While landmark achievements by Perelman, Agol, and others have recently resolved major questions in dimension 3, the field of low-dimensional topology remains vibrant. Significant challenges persist—such as the L-space conjectureand the smooth Poincaré conjecture in dimension 4—alongside emerging questions at the intersection of various mathematical disciplines.
Low-dimensional topology (dimensions 2, 3, and 4) also serves as a vital bridge between several core fields, including mathematics, physics, and computer science. This thematic month aims to deepen the field’s connections with these adjacent disciplines through three specific interfaces:
- Low-Dimensional Dynamical Systems: Focusing on discrete dynamics on surfaces and continuous 3D dynamics, a tradition dating back to Poincaré.
- Interface with Theoretical Computer Science: Addressing the complexity of fundamental problems, such as the classification and recognition of knots.
- Topology and Number Theory: Studying modular groups, their representations, and arithmetic invariants, with further connections to quantum field.