Galois representations and the Langlands correspondence

The Langlands correspondence relates number-theoretic objects to completely different objects. While still largely conjectural, it has attracted interests of many mathematicians over the years.

It is known that the local Langlands correspondence in a special case can be constructed in a geometric way (the non-abelian Lubin-Tate theory). In this talk, I will explain some basic concepts in mathematics (such as groups, representations and Galois groups) and then try to convey some flavor of my result related to the non-abelian Lubin-Tate theory.