Cristian Popescu
Encyclopedia
Cristian Dumitru Popescu is a Romanian-American
mathematician at the University of California, San Diego
. His research interests are in Algebraic Number Theory
, and in particular, in special values of L-functions
. He formulated and proved function-field versions of the Gras conjectures and Rubin's
integral refinement of the abelian Stark conjectures. He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's conjecture. Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension. Recently, Popescu and Cornelius Greither have formulated equivariant versions of Iwasawa's main conjecture over function fields and global fields, proving most the version for function fields. These conjectures have important implications for the Brumer–Stark conjecture and Gross' conjecture on special values of L-functions.
Romanian-American
A Romanian American is a citizen of the United States who has significant Romanian heritage. For the 2000 US Census, 367,310 Americans indicated Romanian as their first ancestry, while 462,526 persons declared to have Romanian ancestry...
mathematician at the University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
. His research interests are in Algebraic Number Theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...
, and in particular, in special values of L-functions
Special values of L-functions
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely...
. He formulated and proved function-field versions of the Gras conjectures and Rubin's
Karl Rubin
Karl Rubin is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. His research interest is in elliptic curves. He was the first mathematician to show that some elliptic curves over the rationals have finite Tate-Shafarevich groups...
integral refinement of the abelian Stark conjectures. He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's conjecture. Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension. Recently, Popescu and Cornelius Greither have formulated equivariant versions of Iwasawa's main conjecture over function fields and global fields, proving most the version for function fields. These conjectures have important implications for the Brumer–Stark conjecture and Gross' conjecture on special values of L-functions.