The KSBA Moduli Space of Log Calabi-Yau Surfaces - Part 1

Explore a 58-minute lecture on the KSBA moduli space of log Calabi-Yau surfaces, delivered by Hülya Argüz from the University of Georgia at the University of Miami. Delve into the natural generalization of the moduli space of stable curves to higher dimensions, introduced by Kollár-Shepherd-Barron and Alexeev. Examine the parametrization of stable pairs (X,B) and their specific conditions. Investigate concrete descriptions of this moduli space in select situations, including toric varieties. Learn about the open question regarding log Calabi-Yau varieties and the conjecture by Hacking-Keel-Yu. Discover the proof of this conjecture for all log Calabi-Yau surfaces, presented as joint work with Alexeev and Bousseau. Gain insights into the tools used in this proof, including the minimal model program, log smooth deformation theory, and mirror symmetry.