## February 28, 2019

### Sporadic SICs and Exceptional Lie Algebras II

#### Posted by John Baez

*guest post by Blake C. Stacey*

Today, we carry forward with the project we began last week: exploring **S**ymmetric **I**nformationally **C**omplete quantum measurements, otherwise known as SICs. They’re really just maximal sets of equiangular lines in a complex vector space!

In our first post, we laid the groundwork and studied one example: a set of four equiangular lines in $\mathbb{C}^2$. Now, we move up a dimension and investigate a set of 9 equiangular lines in $\mathbb{C}^3$. This will bring the exceptional Lie algebras into the narrative, and we’ll also get a chance to greet a biodiversity measure and a polytope known as the 24-cell.

## February 20, 2019

### Tychonoffication

#### Posted by John Baez

Joshua Meyers is a grad student in my real analysis class. We had an interesting conversation about topology and came up with some conjectures. Maybe someone has already proved them. I just want to write them down somewhere.

### Sporadic SICs and Exceptional Lie Algebras I

#### Posted by John Baez

*guest post by Blake C. Stacey*

Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy. I am grateful to John for giving me the opportunity to discuss one such confluence, where quantum information theory comes together with geometry, root systems and even the octonions.

In what follows, I will be divvying up these notes into blog posts. The first step is to introduce the geometrical statement of the *SIC problem.* Then, we’ll establish some basics about quantum theory, which may be fairly standard if you learned out of Mike and Ike while being a little un-standard outside of quantum information.

## February 7, 2019

### Applied Category Theory 2019

#### Posted by John Baez

I hope to see you at this conference!

- Applied Category Theory 2019, July 15-19, 2019, Oxford, UK.

Here’s some information about it, such as how to submit papers.

## February 4, 2019

### Jacobi Manifolds

#### Posted by John Baez

Here at the conference Foundations of Geometric Structures of Information 2019, Aïssa Wade of Penn State gave a talk about Jacobi manifolds. She got my attention with these words: “Poisson geometry is a good framework for classical mechanics, while contact geometry is the right framework for classical thermodynamics. Jacobi manifolds are a natural bridge between these.”

So what’s a Jacobi manifold?