Research on T-duality of Calabi-Yau manifolds of dimension less than or equal to four

点击翻译按钮获取中文摘要

I have studied mainly on the relationship between Calabi-Yau manifolds and derived categories. In particular, we studied how one can recover a complex manifold from its derived category e.g. by defining stability condition, and what should be expected on the equivalence among derived categories of complex symplectic manifolds.I visited Okayama University on behalf of the annual autumn meeting of the Mathematical Society of Japan from September 19 to 23 and made exchanges of information to researchers of algebraic geometry, differential geometry and mathematical physics. I exchanged information at Kinosaki conference hail from October 24 to 28, mainly from the viewpoint of algebraic geometry.I organized an international workshop with Professor Daisuke Matsushita at Hokkaido University from November 21 to 25 on the research subject.There was a meeting on recent development of relating subjects on February 16 and 17. I have sent my graduate students to collect information on behalf of me and had a report from them.In relation to computational learning, I received a prize from The Japanese Society for Artificial Intelligence for the study on Newton diagrams with Professor Akio Yamamoto in Kyoto University and Professor Hiro-o Tokunaga in Tokyo Metropolitan University last year. We continued a study on noetherian rings.I bought relating magazines.