Introduction

About the evolution of the concept of M⁸-H duality

1. The problems with the original forms of M⁸-H duality

2. The recent view of M⁸-H duality

Holography = holomorphy vision

1. About the geometric description of fermion pair creation vertex in the framework of catastrophe theory

2. The tension between the holography = holomorphy vision and  number-theoretic vision

3. Catastrophe theoretic vision of TGD

4. Holography = holomorphy vision as a realization of quantum criticality and the theory of analytic functions