Demetre Kazaras:The geometry and topology of positive scalar curvature
- Graduate/Faculty Seminar,Uploaded Videos ( 1597 Views )I will give an informal overview of the history and status of my field. Local invariants of Riemannian metrics are called curvature, the weakest of which is known as "scalar curvature." The study of metrics with positive scalar curvature is very rich with >100 year old connections to General Relativity and smooth topology. Does this geometric condition have topological implications? The answer turns out to be "yes," but mathematicians continue to search for the true heart of the positive scalar curvature conditions.
Max Xu : Random multiplicative functions and applications
- Probability ( 210 Views )Random multiplicative functions are probabilistic models for multiplicative arithmetic functions, such as Dirichlet characters or the Liouville function. In this talk, I will first quickly give an overview of the area, and then focus on some of the recent works on proving central limit theorems, connections to additive combinatorics, as well as some other deterministic applications. Part of the talk is based on joint work with Soundararajan, with Harper and Soundararajan (in progress) and with Angelo and Soundararajan (in progress).