Talks

I will discuss challenges of quantum gravity, highlighting conceptual, methodological as well as phenomenological aspects. Focusing on asymptotically safe quantum gravity, I will review recent progress in addressing key theoretical challenges using continuum and lattice methods. Furthermore, I will explain how the high predictive power of the asymptotically safe fixed point for quantum gravity and matter might allow us to explain fundamental properties of our universe, for example its dimensionality. Finally, I will point out possible connections between different approaches to quantum gravity, and how these connections might help us formulating a fundamental description of nature.

In string compactifications the roles of physics and geometry are intrinsically intertwined. While the goals of these 4-dimensional effective theories are physical, the path to those answers frequently leads to cutting-edge challenges in modern mathematics. In this talk, I will describe recent progress in characterizing the geometry of Calabi-Yau manifolds in terms their description as elliptic fibrations. This description has remarkable consequences for the form of the string vacuum space and the properties of string effective theories, including particle masses and couplings.