Open problems
These problems are mostly original, and (of course) reflect my
personal taste.
But I have tried to sample different topics.
New (5/10) A broad class of open problems, suitable for thesis topics,
concerns
I categorize problems on a conceptual-technical spectrum.
That is
- Type 1
We have a question in words, but we don't know how to state
a precise mathematical problem
which both seems capable of solution and whose solution would be interesting.
- Type 2
We have
a precise mathematical problem,
but we do not see any plausible outline for a potential proof.
- Type 3
We have
a precise mathematical problem,
and a plausible outline for a potential proof,
but we cannot carry through the technical details.
Of course these overlap.
Continuize by taking "type 2" in the middle of an inteval 1.5 - 2.5.
Then we can order the problems across this spectrum.
In a different realm, I
really
really
really
want
someone to do this simulation.
Of course, it's not easy!
Also, pages 9-12 of Lecture 3 in these
Local weak convergence of random graphs and networks lectures
give a "recursive distributional equation" I would like someone to solve numerically.
Former open problems, now solved or irrelevant.