网站首页  |  实验室概况  |  研究团队  |  新闻中心  |  学术交流  |  学术报告  |  实验室年报  |  联系我们

 
 
  当前位置:首页 -> 学术报告
吴文俊数学重点实验室数学物理系列报告【孙凯文】
题目:Quantum Curves, Toric Calabi-Yau and Non-perturbative Topological String
 
报告人:孙凯文 中国科学技术大学
 
时间:7月14日 周四 下午3:00-4:00
 
地点:管研楼1418
 
摘要: We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Marino conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and enumerative geometry, another quantization scheme was proposed by Grassi-Hatsuda-Marino, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. We also find a set of novel identities among the topological string amplitudes which guarantee the equivalence.
中国科学院吴文俊数学重点实验室