Filled-in example

A proposal, field by field.

This example is fictional and shows the level of detail that helps the triage. You don't need to write this much, or know any AI, to fill in the form.

Fictional example

01About you

Full name: Maria Exemplo
Email: maria@example.org (email of the CBG website account)
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Institution: Example University
Career stage: Faculty or researcher
Main area: Discrete and convex geometry
Are you a member of CBG?: No
Tip Since the automatic standardization consumes tokens, CBG members have priority in the allocation of these resources. Proposals from non-members are just as welcome.

02Your interest

What are you looking for?: I have a concrete problem to propose
I'd also like: an invitation to the MathIA AmLat channel on Zulip

03The problem

Working title: Mapping the local minima of the Thomson problem for n points on the sphere
a) Summary of the state of the art: The Thomson problem asks for the position of n unit charges on the sphere S² that minimises the Coulomb energy E = Σ_i<j 1/|x_i − x_j|. Optimality proofs exist only for a few small values of n; for larger values there are tables of numerically obtained configurations, with no proof that they are optimal. Numerical experiments suggest that the number of local minima grows very fast with n, which makes it hard to know whether the best known configuration is really optimal. The main references would be [the two or three I would point a colleague to].
Tip It doesn't need to be exhaustive. The essentials are enough, with the references you would give a colleague from another field.
b) Your approach: I have Python code that runs gradient descent from random configurations and stores the local minima it finds, about 50,000 so far for n ≤ 200. I suspect that the symmetry group of the final configuration is linked to its energy, but I don't know how to explore this systematically. I would like to understand whether machine learning could (1) predict, from simple invariants, which minima have lower energy and (2) propose candidate configurations for the values of n where the tables seem to have gaps.
Tip Say what you have already tried and what would count as a useful result for you.
PDF attachment: thomson-notes.pdf, with 4 pages of definitions, a table of minima and plots
What kind of help do you have in mind?: Predict · Search
Do examples or data exist?: I can generate many examples by computer
Your programming experience: Some (Python, Sage, Mathematica…)

04To finish

Preferred language for our conversation: Portuguese
Anything else?: I can share the code and the database of local minima.
Consents: ✓ Use of data under the LGPD · ✓ Aware that language models are used in the triage

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