报告题目：The negative flow of the Benjamin-Ono equation
报告人：胡星标 研究员 中国科学院数学与系统科学研究院
报告时间：2026 年6月26日14：00-14：40
报告地点：中关村校区教学楼N108
报告摘要：
The talk is concerned with the negative flow of the Benjamin–Ono (BO) equation, an integrable integrodifferential model that had not previously been studied. We establish its bilinear form and derive both a bilinear Bäcklund transformation and a nonlinear superposition formula. These structures are then combined to develop a unified solution approach, which systematically generates exact solutions in determinant form. The strength of this approach lies not only in its compact algebraic representation but also in its adaptability to rigorous analysis involving the Hilbert transform, thereby revealing deeper structural properties of the system. Within this framework, we obtain a Lax pair and explicitly construct two fundamental classes of solutions—multisoliton solutions and multiphase solutions. This study not only enriches the theory of the BO hierarchy but also provides a theoretical foundation for the investigation of broader classes of integrable integrodifferential equations. This is joint work with Gegenhasi, Ya-Jie Liu, Ling-Juan Yan, Ying-Nan Zhang.
报告题目：Infinite-peakon solutions of the Camassa--Holm equation
报告人：常向科 副研究员 中国科学院数学与系统科学研究院
报告时间：2026 年6月26日14：50-15：20
报告地点：中关村校区教学楼N108
报告摘要：
We describe a class of conservative low regularity solutions to the Camassa--Holm equation on the line by exploiting the moment problem and generalized indefinite strings to develop the inverse spectral method. In particular, we identify explicitly the solutions that are amenable to this approach, which include solutions made up of infinitely many peaked solitons (peakons). As an application, our results are then used to investigate the long-time behavior of solutions. We present three exemplary cases of solutions with: (i) discrete underlying spectrum associated with zero boundary and indeterminate moment problem; (ii) step-like initial data associated with the modified Laguerre weight, and (iii) asymptotically eventually periodic initial data associated with the modified Jacobi weight.
报告题目：Critical Hermitian matrix model with external source and Boussinesq hierarchy
报告人：徐帅侠 教授 中山大学
报告时间：2026 年6月26日15：30-16：10
报告地点：中关村校区教学楼N108
报告摘要：
We consider the Hermitian random matrix ensemble with an external source and quartic potential $V(x) = x^4/4 - tx^2/2$, where the external source has two distinct eigenvalues $\pm a$ of equal multiplicities. We find a new family of limiting correlation kernels, in certain critical regimes of the parameters, as the size of the matrix $n\to\infty$. These kernels are constructed from solutions of the Riemann-Hilbert problem associated with the Boussinesq hierarchy. This talk is based on joint work with Dong Wang from the University of Chinese Academy of Sciences.
