Seminar: Bogdan Simeonov – Homological mirror symmetry for orbifold log Calabi-Yau surfaces (Apr 28, 2026)

Speaker: Bogdan Simeonov (Imperial College London)
Title: Homological mirror symmetry for orbifold log Calabi-Yau surfaces
Time: April 28, 2026 at 19:00 Istanbul local time (17:00 London local time)
Place: Online
Meeting ID: 935 6390 4955
Passcode: 699568

Abstract:
A guiding expectation in mirror symmetry is that adding a compactifying divisor to an open Calabi–Yau variety corresponds to equipping its mirror with a Landau–Ginzburg potential. For smooth projective rational surfaces (Y), this was confirmed by Hacking and Keating (building on foundational work of Gross–Hacking–Keel–Kontsevich), who proved homological mirror symmetry by identifying the derived category of (Y) with the Fukaya–Seidel category of vanishing cycles of a mirror Landau–Ginzburg model.

In this talk, this picture is extended to surfaces with isolated cyclic quotient singularities. To an anticanonical compactification (X) (viewed as a stack) of a smooth open Calabi–Yau surface whose boundary divisor is a cycle of weighted projective lines, a mirror Lefschetz fibration is constructed and the proof of homological mirror symmetry is outlined.

It is further explained how this fibration arises via a sequence of Lefschetz stabilizations from the Hacking–Keating mirror of the minimal resolution (Y) of the coarse space of (X). As an application, a symplectic interpretation is given of the fully faithful embedding (D^b(Y) \to D^b(X)) from the special McKay correspondence of Ishii and Ueda.