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Wahlfächer | Analysis, Algebra und Zahlentheorie, Geometrie, mathematische Physik |
Dozenten | Giovanni Felder, Chenchang Zhu, Carlo A. Rossi |
Ort | HG D3.1 |
Zeit | Di 10.15-12.00 |
Beginnt am | Di 4. April 2006 |
Vorbesprechung | Di 4. April 2006, 10.15, Hermann Weyl-Zimmer HG G43 |
Kontakt | Chenchang Zhu |
Voraussetzungen | Differenzialgeometrie |
Beschreibung |
The notion of generalized geometry was introduced by N. Hitchin to give a geometrical setting for certain computations in string theory. The basic idea is to replace the tangent bundle T by the direct sum T+T* of the tangent bundle and the cotangent bundle. Generalized complex structures interpolate between symplectic and complex structures. They are endomorphisms of T+T* squaring to -1 and obeying an integrability condition. In this seminar we first discuss basic notions of symplectic, complex and Kaehler differential geometry and then turn to generalized complex geometry. Application to complex geometry and possibly physics will also be presented. |
Literatur |
Lectures on Symplectic Geometry by Ana Cannas Da Silva, Principles of Algebraic Geometry by Griffiths and Harris (Chapter 0), New proof for the existence of locally complete families of complex structures, by M. Kuranishi appeared in Proc. Conf. Complex Analysis (Minneapolis, 1964), pages 142–154 Generalized Complex Geometry, by Marco Gualtieri, available online at http://arxiv.org/PS_cache/math/pdf/0401/0401221.pdf |
Weitere Informationen | Syllabus and Lecture Notes |
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