Online talk

Motivic homotopy theory, introduced by Voevodsky to provide a universal framework for motivic cohomology in the spirit of Beilinson, adds a genuinely new dimension to homotopy theory: quadratic information. In this setting, Brouwer degrees take values not in the integers but in quadratic forms, and motivic stable stems encode Witt-theoretic and Milnor–Witt K-theoretic data.

I will recall the main features of motivic homotopy, unstable and stable, discuss Morel’s computation of the first motivic stable stems, and explain the role of the motivic Adams spectral sequence, notably in the computation of the classical stable stems by Isaksen, Wang, and Xu. I will then turn to orientation theories in motivic homotopy and introduce formal ternary laws, a new algebraic tool, developed after Walter by Fasel and myself, for combining quadratic and chromatic information.