Talks

I will discuss aspects of  the path sum of causal set theory, in which the continuum is replaced by a sample space of locally finite partially ordered sets.  This sample space not only contains continuumlike causals of different dimensions, but an entire zoo of non-continuumlike ones.  An open question is whether this path sum can be treated as a UV regularisation of the continuum path integral, as  the number of elements increases. I will discuss some results as well as  challenges in answering this question.

The Planck scale is generally believed to mark the onset of quantum gravity effects. In this talk, I will illustrate some of the most relevant features of models where the Planck scale governs deformations of relativistic symmetries and discuss opportunities for experimental tests of such models arising in physical frameworks much below the Planck scale. This concerns astrophysical observations, sensitive to tiny residual signatures at low energies thanks to amplification mechanisms, and table-top experiments, whose extremely high-precision might soon allow us to test the interplay between (quantum) gravity and quantum systems at ultra-low energies.

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]

Equilibrium multiplicity throws up the question of which equilibria are plausible. How can we distinguish between them? We look to understanding equilibria as emergent properties of dynamic processes of behavioral change and consider some classic behavioral rules and applications, such as the best response rule and coordination problems.

The emergence of cooperation among selfish agents that have no incentive to cooperate is a non-trivial phenomenon that has long intrigued biologists, social scientists and physicists. The iterated Prisoner’s Dilemma (IPD) game provides a natural framework for investigating this phenomenon. The spatial version of IPD, where each agent interacts only with their nearest neighbors on a specified connection topology, has been used to  study the evolution of cooperation under conditions of bounded rationality. This talk will explorehow the collective behavior that arises from the simultaneous actions of the agents (implemented by synchronous update) is affected by the connection topology among the interacting agents. The system exhibits three types of collective states, viz., a pair of absorbing states (corresponding to all agents cooperating or defecting, respectively) and a fluctuating state characterized by agents switching intermittently between cooperation and defection. We show that the system exhibits a transition from one state to another simply by altering the connection topology from regular to random, without altering any of the parameters govering the game dynamics, such as temptation payoff or noise. Such topological phase transitions in collective behavior of strategic agents suggest important role that social structure may play in promoting cooperation.

Beginning with the intimate relationship between recursive algorithms and dynamical systems, I shall describe some common dynamics that serve as templates for `stateless' learning. This will be followed by reinforcement learning for dynamic systems, using Markov decision processes as a test case.