Murilo Zanarella

Murilo Zanarella is an Assistant Professor in the Department of Mathematics at Johns Hopkins University's Krieger School of Arts and Sciences. He maintains active research collaborations with the Institute for Advanced Study and Princeton University, regularly presenting his work at the Joint PU/IAS Number Theory seminars.

Dr. Zanarella's research focuses on advanced topics in number theory, particularly Galois representations attached to automorphic forms on unitary groups. His work centers on explicit reciprocity laws, Friedberg-Jacquet periods, and applications to the Bloch-Kato conjecture. He has developed novel approaches to overcome challenges posed by the lack of local multiplicity one in unitary group representations. His research bridges classical number theory techniques with modern developments in arithmetic geometry and representation theory.

Analysis of his recent publications reveals a consistent pattern of advancing the understanding of bipartite Euler systems and their applications to Selmer groups. His work spans multiple specialized areas within number theory, with particular emphasis on unitary groups over CM fields, Rankin-Selberg constructions, and symmetric cube representations. This research trajectory demonstrates increasing technical sophistication and impact in addressing fundamental questions in arithmetic geometry.

• Number Theory
• Automorphic Forms
• Galois Representations
• Unitary Groups
• Bloch-Kato Conjecture
• Iwasawa Theory

Dr. Zanarella maintains an active research program with approximately 2-3 significant publications per year. His work has established connections between different approaches to bounding Selmer groups and has provided new insights into the arithmetic properties of unitary group representations. Through his collaborations with researchers at Princeton and the Institute for Advanced Study, he contributes to one of the most active areas of contemporary number theory research.

His research environment benefits from connections to major mathematical centers, providing opportunities for students and collaborators to engage with cutting-edge developments in the field. The theoretical frameworks he develops have implications for understanding deep arithmetic properties of algebraic varieties and their associated L-functions.