Alternatively have a look at the program.

## Braids and the Grothendieck-Teichmüller Group -- change of time --

I will explain what are associators (and why are they useful and natural) and what is the Grothendieck-Teichmüller group, and why it is completely obvious that the Grothendieck-Teichmüller group acts simply transitively on the set of all associators. Not enough will be said about how this can be used to show that "every bounded-degree associator extends", that "rational associators exist", and that "the pentagon implies the hexagon".

## Computation without Representation -- change of time --

A major part of "quantum topology" (you don't have to know what's that) is the definition and computation of various knot invariants by carrying out computations in quantum groups (you don't have to know what are these). Traditionally these computations are carried out "in a representation", but this is very slow: one has to use tensor powers of these representations, and the dimensions of powers grow exponentially fast.

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