Three professors in the Department of Mathematics have been named recipients of Simons Foundation Fellowships. Dima Arinkin, Jordan Ellenberg and Sebastien Roch are among 40 outstanding mathematicians awarded fellowships, along with 12 theoretical physicists.
The Simons Fellows program extends academic leave to allow recipients to “focus solely on research for the long periods often necessary for significant advances.”
Arinkin, who joined the UW-Madison faculty in 2012, will be a visiting scholar at Harvard University in the fall and plans to collaborate on several research projects in his field of expertise, the geometric Langlands program, a form of number theory. And in the spring of 2019, he will participate in a program on derived algebraic geometry as a research professor at the Mathematical Science Research Institute in Berkeley, California.
“This is an active area of modern mathematics that has proved invaluable in my research,” he says. “Personally, I feel that this is a very exciting time for people in this area. The influx of ideas from derived algebraic geometry has completely changed — and continues changing — the way we think about geometric Langlands program. We can now prove things that we could not even formulate before.”
Ellenberg, the John D. MacArthur Professor of Mathematics and a Vilas Distinguished Achiever Professor of Mathematics, has been a part of the math department since 2005 and specializes in arithmetic algebraic geometry.
With professors at the University of Waterloo and Emory University, Ellenberg will develop and test a “master conjecture” that will unify two directions in number theory — the Malle conjecture and the Batyrev-Manin conjecture — that have been moving on parallel tracks. And with former Ph.D. student Lalit Jain and current Ph.D. candidate Alisha Zachariah, he will continue to work on the problem of “community detection” in large networks with parts that do not all look the same, the condition of most real networks.
“The more we learn about data science, machine learning and optimization, the more we see that all kinds of math, not just the traditional realms of probability and linear algebra, are relevant to these problems,” he says. “My work with Jain and Zachariah is part of my goal to work on the geometry of learning, an enterprise which I think will bring math and machine learning closer together and develop a bigger interface between the two subjects.”
And Roch, who joined the UW-Madison faculty in 2012, works at the intersection of applied probability, statistics and theoretical computer science, with an emphasis on biological applications. The recent explosion of genomic data available across species presents new opportunities and challenges in reconstructing the history of life on Earth, and he will continue his work on the “Mathematics of the Tree of Life,” which involves a mix of mathematics, statistics, computer science and biology.
“In the coming year, I am particularly interested in exploring new areas of applications in cancer genomics, viral epidemiology and microbial ecology, all of which are of great current interest and raise interesting new foundational questions in the field,” he says.
Roch will also foster new collaborations with the university’s Institute for Foundations of Data Science, which brings together mathematicians, statisticians and computer scientists to research foundational questions in data science. And he will begin work on a new course, Mathematics of Data, that will introduce advanced undergraduates to various mathematical techniques that play a role in the field of data science.
The Simons Foundation’s mission is to advance the frontiers of research in mathematics and the basic sciences. Co-founded by Jim and Marilyn Simons, the organization’s Mathematics and Physical Sciences division supports research in mathematics, theoretical physics and theoretical computer science, including the Simons Fellows program, which began in 2012.