2010 Fiscal Year Final Research Report
Quantum Topology of Fano Varieties
| Project/Area Number |
21840017
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
GALKIN Sergey The University of Tokyo, 数物連携宇宙研究機構, 特任研究員 (10554503)
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| Project Period (FY) |
2009 – 2010
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| Keywords | 幾何学 / トポロジー / 代数学 |
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| Research Abstract |
We had great outreach in media this year and also new exciting results : we constructed mirrors for all 105 families of smooth Fano threefolds, for 104 of these families we give a nice representation as toric complete intersection or its "unabelianization", thus we compute their genus zero Gromov-Witten invariants, and so we prove hypothesis of mirror symmetry (in what concerns differential equations) for these 104 families, we introduce a new but very fundamental notion of extremal local systems - those are acyclic and it is equivalent to minimization of some functional, we support our conjecture that all local systems associated with odd-dimensional Fano varieties via mirror symmetry are extremal by case of 104 families of smooth Fano threefolds. Our method doesn't depend on dimension and now machines in Imperial College are working out half billion four-dimensional candidates (computing the basic invariants will take approximately 2-3 more months).
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[Presentation] Apery Class2009
Author(s)
Sergey Galkin
Organizer
Workshop on HMS and Hodge theory
Place of Presentation
Universitaet Wien, Vienna, Austria
Year and Date
2009-08-12
