Princeton professor presents annual Eisenbud Lectures
Brandeis’ Martin A. Fisher School of Physics of Brandeis hosted the Eisenbud Lectures in Mathematics and Physics this past week. The series included three lectures given by Peter Sarnak of the Princeton University Institute for Advanced Study, who presented the research of forward thinkers in physics and mathematics on topics such as number theory and their application in other disciplines.
In the past, Sarnak’s work on number theory has had an impact on computer science and combinatorics, a “branch of mathematics that studies the enumeration, combination, and permutation for sets of elements and mathematical relations that characterize their properties,” according to the Wolfram MathWorld website.
The title of the series was “Randomness in number theory and geometry.” The series was divided into three lectures, held over the course of three days, from Tues. Dec. 2 through Thurs. Dec. 4.
The topic of the first lecture was the topology of random real hypersurfaces and percolation, limited functions that have universal laws of distribution. In the second lecture, Sarnak discussed nodal domains Maass forms, functions of the upper half plane. The third lecture concerned families of zeta functions and their symmetries and applications, which are functions analogous to the Riemann zeta function
Sarnak opened the third lecture by presenting the definitions of the different matrices that the lecture topic included. He provided proof of the theories that he discussed by displaying the graphs of functions. Sarnak’s field of research focuses on a natural spectral interpretation of the zeroes of the Riemann zeta function. The Riemann zeta function is a function of complex variables traditionally used in the study of general zeta functions. Sarnak explained that it was harder to look at individual cases, and, as a result, when conducting his research, he chose to focus on families of zeta functions
Throughout the lecture, audience members participated in the conversation by asking questions. Sarnak concluded his presentation by discussing the applications of his research. He explained that, with further development, the research will be used in mathematical proofs when the Riemann zeta function is further researched. He also added that the basis for understanding these phenomena is a symmetry type associated with the zeta function that comes from function field considerations.
The lecture series is the result of a donation by Leonard and Ruth-Jean Eisenbud. The donation funds an annual set of lectures by an eminent physicist or mathematician whose work exemplifies the combination of the two subjects.