Intersecting Algebraic Geometry and Combinatorics: Q&A with Shiyue Li

Shiyue Li, Member in the School of Mathematics, is interested in algebraic geometry and combinatorics. Combinatorics can be described as the mathematics of counting and arranging, more specifically involving quantities too large to be counted in the traditional way. Meanwhile, algebraic geometry, as suggested by its name, deals with surfaces or curves (or more abstract generalizations of these) which can be viewed both as geometric objects and as solutions of algebraic equations. Li's work probes combinatorial aspects of algebraic geometry. She comes to IAS from Brown University, where she was awarded her Ph.D. in 2023.

How did you first become interested in algebraic geometry and combinatorics?

I have been fortunate to be guided by many wonderful teachers. Near the end of my undergraduate studies, I was quite touched when learning about the connections between deep and complicated theorems in algebraic geometry and combinatorial questions that are fun and simple to state, so I started exploring more in this direction.

IAS has a long history of collaboration across the four Schools housed on campus. Tell us about a collaboration that has positively impacted your work.

In 2020, I participated in a workshop on Women in Algebraic Geometry held by the Institute for Computational and Experimental Research in Mathematics (ICERM). There, I studied a certain moduli space of curves with four other women mathematicians: Emily Clader, Chiara Damiolini, Daoji Huang, and Rohini Ramadas. We support and learn from each other. Together we have understood better the geometry of the space, which has led us to studying unexpected questions in combinatorics. Three years have passed and we wrote two papers, and we are still collaborating. As the youngest member of the group, it's heartening to see the collaboration mature as we grow together.

What do you enjoy most about being a researcher?

The freedom to wonder about fascinating things in nature, and the connections with other minds from around the world.

What was the last book you finished, and what did you think of it?

This summer I re-read the tales of Chuang-Tzu. The characters are all sorts of creatures: cranes, owls, sea turtles, humans from all walks of life. It often gives me a sense of childlike enjoyment and offers insights on everyday life.

When you aren't researching, how do you like to spend your free time?

As a kid, I used to roam around the hills in my hometown in China. In the past few years, I have enjoyed roaming around the mountains in North America to have a bit of adventure. It feels quite freeing.


Shiyue Li Q&A SoM
Li at the summit of Quandary Peak, the highest of the Tenmile Range in the Rocky Mountains