Doctoral research
Timeline
Timeline
A long-term line of research on the Collatz conjecture: encoding its dynamics as a symbolic system and, from there, proving exact results —from the Fibonacci theorem to the characterization of the cycles—. This timeline gathers the milestones along the way. I carry it out part-time, alongside my teaching, over a seven-year horizon (2026–2033) extendable to 2035.
2026
Apr 2026
Start of the PhD in Applied Mathematics (UPC), part-time, advised by Dr. Jaume Franch.
May 2026
Paper 1 — Fibonacci theorem for Collatz trajectories: arXiv preprint (2606.02621), submitted to Indagationes Mathematicae.
Jun 2026Now
Now: preparing Paper 2 (the $h_m=4$ conjecture and fiber growth).
2027
2028
2029
2030
2031
2032
2033
2033
Thesis deposit and defence (planned).
2034
2035
2035
Maximum limit with extension (only if it needs lengthening).