On the Deligne-Drinfeld conjecture - T. Willwacher

Oct 22, 2026  ·   RIMS Kyoto by Zoom  ·   Event ``Taming the Flow seminar''

Abstract

The Grothendieck–Teichmüller Lie algebra \(\mathfrak{grt}_1\), introduced by Drinfeld through the theory of associators, contains elements σ₃, σ₅, σ₇, … in each odd degree. The Deligne–Drinfeld conjecture predicts that \(\mathfrak{grt}_1\) is freely generated by these elements; equivalently, that the motivic Galois group of mixed Tate motives over ℤ exhausts the graded Grothendieck–Teichmüller group. Willwacher (2026), building on work of Brown (2012), gives one inclusion.

1. T. Willwacher, The Deligne–Drinfeld conjecture after OpenAI, notes of the talk, Preprint (2026) [ArXiv]
2. T. Willwacher, On free generators in the Grothendieck–Teichmüller Lie algebra, arXiv:2607.18793 (2026).
3. F. Brown, Mixed Tate motives over ℤ, Ann. of Math. 175 (2012), 949–976.
4. V. G. Drinfeld, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(ℚ̄/ℚ), Leningrad Math. J. 2 (1991), 829–860.