Beijing Institute of Mathematical Sciences and Applications

This course provides a comprehensive introduction to Frobenius manifolds, a rich and interdisciplinary topic at the intersection of differential geometry, algebraic geometry, integrable systems, and mathematical physics. Frobenius manifolds arise in topological field theory, mirror symmetry, and singularity theory, with deep connections to the WDVV equations. They have a flat metric, a multiplicative structure on the tangent bundle, and a potential function satisfying associativity conditions. We will explore key examples, such as those arising from quantum cohomology and singularity theory, and discuss their applications in physics and geometry.