The 1994 doctoral thesis completed by Eric Jean-Paul Urban under the supervision of Jacques Tilouine at the University of Paris-Sud marked his formal entry into the field of number theory. Currently serving as a professor of mathematics at Columbia University, Urban specializes in automorphic forms and Iwasawa theory, contributing to the advancement of modern mathematical proofs.
Academic Foundations and Career
Urban pursued his graduate studies in France, obtaining his PhD in 1994. Since completing his education, he has transitioned into academia, holding a professorial position at Columbia University. His professional focus remains within the department of mathematics, where his research contributes to the global discourse on number theory and related disciplines.
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Take the IQ test →Contributions to Iwasawa Theory
The research conducted by Urban involves the Iwasawa-Greenberg main conjectures. Collaborating with Christopher Skinner, he successfully demonstrated these conjectures for an extensive class of modular forms.
Elliptic Curves and the Birch-Swinnerton-Dyer Conjecture
Urban’s work extends to the Birch-Swinnerton-Dyer conjecture, providing a conditional proof that connects the L-function to the existence of infinitely many rational points on elliptic curves. By integrating these results with earlier theorems by Gross-Zagier and Kolyvagin, he contributed to evidence suggesting a significant proportion of elliptic curves satisfy the requirements of this longstanding conjecture.
Recognition and Publication
His academic output includes papers published in journals such as Annals of Mathematics and Inventiones Mathematicae. In 2011, he authored Eigenvarieties for reductive groups, and in 2014, he co-authored The Iwasawa Main Conjectures for GL2 with Christopher Skinner. In recognition of his research efforts, he was granted a Guggenheim Fellowship in 2007.
Fast facts
- Born: 2000
- Citizenship: France
- Field: Applied Mathematics
- PhD Advisor: Jacques Tilouine
- Current Employer: Columbia University
- Award: Guggenheim Fellowship (2007)
Questions readers ask
What is Eric Urban's primary area of study?
He specializes in number theory, automorphic forms, and Iwasawa theory.
Where does Eric Urban teach?
He is a professor of mathematics at Columbia University.
Achievements
- Held posts at Columbia University
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