COSAM News Articles 2023 May Auburn mathematician uses $220,000 NSF award for research in commutative algebra and algebraic geometry

Auburn mathematician uses $220,000 NSF award for research in commutative algebra and algebraic geometry

Published: 05/23/2023

By: Maria Gebhardt

Michael Brown, an assistant professor in the Department of Mathematics and Statistics, is the recipient of his first National Science Foundation, or NSF, award for $220,000 in commutative algebra and algebraic geometry. He will attempt a broad generalization of a 1984 breakthrough theorem on the equations defining projective curves.

“Algebraic geometry is the study of spaces, called algebraic varieties, that arise as solutions sets to systems of polynomial equations.” Brown said. “Algebraic varieties are ubiquitous throughout mathematics and the sciences. A fundamental question, which goes back to the origins of mathematics, is: to what extent can one determine the equations defining an algebraic variety by studying its geometric properties? This NSF award will support continued progress on this classical line of inquiry.”

This line of research plays an important role in real-world applications of algebraic geometry.

“The way a computer understands an algebraic variety is through equations that define it,” he said. “So progress in this direction helps leverage computational techniques in applications of algebraic geometry.”

He will be studying a generalization of a 1984 theorem in this vein due to Mark Green.

“Green proved a surprising structure theorem for the polynomials defining a certain kind of algebraic variety called a projective curve. Green’s result launched an entire subfield at the interface of commutative algebra and algebraic geometry, which is now called the geometry of syzygies,” Brown said. “The goal of the project I’m working on is to use recent advances in commutative algebra and algebraic geometry to extend this landmark theorem beyond projective curves to new families of algebraic varieties.”

Brown graduated with his doctorate from the University of Nebraska-Lincoln. He then completed a postdoctoral research position at the Hausdorff Center for Mathematics in Bonn, Germany. Afterwards, he finished a postdoctoral research position at the University of Wisconsin-Madison.

Three years ago, he moved to the Plains.

“I love living in Auburn,” Brown added. “The family-friendly atmosphere is perfect for my wife and four-year-old son.”

A Wisconsin native, Brown is a Green Bay Packers fan. He is also an avid reader.

“Coming to Auburn, I found the Department of Mathematics and Statistics to be a very friendly and supportive place to work,” Brown said. “I really enjoy being part of the Auburn Family.”