1.报告题目：“From the optimal singular stochastic control to the optimal stopping for regime-switching processes”

报告人：邵井海教授（天津大学应用数学中心）

报告时间：2023年10月30日（周一）上午10:10- 10:55

报告地点：数理楼235报告厅

报告摘要: We introduce a result generalizing the connection between optimal singular stochastic control problem and optimal stopping problem for regime-switching processes. Via the optimal singular stochastic control, the optimal stopping time and the continuation region are characterized. Moreover, we prove the existence of optimal singular stochastic control for a finite horizon singular control problem with the cost function containing the terminal cost. We prove it directly by the compactification method, which is based on an elaborate application of the properties of probability measures over the cadlag space. Such a problem was left open in Haussmann and Suo (SICON, 1995). In addition, our compactification method can remove the convexity condition on the coefficients used in Dufour and Miller (SICON, 2004).

简介:邵井海，天津大学应用数学中心教授，博士生导师。邵井海主要从事概率论遍历性理论、随机分析、随机微分方程方面的研究工作，在轨道空间和环空间上运输不等式、最优映射问题，以及带切换扩散过程长时间行为等问题的研究中取得了一些成果。成果发表于PTRF, SICON, JFA, SIMA, SPA等期刊。

2.报告题目：“Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schrödinger equations”

报告人：张登副教授（上海交通大学）

报告时间：2023年10月30日（周一）上午10: 55 - 11:40

报告地点：数理楼235报告厅

报告摘要：In this talk I will review some recent results on multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schrödinger equations. We will show the corresponding construction and conditional uniqueness results, which provide new examples for the mass quantization conjecture and the soliton resolution conjecture. Furthermore, in the very low asymptotic regime, the refined uniqueness is obtained in the deterministic case. At last, we show the direct construction of stochastic multi-solitons in the mass critical and subcritical cases, especially in the absence of the pseudo-conformal symmetry.

简介:张登，上海交通大学数学科学学院副教授，2014年博士毕业于中科院数学与系统科学研究院和德国比勒费尔德大学，师从中科院马志明院士和德国Michael Röckner教授。研究方向包括随机偏微分方程、随机最优控制，随机矩阵理论等，在AOP, PTRF, ARMA, CMP, JMPA, TAMS，SICON等期刊发表多篇论文。