Explore cutting-edge topics in algebraic geometry and commutative algebra through this 44-minute lecture by Tyler Kelly, presented at the 15th ALGA (Commutative Algebra and Algebraic Geometry) conference held at IMPA in Rio de Janeiro. Delve into mirror symmetry, curve counting techniques, and the Lando-Ginsburg model. Examine the analog to periods and related theorems in this advanced mathematical discourse. Gain insights from a renowned expert in the field and connect with the broader mathematical community through this annual event, which has been fostering discussions on algebraic geometry, commutative algebra, and related topics for over two decades.