#introductions I'm interested most seriously in math--analysis more than algebra, learning lately about combinatorial/incidence geometry (e.g. the Erdős distinct-distance problem)--and programming--mostly in Haskell, although I'm curious about C and systems-level things as well. On the amateur plane I like classical music and read haphazardly in the s-f/litfic/poetry space. I try to learn from the example of people who're more knowledgeable or skillful than I am.

@Breakfastisready it asks: if Δ is the set of distances between points of a set of N points in the plane, how small can Δ be in terms of N? It's easy to get as few as O(N) distances, while the best known examples only achieve O(N/√log N), but for a long time after Erdős the only improvements to the lower bound were to O(N^η) for various η < 1. In 2011 Larry Guth and Nets Katz got a lower bound of O(N/log N) using an unexpected reframing of the problem in terms of intersections of lines in R³.

@hexbienium

That's cool.

Are you a PhD student?

@Breakfastisready undergrad! This was the topic of an REU

@hexbienium So I was just wondering, \( O(N) )\ is just by arranging the points in a line, right?

@hexbienium Sorry, still learning Latex usage.

\( O(N) \)

@Breakfastisready exactly! Or a circle.

Breakfastisready@Breakfastisready@mathstodon.xyz@hexbienium

What's the Distinct distance problem?