Dynamical Interpretation of the Asymptotic Distribution of Frobenius Numbers

Given a $d$-dimensional positive integral vector “a” such that $gcd(a_1,…a_d)=1$, the Frobenius number $F(a)$ is defined to be the largest number which is not representable as a non-negative integer linear combination of the coefficients of “a”. In this talk, we will introduce a striking geometric interpretation of Frobenius numbers by Ravi Kannan, and describe recent results on asymptotic distribution of Frobenius numbers by Jens Marklof using homogeneous dynamics.