ICM 2026 Plenary Lecture - Ngaiming Mok

Value of the Information & Strength of the Argument

The lecture provides a comprehensive overview of recent advances in higher-dimensional complex geometry, with a strong emphasis on the speaker’s own contributions. The argumentation is rigorous, with clear logical progression from classical results to modern developments. Mok effectively demonstrates the power of combining different mathematical tools, such as Kähler-Ricci flow, harmonic maps, and ergodic theory, to solve long-standing problems. The presentation is dense but well-structured, making it valuable for researchers in the field.

Scientific Rigor, Source Quality, Title Accuracy

The lecture is scientifically rigorous, with references to key theorems and works by the speaker and others, such as the Frankel conjecture, Mori’s work, Siu’s rigidity results, and the theory of varieties of minimal rational tangents. The title accurately reflects the content, which focuses on uniformization theorems and related results. The speaker’s authority and the context of an ICM plenary lecture further enhance the credibility. No external sources are cited in the description, but the talk itself references established mathematical literature.

The title accurately reflects the content, which focuses on uniformization theorems and related results in higher-dimensional complex geometry.

8/10

The lecture is given by a leading expert in complex geometry, with a clear presentation of results and methods. The content is highly technical and assumes advanced knowledge, but the speaker provides context and references to established theorems. The video is a plenary lecture at the ICM, indicating high scientific standing.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction and overview of uniformization theorems in higher dimensions
• 05:00Discussion of the generalized Frankel conjecture and its solution
• 10:00Introduction to rigidity results for quotients of bounded symmetric domains
• 15:00Hermitian metric rigidity and its consequences
• 20:00Extension to complex Finsler metrics and embedding theorems
• 25:00Use of ergodic theory and boundary holomorphic functions
• 30:00Proof of the isomorphism theorem via retraction maps
• 35:00Introduction to varieties of minimal rational tangents
• 40:00Definition and properties of minimal rational curves and VMRTs
• 45:00Applications and open problems in the theory of VMRTs

• Generalized Frankel conjecture — Mok's solution to the generalized Frankel conjecture, characterizing compact Kähler manifolds with nonnegative bisectional curvature.
• Hermitian metric rigidity — Mok's theorem on uniqueness of Hermitian metrics of semi-negative curvature on quotients of bounded symmetric domains.
• Varieties of minimal rational tangents — Theory developed by Mok and Hwang for studying uniruled projective manifolds.

• Siu's rigidity theorem — Siu's work on rigidity of holomorphic maps between compact quotients of bounded symmetric domains, which is a precursor to Mok's results.
• Mori's theorem — Mori's characterization of projective space by the ampleness of the tangent bundle, which is an algebraic analog of the Frankel conjecture.