Mirrors of Curves and Their Fukaya Categories II

Explore the intricate world of homological mirror symmetry for curves in this advanced mathematics lecture by Denis Auroux from Harvard University. Delve into the symplectic geometry of curve mirrors, comparing coherent sheaves on curves to suitable Fukaya categories of their mirrors. Examine the construction of Landau-Ginzburg models mirror to curves in (C*) or toric surfaces, and investigate the concept of fiberwise wrapped Fukaya categories. Discover the geometric relationships between smooth and singular fibers of Landau-Ginzburg models and their total spaces, along with corresponding functors between Fukaya categories. Learn about applications to hypersurfaces in higher-dimensional toric varieties, abelian varieties, and complete intersections. Explore speculative approaches to viewing mirror symplectic geometry from lower-dimensional perspectives, including "tropical Lagrangians" and geometry within the critical locus. Gain insights into a new flavor of Lagrangian Floer theory in trivalent configurations of Riemann surfaces and its connection to curve geometry.