Abstract：

The first part of the talk will be about a new and simplified presentation of the classical pure braid group. Motivated by twist functors from Algebraic geometry, the generators are given by the squares of longest elements over connected subgraphs, and the relations are either commutators or certain length 5 palindromic relations.

In the second part of the talk, I will summarise a construction of derived autoequivalences associated to an algebraic flopping contraction. These functors are constructed naturally using bimodule cones, and these cones are locally two-sided tilting complexes. The autoequivalences combine to give an action of the fundamental group of an associated infinite hyperplane arrangement on the derived category.

https://us06web.zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09&omn=87944709298