2013 Fiscal Year Final Research Report
Study of mirror symmetry and integrable systems via degeneration of varieties
| Project/Area Number |
22740031
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
NISHINOU TAKEO 東北大学, 理学(系)研究科(研究院), 准教授 (50420394)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 幾何学 |
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| Research Abstract |
We studied aspects of mirror symmetry, which implies deep relationship between complex geometry and symplectic geometry, the geometries whose definitions are completely different. We made use of tropical geometry, a rather new field of research in geometry. With this new idea, we were able to describe several complicated geometric constructions in a simpler, combinatorial manner, and applied these results to mirror symmetry. Moreover, we applied our method to the study of important geometric objects such as flag manifolds or moduli space of vector bundles on Riemann surfaces.
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