This talk provides a gentle, high level introduction to (the beautiful) Invariant Theory, that is aimed at non-experts. It will describe some of its main objects, problems and results.
This study of symmetries and their *invariants* (which *do not* change in certain dynamic processes), interacts with many mathematical fields including group theory, commutative algebra and algebraic geometry, and is a central to modern physics. I will stress some of the many facets of invariant theory which interact with computational complexity, optimization and polyhedral combinatorics. In particular, we'll see how natural objects, problems and results familiar in computer science appear naturally in this field. Time permitting, I will discuss recent work, providing new connections between these fields of study, and new algorithmic techniques benefiting them all.
No special mathematical background will be assumed