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My current research includes
(1) Kahler geometry, extremal Kahler metrics, Kahler-Einstein metrics
(2) the geometry and moduli spaces of K3 and Enriques surfaces, and various lattice-theoretical problems arising from their middle dimensional cohomology.
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Publications
- Einstein-Hermitian 4-Manifolds of Positive Bisectional Curvature, co-author: Mustafa Kalafat, submitted, DG/1206.3941
- Einstein Hermitian Metrics of Positive Sectional Curvature, to appear in Proc. Am. Math. Soc. DG/1112.4181
- Extremal Kaehler Metrics and Bach-Merkulov Equations, submitted, DG/1112.4177
- Irreducible Heegner divisors in the period space of Enriques surfaces, co-author: Sinan Sertöz, Int. J. Math., Vol.19, No.2, 2008. AG/0509687
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PhD Thesis
On Conformal Geometry of Kahler Surfaces, advisor: Claude LeBrun, Stony Brook University, Department of Mathematics, 2012. |
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Master's Thesis
Orbits in the anti-invariant sublattice of the K3-lattice, supervisor: Sinan Sertöz, Bilkent University, Department of Mathematics, Ankara/Turkey, 2005. The text is available at Bilkent Univesity Thesis Database, #0002870. |
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Some of my expository notes:
- Notes on Morrison's paper "On K3 surfaces with large Picard number", 2005. [pdf]
Content: This is a shorth review note on David Morrison's paper "On K3 Surfaces with large Picard number", Invent. Math. 35, 105-121, 1984. A couple of new results and applications are also given in the exposition.
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