# Benjamin Bakker, A Proof of Matsushita’s Conjecture

## April 30 @ 4:00 pm - 5:00 pm KST

B236-1,
IBS
Korea, Republic of

*f*:*X→B* of a compact hyperkahler manifold *X*, the fibers deform either maximally or trivially in moduli. In this talk I’ll explain how to prove this conjecture via Hodge theory. I will also discuss some other features of the topology of Lagrangian fibrations and a result about the density of torsion points in sections. Time permitting, I will discuss some more recent work with C. Schnell from this perspective reproving a result of J.-M. Hwang that *B* is projective space if it is smooth.