| Speaker: | Alexey Bondal (Kavli IPMU / Steklov) |
|---|---|
| Title: | Mathematical theory of mutually unbiased bases |
| Date (JST): | Wed, Oct 31, 2012, 15:30 - 17:00 |
| Place: | Lecture Hall |
| Abstract: |
We first introduce the notion of mutually unbiased bases (MUB's) and discuss its importance in foundations of quantum mechanics and on the example of recent quantum teleportation experiments. We discuss interpretation of MUB's in terms of orthogonal decompositions of the Lie algebra sl(n,C) and formulate so-called Winnie-the-Pooh conjecture, still open, and rediscovered many times in the physical context. We show how MUB's are related to discrete harmonic analysis of local systems on graphs and representations of special class of algebras. We discuss the semi-orthogonal decompositions of the derived categories of representations and its relation to perverse sheaves. We end up with a theorem on existence of 4-dimensional family of pairs of MUB's in dimension 6 and discuss algebraic geometry behind this result. |
