This following is a brief summary of our research meeting on 2024-08-23.

Aaron outlined his findings on the intersections between quadratic congruence varieties and linear congruence varieties. I will add his discoveries (and much more!) to this wiki over the next week or so.

I then talked about some challenges tracking down results in tropical geometry (e.g., competing notions, incoherent papers, etc.), and talked about a promising notion of rank for tropical matrices that might help us detect/understand intersections of tropical curves (at least bend loci, perhaps). Unfortunately, there are many competing notions of rank for tropical matrices (including a fancy new notion called the ultimate rank), so further investigation is needed. We will save that for future investigators, though.

Instead, we will start to wrap up our work this summer and focus on creating a poster summarizing our project, what we found, and what some possible next steps might be.

Tasks for next meeting

• Put together a draft of a research poster for this project. It doesn't have to be perfect. We'll make edits and finalize things at our next meeting.