It’ll probably be a cold summer in Longyearbyen before Anthony Várilly-Alvarado gets a thrill to match the one he’s enjoying this month.
The Rice University assistant professor of mathematics has won a coveted CAREER Award, given by the National Science Foundation to young academics expected to make significant impact on their chosen fields.
The award will support research by Várilly-Alvarado’s research group for the next five years with total funding of around $400,000.
The honor was announced while Várilly-Alvarado, who joined Rice as a postdoctoral researcher in 2009, was at the University of the Andes in Colombia for a week to work on projects with two colleagues from his alma mater, the University of California at Berkeley. One colleague, he said, “went into industry for a couple of years, and now he’s back. So this was the first chance for us to get the band back together and do some math.”
The grant will support Várilly-Alvarado’s quest to learn the properties of points with rational coordinates lying on surfaces. On curves, points of this sort have relevance for encoding data for transmission and secure messaging, he said. The foundations for surfaces are still being laid out.
“In general, mathematics has so many layers that it becomes obscure really fast, but these ideas are actually pretty simple,” Várilly-Alvarado said. “The basic objects I study are literally surfaces. … I study points on these surfaces.
“What I care about is that these points have X-Y-Z coordinates, and I want all these coordinates to be fractions. It turns out that points like these are pretty rare. Most points have some random infinite decimal expansion that you can’t write in a nice way like three-fifths, so finding these points can be a challenge,” he said. “It’s entirely possible we’ll find out at the end of the day that we won’t be able to use these points in applications, but that also is knowledge.”
“Tony brings a lot of things to the department,” said Brendan Hassett, the Milton Brockett Porter Chair of Mathematics at Rice. “Arithmetic geometry and number theory is an area where we’ve been trying to build expertise for a long time, so he fills a niche that’s important to us.
“I’ve seen firsthand his virtuosity from a computational point of view, which helps him uncover deep mathematical results.”
Hassett had high praise for Várilly-Alvarado’s classroom chops. “He’s a wonderful teacher at both the graduate level and in basic calculus courses. He has the highest evaluations I’ve ever seen in calculus. He has a gift with our youngest students.
“Tony epitomizes Rice’s commitment to combining great teaching and the highest quality research in a single individual. He really has the whole package,” Hassett said.
Várilly-Alvarado found his way to Rice through Hassett. “In 2006, I went to a summer school in Germany where he was giving a course,” Várilly-Alvarado said. “I loved his lectures … so when I went for a postdoc, I was really interested in coming to Rice.
“I was a postdoc here for three years, and it was wonderful. When the opportunity to stay came up, I didn’t blink,” he said in reference to joining the faculty in 2012.
Várilly-Alvarado is teaching graduate-level courses in algebraic number theory this semester and is surprised at the number of undergraduates who find their way to his class. “The undergrads at Rice are just phenomenal,” he said. “They’re a pleasure to teach and interact with, and it’s amazing to have five or six taking a topics graduate course — and keeping up.”
The Costa Rica native said he is looking forward to visiting Longyearbyen, an Arctic city on a Norwegian island that is a four-hour plane ride north from Oslo.
“There’s a math conference in July in the northernmost city in the world, way farther north than the entirety of Alaska, at 78 degrees latitude,” he said. “When else am I going to be in the northernmost city in the world? It’s about as close to the North Pole as you can get.
“Of course, this is the trick. Every other mathematician is thinking the same thing. So it appears it’s going to be a great conference, because everybody’s going,” he said.