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This summer, Haotian Wu ’07 (Suzhou, China) built upon his knowledge of advanced calculus and differential geometry to research geometric flows and applications to general relativity.
The mathematics and physics double major studied aspects of Riemannian geometry and geometric partial differential equations with Justin Corvino, assistant professor of mathematics. Riemannian geometry involves the analysis of curved spaces, and contains some of the mathematical framework from which Albert Einstein formed his theory of general relativity.
Corvino and Wu conducted the research through Lafayette’s distinctive EXCEL Scholars program, in which students conduct research with faculty while earning a stipend. The program has helped make Lafayette a national leader in undergraduate research. Many of the more than 160 students who participate each year share their work through articles in academic journals and/or conference presentations.
For most of the study, Wu analyzed research articles by mathematicians Gerhard Huisken and Shing-Tung Yau. These authors developed a geometric notion of the center-of-mass of an isolated gravitational system, by applying the mean curvature flow to geometries which model such systems.
“The papers we read were very advanced for an undergraduate. I am very pleased with Haotian’s work. He is a gifted student with a superb work ethic, and can understand both big mathematical ideas as well as focus on technical details,” Corvino says.
Wu, who plans to continue this research with Corvino in the fall, discusses the benefits of working closely with a professor.
“I definitely enjoy and appreciate working with Professor Corvino. I have taken three mathematics courses with Justin, and I regard him as an excellent mentor.” he says. “While the materials we were working on were not easy, he knew when to guide me through and when to let me work independently. In that way, I was able to appreciate the study of advanced mathematics.”
Wu and Corvino were able to formulate a conjecture, which, if true, will yield a result worthy of publication.
Corvino believes that the EXCEL program is one of the hallmarks of the undergraduate experience, fostering meaningful interaction on advanced topics.
“Haotian and I worked together for several hours a day, three days a week. The process of learning advanced material, reading real research articles, and addressing and posing questions that are not just textbook exercises with recipe solutions is an eye-opening experience. Through the EXCEL program, Haotian has been exposed to material that is often reserved for a first or second-year graduate course,” Corvino says.
Haotian, whose future plans include pursuing mathematics in graduate school, also believes he has benefited from the EXCEL program.
“It certainly makes the education experience more challenging, but it is worth the effort to understand more mathematics. I enjoyed having time to investigate and contemplate my academic future,” Wu says. “The EXCEL program allows a student to receive plenty of individual attention from a professor. I learned advanced mathematics and became familiar with graduate school-style work through this program.”
Aside from his academic endeavors, Wu is a member of the International Students Association (ISA), the Asian Culture Association (ACA), the Physics Club, the Math Club, and the Wine Society. He is a McKelvy House Scholar, and serves as a student representative for the Curriculum Committee.