Copositive geometry of Feynman integrals

Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone. P\'olya's method makes this manifest. We study the copositive cone for the second Symanzik polynomial of any Feynman graph. Its algebraic boundary is described by Landau discriminants.