I was a computer engineer of of basic software. I have very recently retired. I want to study physics and mathematics. In particular, I would like to study "Langlands Correspondence and Physics". It is a very interesting problem related to both MATH. and PHYS.. There might be somewhat of a relationship between Riemann's hypothesis and S-duality.
1,rewrite the circle method. This article needs some improvements. This is needed to rewrite in rather early times.
2,Abel variety -- describe the simplicity of abelian varieties
- There exist the article titled "Semistable abelian variety."
3,Tate conjecture -- describe the formal definition of Tate conjecture
4,Kodaira dimension -- Abundance conjecture and Logarithmistic Kodaira dimension have done to modify Iitaka fibering for the intermediate Kodaira dimension varieties.
5,Classification of super?hyper?elliptic curves the key word is the Weierstrass points
6,Weyl solutions and Tomimatu-Sato solution must be described in "Cosmic Censership Hypothesis."
7,improve "Kahler manifold."
8, partition function (mathematics). the partition function in QFT, TQFT and the knot theory.
- Witten CS theory as a string theory
- Gopakumar-Vafa papers
- topo. vertex
9, Make "automorphic representation" independent on "automorphic form."