Homological Mirror Symmetry - Atsushi Takahashi, Osaka University

Explore a lecture on Homological Mirror Symmetry delivered by Atsushi Takahashi from Osaka University. Delve into the concept of generalized root systems introduced by Kyoji Saito, inspired by the geometry of Milnor fiber and vanishing cycles. Examine the components of a generalized root system, including a lattice, a set of roots, and a Coxeter element from the Weyl group. Discover how this refined notion differs from traditional root systems, particularly in the context of "finite generalized root systems of type D." Investigate the construction of a "natural" Frobenius manifold from a Laurent polynomial in one variable with an involution, leading to a finite generalized root system of type D. Learn about the Frobenius potential as a rational function and its support for Dubrovin's conjecture on algebraic Frobenius manifolds. Gain insights into the collaborative research efforts with Akishi Ikeda, Takumi Otani, and Yuuki Shiraishi. Throughout the 51-minute presentation, encounter topics such as generalizable systems, classification, generation problems, geometric construction, experimental results, multiple optimization, technical remarks, problem structure, and illustrative examples.

Intro
Generalizable system
Classification
Generation
Problems
Geometric Construction
Experimental Results
Progress
Multiple Optimization
Technical remarks
Problem structure
Example