### Benoît Legat

Benoît Legat is a postdoctoral associate at MIT with Prof. Pablo Parrilo

in the Laboratory for Information and Decision Systems (LIDS).

He received his Ph.D. degree in applied mathematics from the UCLouvain, Belgium, in 2020.

His research interests include mathematical optimization, invariant set computation and

optimal control.

#### Sessions

The definition of the arithmetic operations defined in Julia assume that the arguments are not modified.

However, in many situations, a variable represents an accumulator that can be modified to contain the result, e.g., when summing the elements of an array.

Moreover, many types can be mutated and mutating the element may have significant performance benefit.

This talk presents an interface that allows algorithms to exploit a possible mutability while still being completely generic.

In this talk we discuss a symmetry reduction approach relying on the invariance of the polynomial under a group of actions. From the algebraic properties of the group, the SymbolicWedderburn package determines a change of basis that enables the decomposition of the constraints into smaller bases, some of them being equal which further reduces the problem. We show how to specify the group symmetry to allow SumOfSquares to perform this reformulation automatically.