The workshop ``Exponential Sums: Theory, Computations and Applications'' organized by Daqing Wan (CQU) and Ping Xi (XJTU), was successfully held at the Tianyuan Mathematics Research Center from November 17 to 21, 2025.
Aim
l Present recent developments related to exponential sums.
l Explore connections between different fields of mathematics including additive combinatory, algebraic geometry, cryptology, harmonic analysis, number theory, etc.
l Provide a platform for young scholars to present their latest research findings as posters, and an opportunity to discuss in depth with other scholars.
l Enjoy the beautiful nature scenery at the leisure time.
Participants
The seminar attracted over 50 participants from a wide range of institutions, including:
Anhui University
Chinese Academy of Sciences
Chongqing University
Hunan Normal University
Nanjing University
Shandong University
Shanghai Institute for Mathematics and Interdisciplinary Sciences
Southern University of Science and Technology
Tsinghua University
University of Science and Technology of China
Xi'an Jiaotong University
Zhejiang University
etc.
Topics
Yang Cao (SDU) presented new approaches to strong approximation for linear algebraic groups and two recent results.
Changhao Chen (AHU) investigated the metric theory of Weyl sums and its applications to number theory, PDE and ergodic theory.
Zhiguo Ding (HNNU) shared a new approach to the study of permutation polynomials and the applications on some open problems.
Tao Feng (ZJU) proved some recent classification results on finite generalized quadrangles and an application of geometric methods in group theory.
Haoyu Hu (NJU) discussed the quantitative sheaf theory and its applications in the equidistribution of exponential sums.
Zhizhong Huang (CAS) surveyed some results on counting integer solutions related to quadratic forms with a view towards quantitative strong approximation.
Bochen Liu (SUSTech) introduced the relation between zeros of exponential sums and the periodicity of translational multiple tiling, and discussed possible applications of Fourier restriction estimates.
Daqing Wan (CQU) focused on the non-zero exponential sums, and a deeper analogue of the Carlitz-Wan conjecture.
Anyu Wang (THU) introduced a new hybrid algorithm, which can significantly reduce the solving complexity of the RSD problem.
Daxin Xu (CAS) explored the Frobenius structure on theta connections and rigidity of associated local systems.
Dingxin Zhang (SIMIS) established the irregular Newton-over-Hodge conjecture of Deligne for a large class of functions.
Yang Zhang (XJTU) discussed the distinction between Kloosterman sums and multiplicative functions, and reported some recent progresses on the distribution of Kloosterman sums.
Lilu Zhao (USTC) introduced the restriction mean value theorem over minor arcs and its applications to the Roth type theorem for higher degree Diophantine equations.
There are also many postdocs and PhD students sharing their ideas in the poster session.
Summary
The ``Exponential Sums: Theory, Computations and Applications'' was a well-organized, intensive academic workshop focusing on various aspects of exponential sums, and this was a great opportunity for scholars from different fields to exchange the ideas about exponential sums and the allied topics.
Tianyuan Center's strong support and contributions are the key to the success of the event, and we express our sincere gratitude to the Tianyuan Center.