Email: rastegar1352[at]gmail[dot]com

Tel: +98 (21) 6616 5613

Email: rastegar1352[at]gmail[dot]com

Tel: +98 (21) 6616 5613

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**Research interests in mathematics:**

**Diophantine geometry: **Contributions of global geometric approach to solving equations and particularly Diophantine equations. (Or any geometric treatment of arithmetic, algebraic or differential equations.)

**Modular forms: **Arithmetic structures involved in forms over moduli spaces. (Or in finding arithmetic formulations for every piece of mathematics we are faced to.

**Arakelov theory: **Mathematical situations where, the role of one piece of a mathematical framework is locally replaced by mathematics coming from other areas, as in Arakelov theory.

**Deformation of algebras: **Coordinatizing geometric objects and their deformations by translating them to the language of algebras and their deformations. This lead to formulation of Arithmetic Teichmuller Theory.

**Knots and three-manifolds:**Analogy between prime numbers and knots in three manifolds. I have developed a Chebotarev density theorem for knots in three manifolds. I am trying to develop an analogue of Langlands program for 3-manifolds.

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**Research interests in mathematics education:**

-Modeling of mind, while learning and doing mathematics.

-Modeling of interactions between branches of science and branches of mathematics.

-Modeling of educational systems.

-Psychology of problem solving.

-Understanding the roles which mathematical education can play in cognitive structures of students from elementary school to high-school and university.

-Developing a university curriculum for cognitive approach to mathematics.

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**Research interests in philosophy of mathematics, science and education:**

- Development of a cognitive philosophy of mathematics.

-Development a cognitive philosophy of education.

-Development an Islamic philosophy of science according to Islamic anthropology.

-Categorization of cognitive anthropology in the minds of Islamic philosophers.

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**Summary of my research in mathematics**

**Research perspectives in mathematics**