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

主要研究了Calabi-Yau流形与导范畴之间的关系。特别是，我们研究了如何通过定义稳定性条件等方法从复流形的导出范畴中恢复复流形，以及在复辛流形的导出范畴之间的等价性上应该期待什么。我于9月19日至23日代表日本数学学会秋季年会访问了冈山大学，并与代数几何的研究人员进行了信息交流。微分几何和数学物理。10月24日至28日，在城崎会议上，主要从代数几何的观点进行了信息交流。11月21日至25日，在北海道大学与松下大辅教授就该研究课题组织了国际研讨会。2月16日至17日，举行了相关课题最新进展的会议。在计算学习方面，我与京都大学的山本昭夫教授和首都大学的德永博雄教授一起，在牛顿图的研究上，去年获得了日本人工智能学会的奖项。我们继续研究诺特环，我买了相关的杂志。

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.