Journal

The Zu Chongzhi Center conference Advances in Applied Mathematics and its Applications takes place October 26-29, 2023 at Duke Kunshan University. The conference is co-organized by Konstantinos Efstathiou, Jian-Guo Liu, Shixin Xu, and Xiaoqian Xu.

I am in Antwerp for the 7th International Conference on Finite Dimensional Integrable Systems in Geometry and Mathematical Physics (FDIS 2023) organized by Sonja Hohloch. I gave a presentation on Rotation 1-Forms and Non-Compact Monodromy based largely on earlier joint work with Andrea Giacobbe and Pavao Mardešić.

I am currently in Zhangye for the 9th Shanghai International Symposium on Nonlinear Sciences and Applications (SNSA 2023) organized at Hexi University, and then I go to Kunming for the 7th Chinese Conference on Statistical Physics and Complex Systems (SPCSC 2023).

Between June 11 and 15, I am at the SwissMAP Research Station in Les Diablerets for the workshop Finite Dimensional Integrability in Mathematical Physics.

Between June 5 and 8, I visited Prof. Xingang Wang and his group at Shaanxi Normal University in Xi’an, for discussions and I gave a seminar talk to his group about Collective Dynamics of Coupled Oscillators.

On April 14-16, 2023, we are organizing the 2nd Workshop on Collective Dynamics and Networks at the Zu Chongzhi Research Center of Duke Kunshan University, together with Jian Gao (Beijing University of Posts and Telecommunications), Wei Lin (Fudan University), Zhigang Zheng (Huaqiao University). More information on the workshop can be found on the workshop website.

Between February 15 and 18, I visited Prof. Zhigang Zheng at Huaqiao University in Xiamen, for discussions and I gave a seminar talk to his group about Collective Dynamics of Coupled Oscillators. Thank you Prof. Zheng for the interesting discussions and the great hospitality in beautiful Xiamen! 😄

Bohuan Lin successfully defended his PhD thesis, titled Interplay between dynamics and geometry in integrable systems and engineering problems, on January 31. Bohuan was co-supervised by Holger Waalkens and me. I could only attend the defense online, but I had the opportunity to meet Bohuan in person one week later in Suzhou. Congratulations Dr. Lin, and best wishes for the future! 😄

The 2022 Suzhou Area Young Mathematicians Workshop took place on November 26-27. This was the third workshop in this series and it was hosted by XJTLU, the previous two workshops having been hosted by DKU and Soochow University. At the workshop, I gave a presentation about the recently published work on externally forced Winfree oscillators.

A paper with Bohuan Lin and Holger Waalkens on toric foliations has been published in Regular and Chaotic Dynamics. From the paper:

In 2005 Dullin et al. proved that the non zero vector of Maslov indices is an eigenvector with eigenvalue 1 of the monodromy matrices of an integrable Hamiltonian system. We take a close look at the geometry behind this result and extend it to the more general context of possibly non-Hamiltonian systems. We construct a bundle morphism defined on the lattice bundle of an (general) integrable system, which can be seen as a generalization of the vector of Maslov indices. The nontriviality of this bundle morphism implies the existence of common eigenvectors with eigenvalue 1 of the monodromy matrices, and gives rise to a corank 1 toric foliation refining the original one induced by the integrable system. Furthermore, we show that, in the case where the system has 2 degrees of freedom, this implies the existence of a compatible free $S^1$ action on the regular part of the system.