PRIME TIME Melanie Matchett Wood, an assistant professor in the Department of Mathematics who specializes in number theory and algebraic geometry, has made exciting discoveries, fostered collaboration and garnered prestigious awards, such as the Packard Fellowship in 2015. Please explain the work you do. My job at UW-Madison involves research, teaching and outreach. In my research, I find solutions to math problems that no one else knows the answers to. These problems involve things like prime numbers (numbers like 2,3,5,7 whose only factors are 1 and themselves) and also different kinds of shapes and spaces. My work is basic science in that it helps us understand fundamental mathematical structures. These structures underlie many different things in our world, from how particles move in physics to the encryption that keeps all our digital data safe. I teach undergraduates and graduate students in courses, as well as mentor them in doing their own mathematics research. I am the assistant director of the Wisconsin Mathematics, Engineering and Science Talent Search, which is a program for high school students across the state of Wisconsin. Tell us about your recent breakthroughs. The bell curve is ubiquitous in all kinds of science. It turns out that this is not due to laws of nature as much as it a law of mathematics called the Central

Limit Theorem — a mathematical result that says for any different kind of inputs, certain averages always come out shaped like a bell curve. This phenomenon is called universality, and it basically means no matter the input, the output will be the same. That is quite a powerful thing to know when you want to be able to predict outputs! One of my recent breakthroughs was to discover and prove a universality theorem for certain kind of symmetries. This says that no matter how certain objects are made, they will always have symmetries distributed in a kind of “symmetry bell curve.” Studying symmetries is one of the most central themes of mathematics, and so this has far and unexpected connections to everything from factoring integers to the statistical physics of avalanches. What keeps you going in your work? Of course, it is always exciting to have a big breakthrough, but those often take years of work. Along the way, I enjoy working with other mathematicians and students on research. — Story by Katie Vaughn

PHOTOS BY SARAH MORTON (2)

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L&S Annual Review 2015-2016