Abstract: 

In 1987, Hitchin constructed a complete hyperkähler metric on the moduli space of Higgs bundles, which can be generalized to accommodate singularities. In this talk, we consider Higgs bundles with irregular singularities over the Riemann sphere. We construct a generic ray in the moduli space and study the asymptotic behavior of the Hitchin metric along this ray. Using the techniques developed by Biquard-Boalch and Fredrickson-Mazzeo-Swoboda-Weiss, we show that the Hitchin metric is exponentially close to a simpler semi-flat metric. In dimension four, we obtain an explicit asymptotic formula for the semi-flat metric, which is of type ALG or ALG*.