# Presidential Endowed Chair in Mathematics

**Notebook Magazine - Spring 2018**

**University of Utah - College of Science**

Christopher Hacon, Distinguished Professor of Mathematics at the U, has been interested in math for as long as he can remember. As a child, he would spend hours on a calculator trying to count and figure out things—such as how much all the books in his house cost, or the number of seconds in a year or in a lifetime. He particularly enjoyed finding patterns and seeing relationships between numbers.

Today, Hacon has established himself as one of the world’s top mathematicians and has been recognized with numerous awards for his outstanding teaching and research.

In January, Hacon was selected as the first recipient of the McMinn Presidential Endowed Chair of Mathematics at the U. This is a 5-year endowed chair that will provide Hacon with additional research support.

“The McMinn Endowed Chair allows us to further support and promote some of the world-class, groundbreaking mathematics research that is currently being undertaken in our department,” says Davar Khoshnevisan, a professor and chair of the Math Department.

“It is befitting that the first McMinn Presidential Endowed Chair of Mathematics has been awarded to Professor Hacon. He is an internationally-recognized mathematical scientist of the highest caliber, whose work will motivate and deeply affect the next several generations of brilliant algebraic geometers,” says Khoshnevisan.

Hacon studies birational algebraic geometry. He is particularly interested in two topics: TOPIC ONE

The classification of higher-dimensional “complex projective varieties.” These are geometric objects that are described by one or more polynomial equations in many variables, and that typically exist in more than three dimensions. For comparison, consider that a simple geometric object like a sphere can be described by just one polynomial equation in three variables, and therefore exists in three-dimensional space. TOPIC TWO

Questions arising from the “minimal model program.” This is a large-scale effort by a large number of preeminent

mathematicians whose ultimate goal is to understand the properties of complex projective varieties. This is a very active field of research with origins that date back to the Italian algebraic geometers at the beginning of the 20th century.

“One of the things I love about math is that it allows me to find patterns and explain the reasons behind a certain behavior,” says Hacon. “This is really the essence of scientific discovery. All of these patterns are described by numbers. I’m fascinated by them, regardless of their origin. I’m constantly surprised by the power of math and abstract thought in general.”

Hacon admits that the problems he works on and solves typically don’t have immediate practical applications. But he believes that polynomial equations are the most natural equations to study and that proving complex theorems can help us figure out and understand solutions to concrete problems.

“We do a lot of abstract thinking in my field that the average layperson probably wouldn’t understand,” says Hacon. “But on a basic level, I hope people care about the general health of our research communities in mathematics and basic

sciences. There are tens of thousands of amazing scientists out there. It’s difficult to point out how the work of any single one of them will change our lives; however, on the whole, science and technology affect and shape our society.”

“While I have been inspired by many people, I have four mentors who have made a distinct impact in my life. They are Fabrizio Catanese and Fabio Bardelli at the University of Pisa, Robert Lazarsfeld at UCLA, and János Kollár, my postdoctoral advisor at the University of Utah, who now teaches at Princeton,” says Hacon.

Hacon hopes to inspire the next generation of mathematicians. He wants to see his students surpass his own efforts and continue to make strides in further exploring and expanding our understanding of algebraic geometry.

Editor’s Note: Hacon also was awarded a 2018 Breakthrough Prize in mathematics in December 2017. Hacon shared the $3 million award with his collaborator and colleague, James McKernan, Professor of Mathematics at the University of California San Diego.