Hyper-Kähler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence.

We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kähler manifold and its Kuga-Satake variety has been proved to be algebraic. We then turn to recent work of O'Grady and Markman which we combine to prove that the Kuga-Satake correspondence is algebraic for projective hyper-Kähler manifolds of generalized Kummer deformation type.

The Projective Consciousness Model and Phenomenal Selfhood.

We summarize our recently introduced Projective Consciousness Model (PCM) (Rudrauf et al., 2017) and relate it to outstanding conceptual issues in the theory of consciousness. The PCM combines a projective geometrical model of the perspectival phenomenological structure of the field of consciousness with a variational Free Energy minimization model of active inference, yielding an account of the cybernetic function of consciousness, viz.