2011 Fiscal Year Final Research Report
Mirror symmetry and brane tiling
| Project/Area Number |
20740037
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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 | Osaka University |
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Principal Investigator |
UEDA Kazushi 大阪大学, 大学院・理学研究科, 准教授 (60432465)
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| Project Period (FY) |
2008 – 2011
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| Keywords | ミラー対称性 |
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| Research Abstract |
With any two-dimensional toric weak Fano stack, we could associate a combinatorial object called a brane tiling, which allows us to describe the derived category of coherent sheaves on this stack in terms of representations of quivers. We have also proved homological mirror conjecture for a basic class of singularities called Brieskorn-Pham singularities. In a slightly different direction, we have computed the potential function for the torus fiber of the Gelfand-Cetlin system on flag varieties of type A.
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