ABSTRACTS
OF 
PART I: THE RECENT VIEW ABOUT FIELD EQUATIONS 
Quantum TGD should be reducible to the classical spinor geometry of the configuration space ("world of classical worlds" (WCW)). The possibility to express the components of WCW Kähler metric as anticommutators of WCW gamma matrices becomes a practical tool if one assumes that WCW gamma matrices correspond to Noether super charges for supersymplectic algebra of WCW. The possibility to express the Kähler metric also in terms of Kähler function identified as Kähler for Euclidian spacetime regions leads to a duality analogous to AdS/CFT duality. Physical states should correspond to the modes of the WCW spinor fields and the identification of the fermionic oscillator operators as supersymplectic charges is highly attractive. WCW spinor fields cannot, as one might naively expect, be carriers of a definite spin and unit fermion number. Concerning the construction of the WCW spinor structure there are some important clues. 1. Geometrization of fermionic statistics in terms of configuration space spinor structure The great vision has been that the second quantization of the induced spinor fields can be understood geometrically in terms of the WCW spinor structure in the sense that the anticommutation relations for WCW gamma matrices require anticommutation relations for the oscillator operators for free second quantized induced spinor fields.
2. KählerDirac equation for induced spinor fields Supersymmetry between fermionic and and WCW degrees of freedom dictates that KählerDirac action is the unique choice for the Dirac action There are several approaches for solving the modified Dirac (or KählerDirac) equation.

PART II: GENERAL THEORY 
PART III: TWISTORS AND TGD 
TGD variant of twistor story Twistor Grassmannian formalism has made a breakthrough in N=4 supersymmetric gauge theories and the Yangian symmetry suggests that much more than mere technical breakthrough is in question. Twistors seem to be tailor made for TGD but it seems that the generalization of twistor structure to that for 8D imbedding space H=M^{4}× CP_{2} is necessary. M^{4} (and S^{4} as its Euclidian counterpart) and CP_{2} are indeed unique in the sense that they are the only 4D spaces allowing twistor space with Kähler structure. The Cartesian product of twistor spaces P_{3}=SU(2,2)/SU(2,1)× U(1) and F_{3} defines twistor space for the imbedding space H and one can ask whether this generalized twistor structure could allow to understand both quantum TGD and classical TGD defined by the extremals of Kähler action. In the following I summarize the background and develop a proposal for how to construct extremals of Kähler action in terms of the generalized twistor structure. One ends up with a scenario in which spacetime surfaces are lifted to twistor spaces by adding CP_{1} fiber so that the twistor spaces give an alternative representation for generalized Feynman diagrams. There is also a very closely analogy with superstring models. Twistor spaces replace CalabiYau manifolds and the modification recipe for CalabiYau manifolds by removal of singularities can be applied to remove selfintersections of twistor spaces and mirror symmetry emerges naturally. The overall important implication is that the methods of algebraic geometry used in superstring theories should apply in TGD framework. The physical interpretation is totally different in TGD. The landscape is replaced with twistor spaces of spacetime surfaces having interpretation as generalized Feynman diagrams and twistor spaces as submanifolds of P_{3}× F_{3} replace Witten's twistor strings. The classical view about twistorialization of TGD makes possible a more detailed formulation of the previous ideas about the relationship between TGD and Witten's theory and twistor Grassmann approach. Furthermore, one ends up to a formulation of the scattering amplitudes in terms of Yangian of the supersymplectic algebra relying on the idea that scattering amplitudes are sequences consisting of algebraic operations (product and coproduct) having interpretation as vertices in the Yangian extension of supersymplectic algebra. These sequences connect given initial and final states and having minimal length. One can say that Universe performs calculations. 
How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD? The twistor lift of classical TGD is attractive physically but it is still unclear whether it satisfies all constraints. The basic implication of twistor lift would be the understanding of gravitational and cosmological constants. Cosmological constant removes the infinite vacuum degeneracy of Kähler action but because of the extreme smallness of cosmological constant Λ playing the role of inverse of gauge coupling strength, the situation for nearly vacuum extremals of Kähler action in the recent cosmology is nonperturbative. Cosmological constant and thus twistor lift make sense only in zero energy ontology (ZEO) involving causal diamonds (CDs) in an essential manner. One motivation for introducing the hierarchy of Planck constants was that the phase transition increasing Planck constant makes possible perturbation theory in strongly interacting system. Nature itself would take care about the converge of the perturbation theory by scaling Kähler coupling strength α_{K} to α_{K}/n, n=h_{eff}/h. This hierarchy might allow to construct gravitational perturbation theory as has been proposed already earlier. This would for gravitation to be quantum coherent in astrophysical and even cosmological scales. In this chapter this picture is studied in detail. The first interesting finding is that allowing Kähler coupling strength α_{K} to correspond to zeros of zeta implies that for complex zeros the preferred extremals are mimimal surface extremals of Kähler action so that the values of coupling constants do not matter and extremals depend on couplings only through the boundary conditions stating the vanishing of certain supersymplectic conserved charges. The complete decoupling of the two dynamics is favored by both SH, realization of preferred extremal property (perhaps as minimal surface extremals of Kähler action, number theoretical universality, discrete coupling constant evolution, and generalization of Chladni mechanism to a "dynamics of avoidance". This leads to an interpretation with profound implications for the views about what happens in particle physics experiment and in quantum measurement, for consciousness theory and for quantum biology. Second observation is that a fundamental length scale of biology  size scale of neuron and axon  would correspond to the padic length scale assignable to vacuum energy density assignable to cosmological constant and be therefore a fundamental physics length scale. 
PART IV: CATEGORIES AND TGD 
Could categories, tensor networks, and Yangians provide the tools for handling the complexity of TGD? TGD Universe is extremely simple but the presence of various hierarchies make it to look extremely complex globally. Category theory and quantum groups, in particular Yangian or its TGD generalization are most promising tools to handle this complexity. The arguments developed in the sequel suggest the following overall view.
One should assign Yangian to various KacMoody algebras (SKMAs) involved and even with superconformal algebra (SSA), which however reduces effectively to SKMA for finitedimensional Lie group if the proposed gauge conditions meaning vanishing of Noether charges for some subalgebra H of SSA isomorphic to it and for its commutator [SSA,H] with the entire SSA. Strong form of holography (SH) implying almost 2dimensionality motivates these gauge conditions. Each SKMA would define a direct summand with its own parameter defining coupling constant for the interaction in question. 
PART V: MISCELLANEOUS TOPICS 