Summary of the Tianyuan Mathematical Research Center Workshop on “Analysis and Numerics in Grating Diffraction Problems”
The Tianyuan Mathematical Research Center Workshop on “Analysis and Numerics in Grating Diffraction Problems” was successfully held from December 28, 2025, to January 3, 2026. This seven-day event was convened by Professors Ya Yan Lu (City University of Hong Kong), Wangtao Lu (Zhejiang University), and Guanghui Hu (Nankai University). It brought together 36 participants from leading universities and research institutions across mainland China, Hong Kong, France, Germany, and the United States, creating a vibrant and collaborative atmosphere dedicated to advancing the frontiers of research in the analysis and numerical methods for grating diffraction and related wave scattering problems.
A defining feature of the workshop was the profound cross-fertilization among applied mathematics, computational mathematics, and physical optics. The discussions highlighted a synergistic cycle: pressing challenges from engineering physics, such as diffraction with negative-index materials and inverse scattering with phaseless data, inspired new mathematical questions. Concurrently, significant advancements in mathematical tools were presented, providing essential resources for the field. These included advanced Finite Element Methods, high-precision Boundary Integral Equation solvers, and foundational theories like the Limiting Absorption Principle. This bidirectional exchange underscored the deep synergy at the heart of the field.
The scientific program comprised a series of high-caliber reports, with 20 presentations systematically covering the core academic frontiers in this interdisciplinary field. These encompassed the well-posedness theory and numerical challenges of diffraction grating problems involving complex materials and edge conditions, finite element and boundary integral equation methods for nonlinear eigenvalue problems and scattering in periodic structures, inverse scattering theories and reconstruction algorithms particularly with phaseless data, modeling and analysis of novel wave phenomena in quasicrystalline systems and bound states in the continuum, the mathematical theory of computational resolution limit and super-resolution imaging, as well as efficient numerical methods for large-scale metamaterials and rough surface scattering. These talks often took the form of insightful surveys of their respective domains, fostering deep understanding and stimulating enthusiastic discussion.
The event successfully created an open platform for researchers at all levels to exchange the latest achievements and address pressing challenges. It significantly promoted scholarly communication and collaboration across disciplines, thereby actively contributing to the field’s academic progress. Furthermore, the workshop provided valuable opportunities for the professional growth of young scholars, who were able to engage closely with leading international experts within the stimulating environment of the Tianyuan Center.
Participants expressed their sincere appreciation for the world-class platform and exceptional support provided by the Tianyuan Mathematics Research Center. The interdisciplinary insights and collaborations fostered throughout the event are expected to have a lasting impact. We extend our heartfelt gratitude to all organizers, participants, and staff members of TMRC who contributed to the success of this workshop.