Juan Esteban Rodríguez Camargo, Ph.D.

Juan Esteban Rodríguez Camargo’s main area of research is arithmetic geometry, focused on the cohomology of Shimura varieties. He uses tools from condensed mathematics, representation theory and p-adic Hodge theory to understand the deeply involved relation between automorphic forms and Galois representations. During his Ph.D. thesis, in a joint work with J. Rodrigues Jacinto, he developed the theory of solid locally analytic representations via condensed mathematics. He used this tool to construct a geometric Sen operator in p-adic Hodge theory for rigid spaces, which allowed him to relate p-adic automorphic forms with representation theory and arithmetic. In his future work, he will continue the development of the theory of solid locally analytic representations and find more applications to the p-adic local Langlands program.