We shall discuss Legendre Pairs, an interesting combinatorial object related to the Hadamard conjecture. We shall demonstrate the exceptional versatility of Legendre Pairs, as they admit several different formulations via concepts from disparate areas of Mathematics and Computer Science. We shall mention old and new results and conjectures within the past 20+ years, as well as potential future avenues for investigation.

The video of this talk is available on the IISc Math Department channel.