A Fourier-Mukai kernel for Galkin's conjecture

Location: 11th Floor Lecture Hall Speaker Ashesh Bati, Imperial College London Session Chair Sarah Frei, Rice University Abstract Galkin’s conjecture, proven by Kemboi-Segal in ‘25, predicts that the symmetric square of the Kuznetsov component of a cubic fourfold is equivalent to the bounded derived category of its Fano of lines. They proved this using techniques in matrix factorization categories. In this talk I will present upcoming work which provides a natural equivalence between the two categories. This is joint work with Patrick Luo.