• 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.

In seminar today, Okun pointed out the following interesting observation; for any finitely generated group $G$, you can define its growth series $G(t) = \sum_{g \in G} t^{\ell(g)}$, where $\ell(g)$ is the length of the shortest word for $g$. The first observation is that $G(t)$ is often a rational function, in which case $G(1)$ makes sense. The second observation is that $G(1)$ is “often” equal to $\chi(G)$. This is an example of weighted $L^2$ 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

Stoll, Michael. Rational and transcendental growth series for the higher Heisenberg groups. Invent. Math. 1996. 85–109. MR.

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.

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.