Workshop on Computational Harmonic Analysis and Data Science
Location: Tianyuan Mathematical Research Center, Kunming
Time: November 30 – December 6, 2025
The Workshop on Computational Harmonic Analysis and Data Science was successfully held at the Tianyuan Mathematical Research Center in Kunming from November 30 to December 6, 2025. Organized by Bin Dong (Peking University), Song Li (Zhejiang University), Ke Wei (Fudan University), and Shuyang Ling (NYU Shanghai), the workshop brought together leading experts and promising young researchers from China and abroad. Over 30 invited talks were delivered, covering major advances in harmonic analysis, signal processing, optimization, high-dimensional statistics, and machine learning.
Scientific Program
The scientific program (Dec 1–5) featured invited presentations from scholars representing top institutions worldwide. The talks centered around two major themes:
1. Computational Harmonic Analysis and Inverse Problems:
Topics included phase retrieval, sparse recovery, blind deconvolution, sampling theory, tensor and matrix approximation, and spectral methods. Several speakers presented new theoretical results—such as optimal sampling density, stability guarantees, and algorithmic convergence—and highlighted applications in imaging, data reconstruction, and high-dimensional computation.
2. Mathematical Foundations of Deep Learning and Generative Models:
Presentations addressed diffusion models, flow-matching priors, scaling laws, neural network generalization, reinforcement learning, and nonconvex optimization. Speakers introduced new analytical frameworks explaining phenomena such as neural condensation and training dynamics, as well as accelerated sampling methods for diffusion-based generative models.
Outcomes and Impact
The workshop provided an effective platform for substantive academic exchange, leading to several notable outcomes:
1. Identification of new research directions at the intersection of harmonic analysis, high-dimensional inference, and deep learning.
2. Cross-disciplinary dialogue between experts in inverse problems, optimization, statistics, and machine learning theory.
3. Generation of collaborative opportunities, particularly on open problems related to phase retrieval, low-rank models, diffusion generative models, and optimization algorithms.
4. Significant benefit to early-career researchers, including Ph.D. students and postdocs, who engaged extensively in discussions and received direct feedback from senior scholars.
Participants consistently noted that the workshop’s structure—featuring focused morning sessions followed by free discussion periods—facilitated deep technical exchanges.
Community Building
In addition to formal talks, informal discussions, group activities, and excursions created a highly interactive atmosphere reminiscent of international mathematical centers such as Oberwolfach and Banff. These activities played a key role in strengthening the research community working at the intersection of harmonic analysis and data science.
Conclusion
The workshop achieved all its intended goals: advancing scientific understanding, promoting interdisciplinary collaboration, supporting young researchers, and enhancing the visibility of the Tianyuan Mathematical Research Center as a national platform for high-level mathematical exchange. Participants expressed strong appreciation for the Center’s generous support and for the opportunity to engage in a week of intensive and productive academic interaction.