Algebraic geometry2018
Putting limits on families of algebraic shapes
Polynomial equations define endlessly many spaces; birational geometry searches for building blocks and asks how complicated those blocks can become.
The storyAn award edition
2018
Different contributions. A shared moment in mathematics.
4 medalists — explore each contribution below.
Analysis & PDEs2018
The geometry of moving mass at minimum cost
Optimal transport compares distributions by moving mass between them, turning a question about cheapest routes into deep information about geometric regularity.
The storyAlgebraic geometry2018
A bridge between two kinds of arithmetic geometry
Perfectoid spaces let mathematicians transfer difficult geometric questions between characteristic zero and characteristic p, where different tools become available.
The storyNumber theory2018
Watching arithmetic objects spread through geometric spaces
Number-theoretic objects can become points or trajectories in a geometric space, allowing dynamics to reveal patterns that direct calculation hides.
The story