Talks

While a complete theory of quantum gravity remains elusive, several alternative approaches are being explored. Which ones are the most promising, and whether they are connected or fundamentally distinct, remain outstanding open questions. I will argue that looking at quantum gravity through the lens of effective field theory offers a promising path to test the internal consistency of different theories and systematically compare their low-energy manifestations. I will illustrate this perspective using asymptotically safe quantum gravity as a case study, discussing its interface with positivity bounds and swampland conjectures. Finally, I will outline how a similar strategy can be utilized to chart the landscape of quantum spacetimes stemming from an asymptotically safe ultraviolet completion.

Many researchers in quantum gravity favour the notion of a quantum foam, coined by Wheeler 70 years ago to capture "whatever becomes of spacetime at the Planck scale". The underlying idea is that the quantum fluctuations of spacetime are so large that a description based on smooth metrics is no longer adequate. Equally popular is the notion that spacetime as we know it should "emerge" from this primordial quantum foam, alongside interesting quantum-gravitational effects. These ideas are enticing, but remain speculative unless backed up by quantitative analysis and modelling within a coherent, nonperturbative formulation of quantum gravity. Fully nonperturbative computational tools are available in the form of 'lattice quantum gravity 2.0', based on causal dynamical triangulations. The power and beauty of this methodology lies in its use of curved, dynamical lattices, incorporating the principles of quantum field theory and general relativity from the outset. This has produced quantitative blueprints of both quantum foam and spacetime emergence, and a concrete perspective on what it means to “solve" quantum gravity. [arXiv:2501.17972]

I will give a gentle introduction to the moduli space of graphs and its fine moduli space cousin known as Outer Space. This moduli space of graphs has many applications to various branches of mathematical physics, algebraic geometry, and geometric group theory. It is a natural object to consider while studying Feynman amplitudes in parametric space, and it can be seen as the configuration space of one-dimensional quantum gravity. I will explain how this moduli space of graphs recently became the largest provider of information on the homology of the moduli space of curves of genus g and how associated graph complexes can be used to shed light on the 'dark-matter problems' of these moduli space's cohomology.