  In 1988, Fujita conjectured that there is an effective and uniform way to
turn an ample line bundle on a smooth projective variety into a globally
generated or very ample line bundle. We study Fujita's conjecture using
Seshadri constants, which were first introduced by Demailly in 1992 with the
hope that they could be used to prove cases of Fujita's conjecture. While
examples of Miranda seemed to indicate that Seshadri constants could not be
used to prove Fujita's conjecture, we present a new approach to Fujita's
conjecture using Seshadri constants and positive characteristic methods. Our
technique recovers some known results toward Fujita's conjecture over the
complex numbers, without the use of vanishing theorems, and proves new results
for complex varieties with singularities. Instead of vanishing theorems, we use
positive characteristic techniques related to the Frobenius-Seshadri constants
introduced by Musta\c{t}\u{a}-Schwede and the author. As an application of our
results, we give a characterization of projective space using Seshadri
constants in positive characteristic, which was proved in characteristic zero
by Bauer and Szemberg.
