Today, I gave an introductory survey on the Langlands program to a group of mathematicians and physicists at the Simons Center for Geometry and Physics at Stonybrook University.
Many of these connections are well-illustrated on the LMFDB. I highly suggest poking around and clicking on things — on many pages there are links to related objects.
Part of the Langlands program includes the modularity conjecture for elliptic
curves over
During the talk, Brian gave an example or an Artin representation of the
symmetric group
From one perspective, the Langlands program is a monolithic wall of imposing, intimidating mathematics. But from another perspective, the Langlands program is most interesting because it organizes and connects seemingly different phenomena.
It's not necessary to understand each detail — instead it's interesting
to note that there are many fundamentally different ways of producing highly
structured data (like
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