Workshop on Algebraic Geometry

Summary: Workshop on Algebraic Geometry

The “Workshop on Algebraic Geometry”, organized by Zhiyuan Li (SCMS) and Baohua Fu (AMSS), was successfully held at the Tianyuan Mathematics Research Center from September 1–5, 2025.

Aim:

The workshop aimed to

1. Present recent developments in algebraic geometry across both complex and arithmetic settings;

2. Foster collaboration and intellectual exchange between experts working on geometry in mixed and positive characteristics;

3. Explore connections between birational geometry, foliations, hyperkähler manifolds, and arithmetic phenomena such as Galois representations and Frobenius-splitting techniques.

The main scope of the conference:

1. Positivity phenomena in hyperkähler geometry and Rozansky–Witten theory;

2. Birational automorphisms and motivic invariants;

3. Singularity theory in mixed characteristic;

4. Foliations on compact Kähler manifolds;

5. Quasi-F-splitting, quasi-F-regularity, and their relation to singularities;

6. Generic vanishing in positive characteristic;

7. Galois representations arising from hyper-Kähler varieties.

Participants:

The workshop attracted participants from a wide range of institutions, including:

· Fudan University

· National Taiwan University

· Purdue University

· Academy of Mathematics and Systems Science (AMSS)

· Tokyo University of Science

· Peking University

· University of Science and Technology of China

· Tongji University

· Tianjin University

· Universität Bielefeld

· Shanghai Jiao Tong University

· Southwest Jiaotong University

· Tsinghua University

Summary:

The workshop provided a high-level platform for sharing progress in modern algebraic geometry, ranging from birational and Kähler geometry to arithmetic geometry in mixed and positive characteristics. Through lectures, discussions, and informal activities, participants deepened mutual understanding and initiated several collaborative directions. The supportive environment of the Tianyuan Center contributed significantly to the success of the event, making the workshop both productive and memorable.