768 reputation
412
bio website math.dartmouth.edu/~jvoight
location Dartmouth College
age
visits member for 4 years, 1 month
seen Apr 10 at 21:32

Apr
9
accepted Infinite dimensional simple algebras of finite degree
Apr
7
asked Infinite dimensional simple algebras of finite degree
Mar
12
comment Totally real points on curves
Cool, thank you very much!
Mar
11
asked Totally real points on curves
Mar
11
answered Explicit isomorphism for quaternion algebras over $\mathbb{Q}$?
Mar
10
awarded  Yearling
Mar
9
awarded  Revival
Mar
9
answered An application of Strong Approximation
Mar
7
answered Integral elements of quaternion algebras with predescribed properties
Dec
10
comment Finiteness conditions and Veronese subrings
The hypothesis that $R$ is a domain is crucial. Take $R=k[x_2,x_3,x_5,x_7,\dots]/I$ where $I$ contains every binomial $x_ix_j-x_2^{(i+j)/2}$ for $i,j \geq 3$ odd. Then $G=\mathbb{Z}/2\mathbb{Z}$ acts $R$ by $x_j \mapsto (-1)^j x_j$; the invariants are $R^G \cong k[x_2]$, but $R$ is not finitely generated (has generators in every odd degree $\geq 3$). $R$ has plenty of zerodivisors, e.g., $x_5(x_5-x_2x_3)=0$.
Nov
28
awarded  Commentator
Nov
28
comment Is there an algorithm to compute efficiently the dessin d'enfant from a Belyi pair?
If instead you are given the finite index subgroup (or equivalently, the permutation triple), then it is much easier to write down the combinatorial-topological data given by the dessin as a graph: it is explained in Chapter 4 of Girondo, Gonzalez-Diez "Introduction to Compact Riemann Surfaces and Dessins d'Enfants", and presumably elsewhere: you just read off the dessin from the monodromy. In fact, you can do this in a conformally correct way on the desired surface: see another one of my preprints (arxiv.org/abs/1311.2081), where there are lots of pictures.
Nov
28
comment Is there an algorithm to compute efficiently the dessin d'enfant from a Belyi pair?
Hopefully our preprint (arxiv.org/abs/1311.2529) addresses your question. If you are given equations, you "just" need to do some numerical homotopy: choose a base point and trace the preimages of loops on the curve around 0, 1, oo. This has been implemented by Kroeker (github.com/jakobkroeker/HMAC) and Bartholdi (github.com/laurentbartholdi/img). I don't think Bertini or PHCPack will give this to you directly, though they are similar in spirit.
Nov
27
awarded  Nice Answer
Nov
27
awarded  Yearling
Nov
27
answered Which quaternion algebras have class number one?
Nov
16
awarded  Popular Question
Jul
3
awarded  Necromancer
Jul
2
answered Explicit description of a quaternion algebra with a prescribed set of ramified places
May
4
awarded  Teacher