Mathematics

I am broadly interested in probability theory, mathematical physics, and the mathematics of complex systems. So far, my research has focused on Kardar–Parisi–Zhang (KPZ) universality, a phenomenon that governs large-scale fluctuations in many seemingly unrelated random models arising in diverse contexts. As a Miller Fellow, I aim to understand how universal laws emerge from large interacting systems, and to develop mathematical frameworks that explain the emergence of structures from randomness.

Host: Alan Hammond

Ph.D. Institution: Columbia University

I am a mathematician working on nonlinear Partial Differential Equations (PDEs) arising from physics, such as general relativity, astrophysics, and fluid mechanics. My research is often directly connected to fundamental physical issues: during my Miller Professorship, I plan to investigate problems that will elucidate (i) the structure of generic gravitational singularities inside black holes, (ii) the evolution of stars, and (iii) violent instabilities of plasma on the Sun. By studying these problems, I aim to uncover the intricate mathematical structures that underlie complex physical...

My research centers on the spectral theory of quasiperiodic and periodic Schrodinger operators, with applications to quantum dynamics and nonlinear Schrödinger equations. More recently, I have been investigating how tools from analysis, algebraic geometry, and combinatorics can be combined to study spectral properties of periodic graph operators.

Host: Svetlana Jitomirskaya
Home Institution: Texas A&M University

Kenneth Ribet is Distinguished Professor of Mathematics at UC, Berkeley. Ribet studied at Brown University and Harvard University. He received his PhD in 1973 from Harvard, where his advisor was John Tate. After three years of teaching in Princeton and two years of research in Paris, Ribet moved to Berkeley in 1978. Ribet works in number theory and algebraic geometry, especially on modular forms and modular curves. He is best known for his 1986 proof that Fermat's Last Theorem would follow logically from the modularity conjecture, then a well-known unproved conjecture about elliptic curves...