ABSTRACTS
OF 
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.

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. 
Khovanov homology generalizes the Jones polynomial as knot invariant. The challenge is to find a quantum physical construction of Khovanov homology analous to the topological QFT defined by ChernSimons action allowing to interpret Jones polynomial as vacuum expectation value of Wilson loop in nonAbelian gauge theory. Witten's approach to Khovanov homology relies on fivebranes as is natural if one tries to define 2knot invariants in terms of their cobordisms involving violent unknottings. Despite the difference in approaches it is very useful to try to find the counterparts of this approach in quantum TGD since this would allow to gain new insights to quantum TGD itself as almost topological QFT identified as symplectic theory for 2knots, braids and braid cobordisms. This comparison turns out to be extremely useful from TGD point of view. An essentially unique identification of string world sheets and therefore also of the braids whose ends carry quantum numbers of many particle states at partonic 2surfaces emerges if one identifies the string word sheets as singular surfaces in the same manner as is done in Witten's approach. Even more, the conjectured slicings of preferred extremals by 3D surfaces and string world sheets central for quantum TGD can be identified uniquely. The slicing by 3surfaces would be interpreted in gauge theory in terms of Higgs= constant surfaces with radial coordinate of CP_{2} playing the role of Higgs. The slicing by string world sheets would be induced by different choices of U(2) subgroup of SU(3) leaving Higgs=constant surfaces invariant. Also a physical interpretation of the operators Q, F, and P of Khovanov homology emerges. P would correspond to instanton number and F to the fermion number assignable to right handed neutrinos. The breaking of M^{4} chiral invariance makes possible to realize Q physically. The finding that the generalizations of Wilson loops can be identified in terms of the gerbe fluxes ∫ H_{A} J supports the conjecture that TGD as almost topological QFT corresponds essentially to a symplectic theory for braids and 2knots.
