Since the focus since our last meeting was to prepare for yesterday's "share out", we didn't cover any new developments in our current research. The only new thing mentioned was a feature called the "twisted product" for pairs of tropical polynomials, but that's something we'll talk about more when we focus on the second proposal, below.

Proposals

Our goal for the next few weeks is to take a two-prong approach.

1. Peek "under the hood" of the argument for classical conic duality. We should be able to follow one (or more) of the general strategies that (in the classical case) let's one deduce the formula for the dual curve.
2. Work on finding equations for the dual loci, so that we have something to test against (and can start looking for patterns or insights).

For Tuesday's meeting, we'll focus just on the first task.

Tasks for next meeting

• Skim through this paper on "enumerative algebraic geometry," focusing especially on pages 712-715.
• Try writing up a summary in your own words of the theory/steps that let's one deduce the equation for the dual conic.
• Start thinking about how the analogous analysis will look in the tropical setting.
  • What constructions or results will need tropical analogues?
  • Can you try investigating a specific tropical example (or two)?