A finite group is not determined by its order, and everyone who has ever tried to
classify one has been told this early. The order is a first approximation and a poor
one. The question this direction works on is what is available instead — in
particular, how much of a group is pinned down by where its characters vanish.
Let a character take the value zero on an element; call that element vanishing.
Collect the orders of those elements, join two primes whenever a single vanishing
element has an order divisible by both, and what is left is a graph. It is a
surprisingly rigid object: for the groups studied here, the graph forces the group
rather than merely suggesting it.
Core member. My part was the character-theoretic side — starting from the basic
properties of vanishing elements and working out what their prime graph forces. The
project is the mathematical counterpart to the rest of the research on this site: no
data, no model, and nothing that can be fixed by collecting more of it.
A paper, New characterizations of G2(3m) via its vanishing elements, jointly
first-authored, submitted in March 2025 and currently under review at the Czechoslovak
Mathematical Journal (Springer, SCIE-indexed).
Stated precisely: the title's scope is the characterisation of the Chevalley groups.
Working on the sporadic simple groups through the prime graph is the larger direction
this project belongs to; that part is still in progress and is not written here as a
finished claim.
Why this page is short
The mathematics is in the paper, and a summary of a proof written for a general
audience tends to be a summary of the statement instead. When the paper is accepted,
the link goes here.