# Being (re)born(-again)

I wasn’t around these parts much yesterday for a number of reasons: I spent the better part of the midday on campus, splitting time between campus errands, meeting with one professor about the stuff he’s working on, and parsing through another professor‘s latest research paper; the times around that were being occupied by birthday things because yesterday was the twenty-seventh annual celebration of my being birthed.

That’s right: I’m 27 now, which means – among other things – that I have fewer than 365 days (I’m not sure exactly how many) to supplant Jean-Pierre Serre as the youngest Fields Medal winner. Not a good feeling for a just-blossoming mathematician. Le sigh.

I guess the good news is that I have 13 years to maybe squeeze one in there. Thirteen years…that’s 4,747 days from today. That makes it seem like I have plenty of time to work!

</forced optimism>

In any case…

The paper I’m reading is on the behavior of M-conformal mappings taking values in a Clifford algebra $\mathcal{C}\ell_{m,n}$ over $\mathbb{R}$. I’m gonna take a second to discuss some of the preliminaries of that topic and to maybe outline the proof of a basic assertion that’s generally considered general knowledge among those in the know. Worth noting is that the background of Clifford Algebras (and hence of the analysis of functions thereon) extends far more deeply than discussed here and so this should in no way be taken as an actual, worthwhile exposition on the ease/difficulty of the topic.