Algebraic Geometry and the Shape of the Universe

The Research Trajectory of Andrew Harder

Algebraic geometry is one of the most abstract and far-reaching areas of modern mathematics, with strong connections to other fields. For researcher Andrew Harder, it offers both a framework for mathematical exploration and a link to contemporary physics. His work focuses on Calabi-Yau varieties—complex geometric shapes defined by polynomial equations—that are key to efforts to understanding the universe at its most fundamental level.

At the heart of his inquiry lies a deceptively simple yet far-reaching question: Are there finitely many Calabi-Yau spaces? The implications of this question extend beyond pure mathematics. Calabi-Yau spaces have profound significance in theoretical models that attempt to describe the fundamental structure of the universe. If there are finitely many such spaces, it would suggest that the ways in which the underlying geometry of the universe can be configured are themselves limited, imposing fundamental constraints on the nature of physical reality.

Read the full story on the College of Arts and Sciences News.