Mathematical Conversations

Our object of interest will be tuples matrices over a field.

I will explain how different views of this object by diverse fields of mathematics give rise to important questions in these areas, which turn out to be surprisingly tightly connected. These areas include

• Linear algebra
• Invariant theory
• Computational complexity
• Analysis
• Non-commutative algebra
• Quantum information theory

Some of these connections, and more, was only discovered recently through interest in an algorithmic study of the questions above. I will give a high level survey of these problems and connections.