Siqi Liu Wants to Make Better Networks

When was the last time you got stuck in traffic? Or missed your exit and had to drive an extra 20 minutes to get back on track? Just like cars on a highway, information can sometimes get stuck, or slowed down, by clogged networks. 

Not any network, though. Siqi Liu, new assistant professor of Computer Science, studies high-dimensional expanders, exceptionally well-connected graphs (networks) whose local pieces are also highly connected. If these graphs were cities, no neighborhood would be considered isolated, and you’d have such an overabundance of routes to choose from that you’d never get slowed down again. This unusual property could make these graphs powerful assets in solving connectivity problems across computing. 

Liu’s work focuses on making high-dimensional expanders easier to build. The first constructions, developed by mathematicians around 2000, were innovative but technically dense. “The constructions were very algebra-heavy and required deep number theory, so very few people in the world actually understood them,” she said. By the mid-2010s, computer scientists realized these graphs could have interesting applications. “That's when we started wondering if there could be other constructions, or if we could understand these constructions in a more intuitive way.” 

High-dimensional expanders’ applications range from improving the reliability of communication over noisy channels to quantum computing. These graphs’ unique connectivity can theoretically allow them to distribute data long-distance faster and more evenly, even if the channels aren’t great. They are also good examples of the “local-to-global” phenomenon: by understanding things in small, local pieces, you can sometimes figure out the behavior of the whole global object. In other words, by understanding the properties of a small group of nodes, you can get a good idea of how the entire network will perform. 

Liu’s path into this field was a mix of chance and curiosity. As an undergraduate, she took a graduate course in cryptography, which drove her to join a cryptography lab for her Ph.D. “I understood it a bit better, so naturally I felt it was more interesting,” she said. A postdoc in the lab introduced her to high-dimensional expanders, which at the time were a new thing with potential applications to cryptography. The newness of the field and the sense that there was a lot of potential for discovery intrigued her, and she was hooked. 

Fitting to someone studying networks, Liu also recognizes the role played by her own connections. “A lot of people in my cohort worked on graph-related questions, so I heard a lot about it, and as a result I probably felt it was cooler,” she laughed. 

This fall, Liu is teaching a graduate seminar on high-dimensional expanders — likely the first-time many students will encounter the topic. Teaching, she said, sharpens the research: “Before teaching, I thought I understood my area well. But putting things in order, filling in details and explaining each step makes me realize how many gaps there are, not just in my own understanding, but even in the literature.”  

Liu is excited about Duke’s opportunities for collaboration, not only within Computer Science but also with Mathematics, Electrical and Computer Engineering, and even the Duke Institute for Brain Sciences. She is also looking forward to working closely with students. “Undergraduates at Duke participate pretty actively in research,” she said. “There’s no shortage of interesting open problems in my field!” 

Durham’s greenery, sunny weather — it was an exceptionally mild late August day — and hiking trails were also a big draw. “I always want to be close to nature,” Liu said. “We all use our brains so much, I feel like being able to release that tension a little bit outside work is going to be very useful.” 

Liu is one of two faculty joining the Department of Computer Sciences this fall, along with Shuyan Zhou.