Title: Symplectic Birational Involutions of manifolds of OG10 type.

Abstract: Compact Hyperkähler manifolds are one of the building blocks of Kääler manifolds with trivial first chern class, but very few examples are known. One strategy for potentially finding new examples is to look at finite groups of symplectic automorphisms of the known examples, and study the fixed loci or quotient. In this talk, we will obtain a partial classification of birational symplectic involutions of manifolds of OG10 type. We do this from two vantage points: firstly following classical techniques relating birational transformations to automorphisms of the Leech lattice. Secondly, we look at involutions that are obtained from cubic fourfolds via the compactified intermediate Jacobian construction. In this way, we obtain new involutions that could potentially give rise to new holomorphic symplectic varieties. If time permits, we will mention ongoing work to identify the fixed loci in one of these examples.