Ricci flow in quantum gravity

9 Sept 2026, 13:00 → 11 Sept 2026, 12:50 Europe/Zurich

28B 110 (RWTH Aachen University)

The mini-workshop is intended to discuss the possibilities for implementing the Ricci flow in quantum gravity, and to explore possible applications. The number of talks will be kept at a minimum, the majority of the time will be reserved for discussions. If you would like to propose a talk which may serve as a seed for discussion, please submit an abstract here.

Participation at the workshop is free of charge; in return, please understand that we cannot offer any financial support for the participants.

The location of the workshop is the Physikzentrum at RWTH Aachen University, Sommerfeldstr. 16 in Aachen, Germany.

Wednesday 9 September

14:00 → 15:30 Evidence for Asymptotic Safety

In this talk I will introduce the asymptotic safety scenario for quantum gravity and the search for viable interacting fixed points. After covering the basic concepts — fixed points and their UV critical surfaces — I will explain how these are studied using the functional renormalization group, and close with an overview of the results obtained so far, as well as open questions.

Speaker: Yannick Kluth (University of Toronto)

AS_Evidence.pdf

15:30 → 16:00 Coffee break

16:00 → 17:30 Gradient flow on the lattice

t.b.a.

Speaker: Antonio Rago

Thursday 10 September

09:00 → 10:30 Causal Dynamical Triangulations. From the infrared to the ultraviolet.

One of key questions of quantum gravity is whether it can be formulated as a non-perturbatively renormalizable quantum field theory valid up to arbitrarily large energy scale as predicted by the, so-called, asymptotic safety conjecture. Causal Dynamical
Triangulations (CDT) is a lattice quantum field theory of gravity based on the formalism of Regge Calculus and Feynman path integrals. It is studied by numerical Monte Carlo simulations. In my talk I will briefly introduce the four-dimensional CDT and present
its most important results, including the non-trivial phase structure and the dynamically emerging semiclassical universe. I will discuss how one can define the infrared and ultraviolet limits of CDT and thus provide evidence in favour of asymptotic safety.

Speaker: Jakub Gizbert-Studnicki (Jagiellonian University)

JGS_Aachen_2026.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 EDT as a tool to explore asymptotic safety

I will introduce EDT as a tool suitable to explore asymptotic safety on the lattice. In particular, I will show recent results that, if a non-trivial measure term is included, EDT might feature a physical phase, and a continuum limit.

Speaker: Marc Schiffer (Radboud University)

14:00 → 15:30 The perturbative gradient flow

I will give an introduction to the perturbative approach to the gradient flow in QCD and other field theories. The short-flow-time expansion will be discussed, and technical aspects for the calculation of the perturbative matching coefficients will be outlined. I will also present a number of examples, highlighting the benefits of the gradient flow in the calculation of physical observables.

Speaker: Robert Harlander (RWTH Aachen University)

Ricci-flow-2026.pdf

15:30 → 16:00 Coffee break

16:00 → 17:30 The perturbative Ricci flow

One candidate for a quantum theory of gravity is the Asymptotic Safety conjecture, which postulates the existence of a non-trivial fixed point for the gravitational couplings. We investigate the search for such a fixed point within the framework of perturbation theory.

For this, we employ the Ricci flow as the central tool, pursuing a perturbative scheme analogous to the gradient flow formalism in QCD. In QCD, the gradient flow was introduced to bridge the gap between lattice simulations and perturbative calculations, allowing for a definition of a renormalization scheme that is accessible in both settings. Applied to gravity, the gradient flow is known as Ricci flow.

In this talk, I will describe the perturbative implementation of the Ricci flow: the flow equation for the graviton field and its gauge fixing, the resulting Feynman rules, the BRST symmetry of the flowed theory, and its renormalization. On this basis we define Newton's coupling in the Ricci flow scheme and investigate its renormalization group behavior.

Speaker: Henry Werthenbach (RWTH Aachen University)

talk_ricciflow.pdf

Friday 11 September

09:00 → 10:30 Gradient flow: applications not only to lattice QCD

Gradient flow equations provide continuous deformations of fields (gauge potentials, metrics, neural weights, etc.). They have been extensively studied and used in classical gravity, where they have allowed solving important problems. They are also employed routinely in lattice QCD calculations as a tool to define the strong coupling constant and thus to set the physical scale of simulations. The gradient descent algorithm used to train neural networks is yet another version of the same gradient flow equation. In the talk, I will introduce the gradient flow and describe its advantages and relationships in various contexts.

Speaker: Piotr Korcyl (Jagiellonian University)

10:30 → 11:00 Coffee break

11:00 → 12:30 A Preliminary Approach to Ricci Flow in Dynamical Triangulations

I will present a preliminary approach to Ricci flow in the framework of Dynamical Triangulations. In particular, I will describe how to compute the geometric quantities required for evaluating the Regge action, including triangle areas, dihedral angles, and simplex volume, in a form suitable for numerical simulations. I will then discuss how to obtain the variations of these quantities with respect to the edge lengths. Finally, I will introduce and analyze the Ricci flow in the simple case of a single simplex.

Speaker: Dr Andrzej Görlich (Jagiellonian University)