WKB-analysis of nonabelian Hodge theory

Hybrid. Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)

We discuss the P=W (perversity equals weight) conjecture in non-abelian Hodge theory (recently proven by Maulik--Shen and Hausel--Mellit--Minets--Schiffmann), and our Geometric approach to attacking it that could be turned to an actual proof in several particular cases. The idea is to use recent advances on the large-scale asymptotic behaviour of solutions to Hitchin's equations due to T.Mochizuki and R.Mazzeo et al. Time permitting, relationship to the Gaiotto--Moore--Neitzke conjecture and the Hitchin WKB-problem will also be mentioned.