Geometry of the mirror curve
10:40:00 - 12:00:00
101, Mathematics Research Center Building (ori. New Math. Bldg.)
Mirror symmetry relates the A-model topological string theory (Gromov-Witten theory) on a toric Calabi-Yau 3-fold to the B-model topological string theory on its mirror Calabi-Yau 3-fold. By the remoding conjecture, the latter can be reduced to invariants of the mirror curve defined by the Eynard-Orantin topological recursion. In the first talk, I will describe the geometry and topology of the mirror curve and its compactification, as well as the B-model open-closed topological string moduli. In the second talk, I will define all genus B-model topological string theory by applying the Eynard-Orantin topological recursion to the mirror curve, and express generating functions of open-closed topological string amplitudes as graph sums.