A University of Nebraska–Lincoln mathematician has received the department’s first-ever Faculty Early Career Development Program award from the National Science Foundation.

Jack Jeffries, assistant professor of mathematics, will use the $400,000, five-year grant to advance his research in commutative algebra, a field of abstract algebra that, at its heart, is focused on polynomials in many variables. More specifically, he will study singularities — points at which a mathematical object, or geometrical shape, is not “well-behaved” in some way — using differential operators and p-derivations.

“Systems of polynomial equations are ubiquitous throughout the sciences,” Jeffries said. “Singular points are of interest because many standard techniques and algorithms can go haywire at those points.”

Jeffries focuses on the solution sets of polynomial equations, a particular type of algebraic expression involving variables, coefficients and non-negative exponents. Over the most familiar number systems — real numbers and complex numbers — the solution sets to these types of equations can be visualized geometrically via Cartesian coordinates on the x- and y-axis. Each polynomial equation has a solution set that “cuts out” a geometric shape.

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https://news.unl.edu/newsrooms/today/article/jeffries-career-award-bolsters-nebraskas-mathematics-expertise/