Emergence of Integrability in Gauge Theory and String Theory and Nonperturbative Effects

1)在国际上首次解析地阐明了对BDS猜想的偏离。2)建立了Fujiwara-Itoyama-Sakaguchi模型中NG费米子的低能定理。3)在Itoyama-Tokura的USp矩阵模型中，我们证明了时空点与它的像之间的自相互作用在长距离上是吸引的，在短距离上是排斥的。暗示了在这个模型中四维时空的形成。4)2d-4d连接，建立了Gaiotto-Witten型SW曲线与非Gaiotto-Witten型SW曲线的谱曲线等价性。建立了0 d-4d字典。

1) Elucidated the deviation from BDS conjecture first in the world analytically. 2) Established the low energy theorem for the NG fermion in the model of Fujiwara-Itoyama-Sakaguchi. 3) In the USp matrix model of Itoyama - Tokura, we showed that the self-interaction between a spacetime point and its image is attractive in the long distances and repulsive in the short distances. Suggests the formation of 4 dimensional spacetime in this model. 4) 2d-4d connection, equivalence established between the spectral curve of the quiver matrix model and that of SW curve of Gaiotto-Witten type. 0d-4d dictionary was established.