Global phase portrait and large degree asymptotics for the kissing polynomials

In this talk we present recent results on orthogonal polynomials (OPs) with respect to the weight function $w(z;s)=e^{-sz}$ on $[-1,1]$, where $s\in\mathbb{C}$ is an arbitrary complex parameter. We are particularly interested in the limit zero distribution and asymptotic behavior of recurrence coefficients as $n\to\infty$. To investigate this, we determine the geometry of breaking points and breaking curves in the $s$ plane, which separate regions where different asymptotic behaviors occur.