Professor Alessandro Neri (University of Naples Federico II)
will speak on
After the counterexample: What remains of the Etzion–Silberstein conjecture?
Time: 2:00PM
Date: Wed 9th September 2026
Location: N0.20 - Science North
[map]
Abstract: The Etzion–Silberstein conjecture has been a central existence problem for optimal Ferrers diagram rank-metric codes for more than fifteen years. Recent work on reducibility and irreducible Ferrers diagrams has significantly clarified the structure of the problem, reducing a seemingly vast collection of cases to a much smaller and more structured family.
Very recently, a counterexample found by Prajapati (arXiv:2608.08478), with a wide use of AI, showed that the conjecture, in its original form, is false. Rather than closing the problem, however, this development opens a new phase: How much of the conjecture survives? Where and why can counterexamples occur? What is the actual boundary between existence and non-existence?
In this talk I will survey the current state of the problem, describe recent progress obtained with Hugo Beeloo-Sauerbier Couvée and subsequent developments, and discuss what the counterexample tells us about the remaining picture.
(This talk is part of the Discrete Mathematics series.)
PDF notice
Return to all seminars