Duchin was given her first name, Moon, by parents "on the science-y fringes of the hippie classification". She grew up knowing from a young age that she wanted to become a mathematician. As a student at Stamford High School in Connecticut, she completed the regular high school mathematics curriculum in her sophomore year, and continued to learn mathematics through independent study. She was active in math and science camps and competitions, and did a summer research project in the geometry of numbers with Noam Elkies. Duchin studied at Harvard University as an undergraduate, where she was also active in queer organizing, and finished a double major in mathematics and women's studies in 1998. As a graduate student in mathematics at the University of Chicago, she continued her feminist activism by teaching gender studies and pushing the university to add gender-neutral bathrooms, and was mentioned mockingly by name on the Rush Limbaugh show. She completed her doctorate in 2005, under the supervision of Alex Eskin. She was a postdoctoral researcher at the University of California at Davis, and the University of Michigan, before joining the Tufts faculty in 2011.
Work
Duchin's mathematical research has focused on geometric topology, geometric group theory, and Teichmüller theory. For example, one of her results is that, for a broad class of locally flat surfaces, the geometry of the surface is entirely determined by the shortest length in each homotopy class of simple closed curves. Duchin's expertise in geometry has led her to conduct research on the mathematics of gerrymandering. A key aspect of this research is the geometric notion of the compactness of a given political district, a numerical measure that attempts to quantify how extensively gerrymandered it is. “What courts have been looking for is one definition of compactness that they can understand, that we can compute, and that they can use as a kind of go-to standard”, she said in an interview with The Chronicle of Higher Education. To help tackle the challenge of finding an agreed-upon standard, Duchin has developed a long-term, wide-ranging project on the mathematics of gerrymandering. As a part of this project, she founded a summer program to train mathematicians to become expert witnesses in related legal cases. In 2016, she founded the Metric Geometry and Gerrymandering Group, a nonpartisan research group which coordinates and publicizes research on geometry and computing, and their application to the redistricting process in the US. In 2018-2019 she was on leave of absence from Tufts, and was a Fellow at the Radcliffe Institute for Advanced Study at Harvard University. Her research focus was "Political Geometry: The Mathematics of Redistricting". In 2018, Democratic Governor of PennsylvaniaTom Wolf enlisted Duchin to help him evaluate newly drawn redistricting maps for fairness. This happened as a consequence of the Pennsylvania Supreme Court decision declaring the 2011 U.S. congressional districting map unconstitutional. Duchin generated a report published on February 15, 2018.
