Braids, knots and singular set of q-numbers

par Alexander Veselov (Loughborough)

vendredi 4 sept. 2026, 09:30 → 10:30 Europe/Paris

Amphi Jordan (Bat. Braconnier)

Few years ago, Sophie Morier-Genoud and Valentin Ovsienko introduced a remarkable quantization of the rational numbers as certain rational functions of the deformation parameter q. It turned out that the corresponding singular set, consisting of poles of all such functions, plays an important role in the theory of the braid group B_3, providing an answer to the faithfulness problem for the corresponding specialised Burau representation.
I will present the latest results about the structure of this singular set, including classification of the quantum Kronecker fractions, having all poles on the unit circle, and discuss the relation with the theory of braids and knots.
The talk is based on joint works with S. Morier-Genoud, V. Ovsienko, S. Evans and B. Winn.