Monday 30th of January 2023, 15:00-16:00 in HG03.085
Maxime Wybouw
The tensor product of Banach spaces.
You won't believe what happens when you tensor two Banach spaces! In this talk I will tell the story of a result due to Alexander Grothendieck in the time that he was still doing functional analysis. The result is a striking inequality in the theory of norms on the tensor product of Banach spaces. We will start by building this theory from the ground up to appreciate the structure that arises from a natural definition and how Grothendieck's inequality is fundamental herein. Grothendieck's inequality has applications in quantum theory and optimization that are still explored to this day. I will in the second part explain how the inequality relates to these modern fields.