This talk studies how p-adic Hodge-theoretic invariants vary in families near rank-1 points of adic spaces. I will begin with joint work with Tong Liu, Yong Suk Moon, and Koji Shimizu establishing a purity theorem for semistable p-adic local systems. I will then outline a geometric approach via vector bundles on the relative Fargues–Fontaine curve. In ongoing work, we investigate how these vector bundles vary in neighborhoods of rank-1 points.

Speaker Biography: Du Heng, Ph.D., graduated from Purdue University and currently serves as an Assistant Professor at the Center for Mathematical Sciences, Tsinghua University. Research focuses on number theory and p-adic Hodge theory.