Hilton Memorial Lecture: This lecture series was established in memory of Peter Hilton (1923-2010), a distinguished member of the Binghamton Mathematics Department from 1982 until his passing in November 2010. An internationally renowned mathematician, Hilton played a significant role in the code-breaking operations at Bletchley Park during World War II, working alongside Alan Turing. His research contributions spanned topology, homological algebra, elementary number theory, combinatorics, and polyhedral geometry. Additionally, he made substantial contributions to mathematics education at all levels.