AWM Microsoft Research Prize in Algebra and Number Theory 2020

Citation

The 2020 AWM Microsoft Research Prize in Algebra and Number Theory is presented to Professor Melody Chan, in recognition of her in recognition of Chan’s advances at the interface between algebraic geometry and combinatorics.

Professor Chan received her doctorate in 2012 from University of California, Berkeley and held an NSF Postdoctoral Fellowship at Harvard University. She is currently an Assistant Professor at Brown University, a Sloan Research Fellow, and has recently won an NSF CAREER Award.

Chan is known for an exceptional combination of strength in both combinatorics and algebraic geometry, as well as her ability to fearlessly digest difficult techniques from other fields of mathematics. Chan has proved numerous conjectures across tropical geometry, graph theory, and algebraic geometry.

In Chan’s recent work with Galatius and Payne, they showed that the cohomology of the moduli space of genus g curves grows exponentially in a particular degree, an astounding result which contradicts conjectures of Kontsevich and Church-Farb-Putman that said this cohomology should vanish. This breakthrough comes from a deep study of moduli spaces of tropical curves.

Chan’s foundational work on the moduli of metric graphs and tropical curves, both solo and with several co-authors, is central to the field, already having important applications, and is expected to continue to lead to further work far beyond the original papers. Chan’s work with López Martín, Pflueger, and Teixidor i Bigas proves beautiful new results on the expected number of turns in a random Young tableau and then applies them to give explicit topological information on Brill-Noether varieties that seemed beyond reach before their work.

Beyond her outstanding scientific achievements, Chan has assumed leadership roles to promote the participation of women in research, co-organizing Women@AGNES (Algebraic Geometry Northeastern Series) at Brown and Yale; serving as Faculty Advisor for the Horizons Seminar at Brown, featuring talks and workshops on topics including diversity, community, and career development for young mathematicians; and organizing the peer Mentoring Network for women in math at Brown.

Researchers call Chan a “leader” and a “major force” and are impressed by both her insights and her technical prowess. AWM congratulates Melody Chan for her well-deserved AWM Microsoft Research Prize.

Response from Melody Chan

I am happy to receive the 2020 AWM Microsoft Prize in Algebra, and I thank the AWM and Microsoft for their generosity in recognizing my work. I have learned so much from my close collaborators: Renzo Cavalieri, Soren Galatius, Sam Payne, Nathan Pflueger, Martin Ulirsch, and Jonathan Wise. I’m also grateful for the support and mentorship of Dan Abramovich, Matt Baker, Lucia Caporaso, Joe Harris, Diane Maclagan, and especially my PhD advisor Bernd Sturmfels; and many other mathematicians, including my many supportive colleagues at Brown.

Getting to do research in mathematics is a privilege. After all, basic research in math and science is a long game: we get to study fundamental questions that may have no applications right now but, in totality and over the course of history, make an outsize impact in ways we couldn’t have predicted. And we get to have fun while doing it, too. But that whole calculus is predicated on having time, having breathing room, to think about the long game at all. Right now, I’m less and less sure that we have that room. We have a climate crisis on our hands, crises of civil rights and human rights, crises of democracy and disenfranchisement, entire crises of empathy. Our country is taking children from their parents. I’ve never been more concerned for my country and my community than I am now.

Being a math professor is, I think, still the best thing I personally know how to do. It’s getting harder to carry out basic math research—like research on the combinatorics and geometry of moduli spaces, say—with any moral certainty. But there are many parts of the job that do have an immediate impact. We must train students well, and find ways to support and include more of them in the first place; we must be role models, while interrogating our role as scientists; we must make more noise altogether. Let’s work together on prioritizing these aspects of the profession, even while we push on our foundational research.