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Universität Augsburg
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Universität Augsburg
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Herr Alexander Hilpert
Universität Augsburg
spricht am
Donnerstag, 1. Februar 2024
um
12:30 Uhr
im
Raum 3008 (L1)
über das Thema:
| Abstract: |
| Compact hyperkähler manifolds are a special kind of kähler manifolds. They appear as part of Bergers classification of simply connected, irreducible, nonsymmetric riemannian manifolds and as part of the decomposition theorem of compact kähler manifolds whose first chern class vanishes. Still, only few compact examples are known today. To work towards a classification of compact hyperkähler manifolds one wants to understand their cohomology. The Riemann-Roch polynomial is a deformation invariant of hyperkähler manifolds with cohomological information. It is obtained by combining the Hirzebruch-Riemann-Roch theorem together with the Beauville-Bogomolov-Fujiki form. Jiang studies the Riemann-Roch polynomial in his paper [Jia23] via a new Lefschetz type decomposition of td^1/2, the square root of the Todd genus. He uses Rozanksy Witten theory and combinatorial tools to show that all coefficients of the Riemann-Roch polynomial are positive. In my thesis I focused on the combinatorial tools Jiang uses. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Marc Nieper-Wißkirchen |