We introduce 'braidability' as a new symmetry for (infinite) sequences of noncommutative random variables related to representations of the braid group B∞. It provides an extension of exchangeability which is tied to the symmetric group S∞. Our key result is that braidability implies spread-ability and thus conditional independence, according to the noncommutative extended de Finetti theorem [K...

We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel-Thomas) twists and are reminiscent of the Rickard complexes defined by Chuang-Rouquier. Conjecturally, one can relate our complexes to Rickard complexes using categorical vertex operators.

Smale's method is of very general character: it provides an estimate of the topological complexity of any nonlinear ill-posed problem by means of a topological characteristic of the corresponding fibration, namely, its genus introduced and studied by Shvarts in[7] (and rediscovered in [8]). In the case of the problem on polynomial roots, an estimate of the genus [of which the inequality (i) is ...

We construct an action of a braid group associated to a complete graph on the derived category of a certain symmetric Nakayama algebra which is also a Brauer star algebra with no exceptional vertex. We connect this action with the affine braid group action on Brauer star algebras defined by Schaps and Zakay-Illouz. We show that for Brauer star algebras with no exceptional vertex, the action is ...