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.

What is a Galois representation kisin?

a Galois Representation? Mark Kisin. Let Q be the field of algebraic numbers. The Galois group GQ = Gal(Q/Q) is the group of automor- phisms of the field Q. A Galois representation is simply a representation of this group, or indeed of any Galois group.

Is the ABC conjecture proved?

Various attempts to prove the abc conjecture have been made, but none are currently accepted by the mainstream mathematical community and as of 2020, the conjecture is still regarded as unproven.

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.

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 useful for physics?

Algebraic geometry is the central aspect of geometry for the physicists now.” “In recent years algebraic geometry and mathematical physics have begun to interact very deeply mostly because of string theory and mirror symmetry,” said Migliorini.

What is the Galois group of a polynomial?

Definition (Galois Group): If F is the splitting field of a polynomial p(x) then G is called the Galois group of the polynomial p(x), usually written \mathrm{Gal}(p). So, taking the polynomial p(x)=x^2-2, we have G=\mathrm{Gal}(p)=\{f,g\} where f(a+b\sqrt{2})=a-b\sqrt{2} and g(x)=x.

Who proved abc conjecture?

Shinichi Mochizuki
After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in number theory, has been accepted for publication.

Is Shinichi Mochizuki A Nakamoto Satoshi?

Satoshi Nakamoto, the pseudonymous creator of Bitcoin, has many possible identities, and a forgotten name has just resurfaced – Japanese mathematician Shinichi Mochizuki.

How is geometry different from arithmetic?

What is arithmetic and geometric?

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.