Algebra, Algebraic Geometry, Number Theory
Algebra and Number Theory have been mainstays of mathematical research and interest for centuries. A combination of techniques and tools from commutative algebra with motivation and language from geometry has made Algebraic Geometry one of the most exciting and active fields of research in modern mathematics. Ideas from Algebraic Geometry now help inform developments in a range of disciplines from Topology to Cryptography and classical Number Theory.
My research in number theory is motivated by the study of special values of L-functions, and in particular the equivariant Tamagawa number conjecture. The general conjecture is an elegant, yet powerful, statement which implies, among other things, the Birch and Swinnerton-Dyer conjecture and Stark's conjecture.
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