Orthogonal polynomials with respect to varying exponential weights

In the last few decades, Riemann-Hilbert analysis has become a powerful tool for arriving at strong asymptotics for orthogonal polynomials. However, orthogonality with respect to a complex weight introduces many challenges that manifest themselves in interesting ways throughout the analysis. In this talk, I will highlight some of these challenges as they arise in the study of polynomials orthogonal with respect to an exponential weight with a cubic polynomial potential. This is joint work with Pavel Bleher, Alfredo Deaño, and Maxim Yattselev.