## Bhargava’s Factorials

8 February 2010

Wow. Hard to believe we’re already a week into February. I began my new year with a trip to the 2010 Joint Mathematical Meetings, and I came back with a head and several notebooks full of ideas to contemplate and problems to solve. I’ve missed my little blog here while I’ve been lost in the unexplored corners of the mathemativerse. Sad truth that, until and unless I am tenured, I can’t afford to pass up any opportunities for research; I do have a family to think of. I haven’t been around here for a while, and I’m sorry for that. But today’s post should be a doozy.

Our topic for today comes from this year’s JMM, where the inimitable Manjul Bhargava gave an MAA invited address on factorial functions. (Coincidentally, I first learned about the topic of his talk when I read an article of his, reprinted in the charming book Biscuits of Number Theory, which I bought at the 2009 JMM.)

Wait a minute, factorial functions? That’s what gets talked about at the biggest math conference of the year, where people on the cutting edge of research mathematics get together, factorials? The ones you learned about in high school? Can there really be more to learn about $n!$?

Amazingly enough, yes. In a conference full of zonotopal algebra and cohomology and harmonic analysis, one of the invited addresses was about factorials. And it turns out that there is more to learn; factorials are really just the tip of an enormous iceberg.