Introduction
Various approaches to classical TGD
Could one identify space-time surfaces as zero loci for octonionic polynomials with real coefficients?
Topics to be discussed
Some basic notions, ideas, results, and conjectures of algebraic geometry
Algebraic varieties, curves and surfaces
About algebraic curves and surfaces
The notion of rational point and its generalization
About enumerative algebraic geometry
Some examples about enumerative algebraic geometry
About methods of algebraic enumerative geometry
Gromow-Witten invariants
Riemann-Roch theorem
Does M^{8}-H duality allow to use the machinery of algebraic geometry?
What does one really mean with M^{8}-H duality?
Is the associativity of tangent-/normal spaces really achieved?
M^{8}-H duality: objections and challenges
Some challenges of octonionic algebraic geometry
Could free many-particle states as zero loci for real or imaginary parts for products of octonionic polynomials
Questions related to ZEO and CDs
About singularities of octonionic algebraic varieties
The decomposition of space-time surface to Euclidian and Minkowskian regions in octonionic description
About rational points of space-time surface
About h_{eff}/h=n as the number of sheets of Galois covering
Connection with infinite primes
Super variant of octonionic algebraic geometry and space-time surfaces as correlates for fermionic states
About emergence
Does physics emerge from the notion of number field?
About physical interpretation
Could scattering amplitudes be computed in the octonionic framework?
Could scattering amplitudes be computed at the level of M^{8}-H?
Interaction vertices for space-time surfaces with the same CD
How could the space-time varieties associated with different CDs interact?
Twistor Grassmannians and algebraic geometry
About the concrete construction of twistor amplitudes
From amplituhedron to associahedron
Associahedrons and scattering amplitudes
Associations and permutations in TGD framework
Questions inspired by quantum associations
Gromov-Witten invariants, Riemann-Roch theorem, and Atyiah-Singer index theorem from TGD point of view
About the analogs of Gromow-Witten invariants and branes in TGD
Does Riemann-Roch theorem have applications to TGD?
Could the TGD variant of Atyiah-Singer index theorem be useful in TGD?
Could the precursors of perfectoids emerge in TGD?
About motivations of Scholze
Attempt to understand the notion of perfectoid
Second attempt to understand the notions of perfectoid and its tilt
TGD view about p-adic geometries
Cognitive representations and algebraic geometry
Cognitive representations as sets of generalized rational points
Cognitive representations assuming M^{8}-H duality
Are the known extremals in H easily cognitively representable?
Twistor lift and cognitive representations
What does cognitive representability really mean?
Galois groups and genes
Could DNA sequence define an inclusion hierarchy of Galois extensions?
Could one say anything about the Galois groups of DNA letters?
A possible connection with family replication phenomenon?
How the homology charge and genus correlate?
Euler characteristic and genus for the covering of partonic 2-surface
All genera are not representable as non-singular algebraic curves
Secret Link Uncovered Between Pure Math and Physics
Connection with TGD and physics of cognition
Connection with Kim's work
Can one make Kim's idea about the role of symmetries more concrete in TGD framework?
Are fundamental entities discrete or continuous and what discretization at fundamental level could mean?
Is discretization fundamental or not?
Can one make discretizations unique?
Can discretization be performed without lattices?
Simple extensions of rationals as codons of space-time genetic code
Are octonionic polynomials enough or are also analytic functions needed?
Summary and future prospects
Appendix: o^{2} as a simple test case
Option I: M^{4} is quaternionic
Option II: M^{4} is co-quaternionic