What is... the Fontaine-Mazur conjecture?

Cody Gunton will explain what the Fontaine-Mazur conjecture is.

Abstract: Let G be the absolute Galois group of the rational numbers, a profinite group which is conjectured to surject onto every finite group. The finite-dimensional representations of G are central objects in number theory, where their study has yielded progress on a wide range of Diophantine, geometric, and analytic questions. This talk will situate and state the bold conjecture of Fontaine and Mazur that a small list of necessary conditions is sufficient to ensure that a representation of G can be constructed from the étale cohomology of an algebraic variety. No knowledge about anything more complicated than a group or a rational number will be assumed!

"What is...?" is an accessible and non-technical seminar where speakers explain in one (short) lecture some object or theorem that they think is interesting. There will be drinks and snacks during the talk. See the seminar website for more information.