3 problems

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Fontaine–Mazur conjecture
32 years old
Conjecture (Fontaine–Mazur). Every irreducible geometric representation $\rho\colon G_K\to\mathrm{GL}_n(\overline{\mathbb Q}_p)$ comes from algebraic geometry.
openThe Justin Sun Prizealgebra number-theory unsolved-problem
118
Hadamard conjecture
133 years old
Conjecture. For every positive integer $k$ there is a Hadamard matrix of order $4k$ : …
openThe Justin Sun PrizeFormal statementalgebra unsolved-problem
028
Farrell–Jones conjecture in algebraic K- and L-theory
33 years old
Conjecture.
openThe Justin Sun Prizealgebra unsolved-problem
017

Fontaine–Mazur conjecture