When Christopher Hacon won the celebrated Breakthrough Prize in 2018, his work was described as extending a foundational principle of geometry into higher dimensions. The award is designed to honor scientists as heroes of our society, to inspire the next generation and to champion science as a global, apolitical endeavor.

International stature

Now the incoming Chair of the Department of Mathematics at the University of Utah, Hacon brings that same ambition to a new role, this time as an ambassador of math and science at the U and beyond. The appointment, according to outgoing chair Tommaso de Fernex, could not be more fortuitous. "His international stature in the field of algebraic geometry is immense," De Fernex says of his colleague, "marked by revolutionary research and a prominent global standing" further reflected in numerous prestigious awards, distinguished memberships and service to the profession in several prominent roles.

And yet, de Fernex continues, Hacon "is equally defined by his exceptional departmental citizenship and humble leadership, . . . choosing to dedicate his career to this university despite competing offers from several top institutions."

That same grounding carries into how Hacon thinks about his work. He describes his research in the language of curiosity and incremental understanding. He admits to spending "countless hours trying to prove algebraic lemmas and theorems, and most of the time getting it wrong and having to start from scratch." His intuition comes from abstract pictures in his mind that try to capture a few key elements of a problem before the real work of proof-writing, the algebraic part of doing what he does, begins. That blend of imagination and rigorous logic—the visual and the algebraic working in tandem—sits at the heart of his field.

Two-holed donut

Algebraic geometry uses algebra to define curves, surfaces and high-dimensional spaces, studying the geometry of zero sets of polynomials. What this means is that geometric shapes can be perfectly defined and analyzed by finding where polynomial equations equal zero. Since the Breakthrough Prize, Hacon has focused particularly on moduli spaces: the systematic cataloguing of all possible shapes within a given class, such as identifying the precise number of parameters needed to fully describe every possible two-holed donut.

A central open question driving this work is whether the number of possible shapes in high dimensions is finite or infinite. He and others conjecture finiteness, and have proved it in most cases, but a complete proof remains elusive. His research also reaches into theoretical physics, where the mathematical operation known as a "flop,” one of the topics for which he won the prize, describes how the hidden six-dimensional structures of the universe might transition from one shape to another.

As for his new role, Hacon's aspirations are modest and duty-driven. He'll scale back teaching and hopes to maintain research, but his primary goal is simply to give back to a department that has served him well. He aspires to do as good a job as his predecessors and leave the math department in as good a shape as he found it. It's less a grand transformational agenda than a quiet expression of stewardship and gratitude.

Dean of the College of Science Pearl Sandick applauds that approach. “Christopher is an incredible mathematician who has profoundly shaped the math program at the U. I’m looking forward to working with him as a new department chair. ”  

For Christopher Hacon who has spent nearly three decades at Utah—as post-doctoral researcher and faculty—the appointment to chair feels less like an arrival than a natural continuation, the work of building something that outlasts any single result. To quote him from his 2018 Breakthrough Prize: "this work is the culmination of sustained efforts by many brilliant mathematicians."

By David Pace