The Department of Mathematics hereby invites you to attend two inaugural lectures on 18 February 2025.
Inaugural lecture by professor Fabrice Baudoin: Analysis and Geometry of Dirichlet forms
Abstract: What does it mean for a space to be positively or negatively curved ? The notion of curvature has fascinated mathematicians for over three centuries and has found fundamental applications in physics. While it is well understood what curvature means in the context of Riemannian manifolds, the exploration of a notion of curvature in more degenerate context like fractals is an emerging field of research. In this talk I will demonstrate how the theory of Dirichlet forms which arose from potential theory makes a bridge between the geometric concept of "Ricci curvature" and analysis and probability.
Inaugural lecture by tenure track assistant professor Nina Therese Dörnemann: An Invitation to Principal Component Analysis in High Dimensions
Abstract: Principal component analysis (PCA) is a cornerstone of multivariate statistics and a widely used tool for dimension reduction. Traditionally, PCA assumes that the number of variables is much smaller than the sample size. However, in modern high-dimensional applications, the number of variables often rivals or even exceeds the number of samples, leading to unexpected statistical phenomena. This lecture offers an invitation to explore PCA in modern settings. A central focus will be on the so-called BBP phase transition - a phenomenon where the largest eigenvalue of the sample covariance matrix undergoes a phase transition as the sample size and dimensionality increase proportionally. We will also discuss recent advancements in statistical testing to determine whether the largest eigenvalue lies in the subcritical (noise-dominated) or supercritical (signal-detectable) phase, a question of critical importance for high-dimensional inference.
Reception After the last lecture, the Department will host a small reception in Vandrehallen, building 1530.