Introductory Lectures on Singularities and Mirror Symmetry - Part 1

Explore fundamental concepts of mirror symmetry and singularities in this introductory lecture from Osaka University's Professor Atsushi Takahashi. Delve into four key areas: the general principles of mirror symmetry for singularities, the relationship between invertible polynomials and topological mirror symmetry, the connection between matrix factorizations and homological mirror symmetry, and practical applications focusing on exponents and vanishing cycles. Learn advanced mathematical concepts through this 72-minute academic presentation that bridges theoretical foundations with practical mathematical applications.