# My mathematical genealogy

##### June 11, 2009 general

- Luca Pacioli
- Domenico Maria Novara da Ferrara
- Nicolaus Copernicus
- Georg Joachim von Leuchen Rheticus
- Caspar Peucer
- Salomon Alberti
- Ernestus Hettenbach
- Ambrosius Rhodius
- Christoph Notnagel
- Johann Andreas Quenstedt
- Michael Walther, Jr.
- Johann Pasch
- Johann Andreas Planer who doesn’t have a Wikipedia page
- Christian August Hausen
- Abraham Gotthelf Kästner
- Johann Friedrich Pfaff
- Carl Friedrich Gauss
- Christian Ludwig Gerling
- Julius Plücker
- C. Felix (Christian) Klein
- William Edward Story
- Solomon Lefschetz
- Norman Earl Steenrod
- George William Whitehead, Jr.
- John Coleman Moore
- William Browder
- Sylvain Edward Cappell
- Shmuel Aaron Weinberger

There are some branches to choose among, but I think the branch starting with Pacioli is the most appropriate.

# Growth series.

##### November 30, 2006 general

In seminar today, Okun pointed out the following interesting observation; for any finitely generated group , you can define its growth series , where is the length of the shortest word for . The first observation is that is often a rational function, in which case makes sense. The second observation is that is “often” equal to . This is an example of weighted cohomology.

Grigorchuk’s group (and generally any group with intermediate (i.e., subexponential but not polynomial) growth) does *not* have a rational growth function; the coefficients in a power series for a rational function grow either polynomially or exponentially. This observation appears in [1]. More significantly, this paper constructs groups which, being nilpotent, have polynomial growth, but nonetheless have generating sets for which that the corresponding growth series is not rational.

[1] M. Stoll, Rational and transcendental growth series for the higher Heisenberg groups, Invent. Math. 126 (1996) 85–109.

# Research Blog

##### March 5, 2006 general

I’ve been thinking for a while that I ought to start a research blog–something just to keep myself organized about the things I am thinking about, my thoughts on the papers I’ve read, my ideas, my questions. I figure I might as well make it public, though I seriously doubt anyone is going to read this.

Anyway, hence this blog. We’ll see how it works.