09-23-2026, 02:46 PM
The article profiles Dhruv Ranganathan, a Cambridge professor of algebraic geometry who won the 2026 London Mathematical Society Whitehead Prize. His research combines algebraic geometry, moduli spaces, and log geometry. The article explains how algebraic varieties—geometric shapes described by polynomial equations—can be studied through numerical and counting problems.
For example, the bitangent problem asks how many lines can touch a curve at two points; such counts can reveal important information about the underlying geometric object. Moduli spaces take this idea further by treating all possible configurations of an object themselves as a geometric space.
The central metaphor of Ranganathan's work is “shattering” a complicated geometric object into simpler pieces. In log geometry, one can study what happens when changing the coefficients of polynomial equations causes a variety to break into simpler components; tropical geometry then provides tools for understanding how those pieces can be reassembled.
Ranganathan has applied these ideas to major theories such as Gromov–Witten and Donaldson–Thomas theory, helping demonstrate connections between approaches that initially look very different. The article presents this as a powerful strategy for turning difficult problems about complicated geometric spaces into more manageable problems about their simpler pieces.
ARTICLE
For example, the bitangent problem asks how many lines can touch a curve at two points; such counts can reveal important information about the underlying geometric object. Moduli spaces take this idea further by treating all possible configurations of an object themselves as a geometric space.
The central metaphor of Ranganathan's work is “shattering” a complicated geometric object into simpler pieces. In log geometry, one can study what happens when changing the coefficients of polynomial equations causes a variety to break into simpler components; tropical geometry then provides tools for understanding how those pieces can be reassembled.
Ranganathan has applied these ideas to major theories such as Gromov–Witten and Donaldson–Thomas theory, helping demonstrate connections between approaches that initially look very different. The article presents this as a powerful strategy for turning difficult problems about complicated geometric spaces into more manageable problems about their simpler pieces.
ARTICLE
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