Algebra and Number Theory

Algebra and Number Theory form an important area within fundamental mathematics with a surprisingly large number of links to other fields of mathematics, including applied mathematics. In Utrecht members of both the algebra/number theory group and the (algebraic) geometry group are involved in research and graduate teaching in this area. We give a brief overview of the members of the algebra/number theory group (click on the links if you want to know more about the subject and, more in particular, the Utrecht activities). For algebraic geometry please go to the Geometry pages.

Number Theory This is one of the oldest branches of mathematics, and even more alive than ever before. The subject holds an attraction to both mathematics amateurs and professional mathematicians. Utrecht activities range from classical number theory to diophantine geometry. Key results and methods are in: diophantine equations, rational points, algebraic numbers, modular forms, elliptic curves, transcendental numbers.

Arithmetic Geometry. In modern number theory it is realised that many of its concepts have their geometric counter parts and vice versa. Several of the more spectacular developments in number theory owe their existence to this insight.

Representation of algebraic groups. The theory of algebraic structures and their representations is an area with its roots in 19th century mathematics under the names of invariant theory and Lie algebras. Nowadays the subject of representation theory is inspired with insights in homological algebra and new structures deriving from applications in physics.

Lie algebras, integrable systems. Algebra and number theory have strong links with other areas of mathematics and mathematical physics. For example, certain branches in number theory deal with subjects in linear differential equations and hypergeometric functions. Representations of Lie algebras play an important role in (infinite dimensional) integrable dynamical systems such as the soliton equations.