PROJECT GROUPS

Computing the Cartier operator acting on 1-forms

PEOPLE: Rachel P., Aly, Gagan, Anja, Sarah, Marina, Kate

• See this page.

• sage worksheet that is slow and just implements algorithm (correctly!)
• make it really, really fast.
• get included in sage itself
• make a big table or something? Rachel: "I would love to find a curve with p-rank 0 and a-number 1. I did genus 4 and p=3."

Making Drew Sutherland's smalljac code usable in Sage and extending Kate's data

PEOPLE: Kate, William S., Lola, Aly, Erin, Bianca

• make code usable from Python (involves Cython); see this psage issue.

• use code:
  • - replicate and extend data in Kate's talk - maybe try genus 2 analogue?
• possibly implement cubic and sextic residue symbol. make it really really fast, even if it is implemented, since Kate wants lots of data.
• explicit calculation of Grossencharacters.

Computing L-series of Jacobians of Certain Hyperelliptic Curves

PEOPLE: Jennifer B., Jennifer P., Jennifer J.

• Decide if curve is attached to a modular form, and if so find it, then use that to compute L-series.
• Plug L-series into Dokchitser and get numbers.

• Make a table. Starting with "van Wamelen"'s table. See also Kohel's tables.

Computing in the class group of non-maximal orders of quadratic imaginary fields

PEOPLE: William S., Bianca,

• Make a list of what you want to be able to do
• List why Magma/PARI aren't good enough (bugs, issues, speed, etc.)
• Write really really fast code to implement some of this.