Engagement photo

I am a PhD student in the Department of Mathematics at the University of Georgia, where I study algebraic geometry under the direction of Valery Alexeev.

I study moduli spaces of algebraic varieties, with current emphasis on compactifications and universal families. Much of my recent work focuses on KSBA compactifications of marked surface pairs, especially marked cubic surfaces and related del Pezzo surfaces.

I am interested in how geometric constructions on algebraic varieties extend to universal families and how these constructions affect the moduli spaces. I am particularly interested in explicit descriptions of moduli spaces and the families they carry.

At the moment, my main project studies the universal family over a weighted KSBA compactification of the moduli space of marked cubic surfaces. The project focuses on understanding how geometric constructions on smooth cubic surfaces extend across the compactification and what this tells us about the universal family.

On this site, you can find information about my research, teaching, notes, and other mathematical interests.


Kaden Saucedo