What is the Langlands conjecture?

In mathematics, the local Langlands conjectures, introduced by Robert Langlands (1967, 1970), are part of the Langlands program. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.

Is Geometry an arithmetic?

Arithmetic ‘“ is the most elementary division of mathematic. It involved computation with numbers. Geometric ‘“ refers to the branch of mathematics that describes the properties of bodies in space. This can refer to points, planes, lines, angles, and figures.

Why is number theory important?

As it holds the foundational place in the discipline, Number theory is also called “The Queen of Mathematics”. Description: The number theory helps discover interesting relationships between different sorts of numbers and to prove that these are true . Number Theory is partly experimental and partly theoretical.

Why is the Langlands program so important?

As an analogue to the possible exact distribution of primes, the Langlands program allows a potential general tool for resolution of invariance at generalized algebraic structures. This in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions.

Is algebraic geometry active?

Now, Algebraic Geometry is one of the oldest, deepest, broadest and most active subjects in Mathematics with connections to almost all other branches in either a very direct or subtle way.

Is algebraic geometry algebra or geometry?

Algebraic geometry applies commutative algebra to sets described by algebraic equations. It gives information about the shape of such sets. As its name implies, it uses both algebra and geometry. It might be better to say it uses algebraic techniques to answer geometric questions.

What is geometric and arithmetic?

An arithmetic sequence is a sequence of numbers that is calculated by subtracting or adding a fixed term to/from the previous term. However, a geometric sequence is a sequence of numbers where each new number is calculated by multiplying the previous number by a fixed and non-zero number.

How is number theory used today?

The best known application of number theory is public key cryptography, such as the RSA algorithm. Public key cryptography in turn enables many technologies we take for granted, such as the ability to make secure online transactions. Random and quasi-random number generation.

Why does number theory refer as the queen of mathematics?

German mathematician Carl Friedrich Gauss (1777–1855) said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations …