Universal higher Teichmuller theory and harmonic maps

par Peter Smillie (Leipzig (MPIM))

jeudi 6 nov. 2025, 14:00 → 16:00 Europe/Paris

Assuming basic familiarity with Teichmuller space, I will explain in turn harmonic maps, higher Teichmuller space, and universal Teichmuller space. Each pair of these three is the beginning of a fascinating story (to which we will sadly not do justice): respectively Higgs bundles, the Schoen conjecture, and cross ratios. Instead we will jump straight to a synthesis of all three, as suggested in a brief remark in a visionary 2004 paper by François Labourie. In joint work with Max Riestenberg, we prove a very general existence theorem for harmonic maps, and as a consequence we realise at least part of Labourie’s vision.