Microsoft Researcher and Collaborator Prove 31-Year-Old KLS Conjecture

Microsoft Research's Xinzhi Zhang and collaborator Zhao Song proved the 31-year-old Kannan–Lovász–Simonovits (KLS) conjecture, resolving a major open problem in high-dimensional geometry and probability with a fixed universal bound. Their 140-page paper, submitted to arXiv in October 2026, shows that the KLS constant is bounded above by a universal constant, improving on previous bounds that grew with dimension. This breakthrough was achieved using a human-directed agentic AI research process.