## Hyperdeterminants

September 25, 2008

This may turn out to be one of the least read blogs in all the blogosphere but never mind.  It is going to be all about mathematical structures called hyperdeterminants and other things related to them. I think it is fair to say that even most mathematicians fall asleep when the subject of hyperdeterminants is mentioned but actually they are really interesting. They just tend to hide their best assets in dark corners where few people find them.

Hyperdeterminants are a generalisation of determinants to multi-dimensional arrays.  I’ll be explaining more about how they are defined and what their properties are in later posts. If you don’t already know what determinants are then I’m afraid you may not ready for this blog. But don’t despair. You can turn to wikipedia to read up on determinants or anything else unfamilair that comes up.

Any mathematicians who has been around awhile knows of many surprising connections that have been found between parts of mathematics that at first seemed separate. Examples include modular forms, elliptic curves, exceptional groups, lattices, coding theory, special functions, cohomology, octonions and even quantum physics and superstrings. Many of these beautiful subjects have deep connections that suggest the existence of some unknown master structure that encompasses them all in some elegant way. Hyperdeterminants are not the answer but they are a missing link that might help us find it.  They are in fact connected with all the above things in remarkable and unexpected ways some of which are only known to a very small group of researchers, so if you want to know more you had best follow this blog.

### 6 Responses to “Hyperdeterminants”

1. John Baez Says:

This is a cool blog!

I just wrote a little about hyperdeterminants in week298, and I found your blog to be one of the easiest ways to learn about these creatures.

2. PhilG Says:

Thank you John, you have just increased the readership of this blog by a factor of about Graham’s number.

I’m pleased that after all the things I learnt in TWF I have managed to pay back a tiny bit.

Now I will have to do some new posts in case someone has subscribed.

3. Leonel Says:

Always happy to know about new (at least to me) things in math

4. bryan l Says:

Had to come here and have a look since John said to in TWF 298.

Cool site!!

(I think i have been reading TWF’s for 12 years now !…from before the time when a blog was called a blog)

5. This blog is awesome. I am glad I found it, since it seems hyperdeterminants play some role in my research. Cheers!

• PhilG Says:

That’s great! I’d love to hear more about how hyperdeterminants appear in your research