Hartford, CT, September 30, 2014 – The research by David Cruz-Uribe, professor of mathematics, can be difficult to understand if you don’t also have a Ph.D. in mathematics. Recently, though, Cruz-Uribe was inspired by the work of a colleague to collaborate with his undergraduate students. He’s now doing just that, and has been awarded a grant of $105,772 by the National Science Foundation (NSF) for his work.

Photo by Pablo Delano

Cruz-Uribe’s research is a continuation of the approach taken by 19th century French mathematician Joseph Fourier, who used who used simple functions with smooth graphs to approximate the graphs of complicated functions with sharp corners while studying the flow of heat in solid objects. Exploring this approach, mathematicians have developed powerful tools and discovered solutions to differential equations that arise in various branches of science. With the support of the NSF, Cruz-Uribe hopes to continue that trend.

“My work is devoted to developing new tools within the field of harmonic analysis, and then applying them to the study of more abstract differential equations,” he says. “This kind of mathematical research deepens our understanding of a wide range of mathematical ideas and these in turn can have surprising and unforeseen applications in many different areas.”

The grant from the NSF, in addition to supporting the continuation of Cruz-Uribe’s research into weighted norm inequalities and partial differential equations, will support him engaging advanced undergraduate students to join in his research.

Scott Rodney, an associate professor of mathematics at Cape Breton University in Canada, is a colleague of Cruz-Uribe who has successfully involved undergraduate students in his research, something that can be a challenge for researchers in pure mathematics. Inspired by this, Cruz-Uribe has sought to do the same thing.

“When students used to ask me what I did, my standard answer was to tell them to go to graduate schools, and when they had passed their qualifying exams to come back and ask me again!” he says. “However, this year my senior thesis student, Philip Cho ’15, is writing his thesis on Sturm-Liouville theory, an area I want to learn more about. And I am currently working on a project with Greg Convertito ’16, that is related to my research.”