(13:30~14:30 강연, 14:30-15:00 질의응답)

Title. Sharp threshold for universality of cokernels of random matrices over the p-adic integers
Abstract. In this talk, we present a sharp universality theorem for cokernels of classical random matrix models over the ring of p-adic integers Z_p. For nonsymmetric, symmetric, and alternating models satisfying a balanced condition at scale (clogn)/n, universality holds for every c>1 and fails at c=1, showing that the threshold is sharp. We also improve the universality result for sandpile groups of Erdős–Rényi random graphs. The proof is based on a unified framework that applies to all three random matrix models and the random graph model. This talk is based on joint work with Jiwan Jung and Myungjun Yu.