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math.SG2025
Lagrangian Floer theory, from geometry to algebra and back again
Denis Auroux
We survey various aspects of Floer theory and its place in modern symplectic geometry, from its introduction to address classical conjectures of Arnold about Hamiltonian diffeomorp…
math.SG2025
Holomorphic discs of negative Maslov index and extended deformations in mirror symmetry
Denis Auroux
The SYZ approach to mirror symmetry for log Calabi-Yau manifolds starts from a Lagrangian torus fibration on the complement of an anticanonical divisor. A mirror space is construct…
math.SG2024
Lagrangian Floer theory for trivalent graphs and homological mirror symmetry for curves
Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov
Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greate…