ICM 2026 Invited Section Lecture - Thomas Rothvoss

Value of the Information & Strength of the Argument

The lecture provides significant value by presenting new results that improve bounds for the Subspace Flatness Conjecture, with applications to integer programming. The argumentation is rigorous, based on proofs and citations of prior work, and the speaker carefully explains the logical flow. The value lies in both the originality of the results and the clarity of the exposition, which allows experts to grasp the main ideas.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high; the speaker cites specific papers and acknowledges contributions. The title is generic, but the description and content align well with the expected topic. No comments were provided, so no public reaction analysis is possible.

The title is generic but the description clarifies the specific topic; the content matches the expected subject of the lecture.

9/10

The talk is by a leading researcher in the field, presents rigorous proofs and cites prior work. The content is technically sound and well-structured.

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

• 02:00Introduction and definition of lattices
• 05:00Definition of covering radius and convex bodies
• 10:00Classical results by Kannan and Lovász
• 15:00Main theorem of Reis and Rothvoss
• 20:00Applications to flatness and integer programming
• 30:00Proof sketch using reverse Minkowski theorem

• Kannan and Lovász, Covering minima and lattice-point-free convex bodies (1988) — Foundational work on covering radius approximation via projections
• Daniel Dadush, PhD thesis on Integer Programming, Lattices, and Convexity (2012) — Introduction of the Subspace Flatness Conjecture and algorithmic implications
• Regev and Stephens-Davidowitz, covering radius for ellipsoids (2016) — Resolution of the conjecture for ellipsoids
• Reis and Rothvoss, general convex bodies (2023) — Main result of this lecture, achieving polylog gap