Arithmetic geometry explores deep connections between number theory and geometry by investigating solutions to polynomial equations over various fields. The subject has expanded to include the study ...

Algebraic geometry; commutative algebra; homological algebra; algebraic K-theory. My research has been mainly in algebraic geometry, with an abiding interest in the study of algebraic cycles, ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...