Research

Current doctoral research

From Existence to Equations

An existence theorem may guarantee that a mathematical object exists without providing a way to construct it. My research studies this gap in algebraic geometry: how to turn abstractly known algebraic surfaces into explicit equations that can be computed and studied.

I develop computational methods for finding defining equations of algebraic surfaces embedded in projective space, bridging abstract algebraic geometry with symbolic computation.

Fake Projective Planes

Fake projective planes form a class of complex algebraic surfaces whose first example was constructed by David Mumford in 1979. Later work classified further examples, but realizing these abstractly known surfaces in chosen projective coordinates requires substantial additional computation.

Related work: Finding equations of the fake projective plane (C18, p=3, {2I}).