Brian Lawrence received a PhD in mathematics from Stanford in June 2017. As an undergraduate he worked on problems in mathematical physics and number theory. Working under Joe Gallian and Nathan Kaplan at the Duluth REU, he investigated bounds on the coefficients of ternary cyclotomic polynomials. At Caltech, he studied semiclassical limits of chaotic quantum systems under Barry Simon, and worked under Dinakar Ramakrishnan to study the zeroes of quadratic twists of L-functions of modular forms. In particular, building on a classic paper of Gross and Zagier, he generalized an averaging formula due to Michel and Ramakrishnan, and used it to prove a nonvanishing result for these L-functions. His more recent work has focused on p-adic methods in number theory, with a focus on Diophantine problems of classical interest.
Brian has a longstanding interest in mathematics, developed from grade school through the Mathematical Olympiad Summer Program and problem-solving contests. He has participated in the Putnam Mathematical Competition for undergrads, considered by many to be the most prestigious university-level mathematics examination in the world, and has been in the top five winners for his four years at Caltech. In the history of Competition (since 1938), only eight students have been named a Putnam Fellow four times.
Outside of math, Brian enjoys studying foreign languages and learning about different cultures. He taught himself Chinese in high school, and he took a yearlong sabbatical from his undergraduate studies at Caltech to study Chinese history at Peking University. There he learned about the political culture of ancient China, the civil service exam, and the ideas of Confucius, as well as studying Classical Chinese. He is still working to improve his Chinese.