Witten's Conjecture

Witten's Conjecture suggests a deep connection between two areas of mathematics: the study of how geometric shapes (specifically, surfaces) can be deformed, and quantum physics. It proposes that certain mathematical objects called "intersection numbers," which count how different geometric features intersect on surfaces, are directly related to solutions of integrable systems known as KdV equations, originating from quantum field theory. In essence, it bridges complex geometry and mathematical physics, revealing that the ways surfaces can be "twisted" or "stretched" encode information connected to fundamental physical theories.