I study various structures on Calabi-Yau manifolds related to mirror symmetry from the geometric point of view. In particular, this includes homological mirror symmetry, Strominger-Yau-Zaslow conjecture and a link between these two provided by the metric collapse and its algebraization via non-archimedean geometry. Recently I have a strong inlcination towards tropical geometry and, in particular, its application to Hodge theory.
Diploma | Moscow Institute of Physics and Technology | 1994 | |
Ph.D. | University of Pennsylvania (Thesis advisor: Ron Donagi ) | 2000 |
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Last modified: 08/20/15