This following is a brief summary of our research meeting on 2024-07-02.

What happened

I gave a overview of our plan for the summer. See the Summer REU 2024#Project timeline for a quick summary. I then gave a brief (possibly incoherent) condensed preview of our ultimate goal: a duality for tropical projective plane conics.

Our first goal: learn the duality map for classical projective plane conics.

Step 1: Learn the foundations of algebraic geometry, focusing on:
- affine varieties
- the algebra-geometry correspondence
- the projective plane
- projective plane curves

Tasks for next meeting

• Read Section 1.1 in Cox, Little, Oshea - Ideals, Varieties, and Algorithms
• Read Section 1.2 in Cox, Little, Oshea - Ideals, Varieties, and Algorithms
• Work through the following exercises:
  - Section 1.2: 1, 3, 4abd, 6, 8, 15abc