | 2018 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1178732019-04-11T05:19:59Z Power operations and central maps in representation theory Lonergan, Gus (Gus C.) Roman Bezrukavnikov. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 153-155). The theme of this thesis is the novel application of techniques of algebraic topology (specifically, Steenrod's operations and Smith's localization theory) to representation theory (especially in the context of the geometric Satake equivalence). In Chapter 2, we use Steenrod's construction to prove that the quantum Coulomb branch is a Frobenius-constant quantization. We also demonstrate the corresponding result for the K-theoretic version of the quantum Coulomb branch. In Chapter 3, we develop the theory of parity sheaves with coefficients in the Tate spectrum, and use it to give a geometric construction of the Frobenius-contraction functor. In Chapter 4, we discuss some related results, including a geometric construction of the Frobenius twist functor, and also discuss future directions of research. The content of Chapter 3 is joint work with S. Leslie. by Gus Lonergan. Ph. D. 2018-09-17T15:48:01Z 2018-09-17T15:48:01Z 2018 2018 Thesis http://hdl.handle.net/1721.1/117873 1051190363 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 155 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Lonergan, Gus (Gus C.) Power operations and central maps in representation theory |
| title | Power operations and central maps in representation theory |
| title_full | Power operations and central maps in representation theory |
| title_fullStr | Power operations and central maps in representation theory |
| title_full_unstemmed | Power operations and central maps in representation theory |
| title_short | Power operations and central maps in representation theory |
| title_sort | power operations and central maps in representation theory |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/117873 |
| work_keys_str_mv | AT lonergangusgusc poweroperationsandcentralmapsinrepresentationtheory |