Analytic torsion is a real number defined by a compact Kähler manifold and a holomorphic Hermitian vector bundle. Yoshikawa constructed an invariant of K3 surfaces with antisymplectic involution by using equivariant analytic torsion. This invariant is expressed as the Petersson norm of a certain automorphic form on a bounded symmetric domain of type IV and a certain Siegel modular form, and is applied to various calculations of BCOV invariants. In this talk, we consider irreducible holomorphic symplectic fourfolds which are deformation equivalent to Hilbert schemes of K3 surfaces with antisymplectic involution. We will construct an invariant by using equivariant analytic torsion, and prove that this invariant satisfies a certain differential equation on the deformation space.

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In Student Colloquium, we do not fix the end time. Though a nominal time is shown above, we mean neither that it will be so, nor that it was so.