Talks

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

We will consider further applications in game theory and economics, such as bargaining problems, coalitional processes, bounded rationality, matching problems, housing markets. More detail will be provided on useful tricks and techniques used to prove these kinds of results.

The hawk–dove game admits two types of equilibria: an asymmetric pure equilibrium, in which players in one population play “hawk” and players in the other population play “dove,” and a symmetric mixed equilibrium, in which hawks are frequently matched against each other. The existing literature shows that when two populations of agents are randomly matched to play the hawk–dove game, then there is convergence to one of the pure equilibria from almost any initial state. By contrast, we show that plausible dynamics, in which agents occasionally revise their actions based on the payoffs obtained in a few trials, often give rise to the opposite result: convergence to one of the interior stationary states.

Cooperation is vital in both human and animal behavior, allowing individuals to achieve goals that would be difficult alone, such as hunting large, elusive prey. This cooperation has been integral to the evolution of conformity and group norms. However, it is unclear whether individuals conform primarily to acquire valuable information (informational conformity) or to blend in with the group (normative compliance), and under what conditions each form of conformity is exhibited. The degree of conformity may depend on factors like the nature of the activity, an individual’s expertise, and the reward structure. In activities such as foraging, where individuals often exhibit nearly optimal behaviors, one might expect informational conformity, as foragers likely know what is best for them. However, whether individuals conform in this way or are motivated by the desire to conform to group norms remains uncertain. This question forms the basis of our study. While patch foraging has been well studied in both wild and lab settings, most research has focused on individual foraging behavior, overlooking the role of group dynamics. In patchy environments, animals and humans typically behave in ways that align with the Marginal Value Theorem (MVT), but little attention has been given to how group foraging might influence individual behavior. Can suboptimal foragers influence others, leading to less optimal group outcomes? This study explores the social dynamics of group foraging through a novel task, examining whether collective behavior can lead individuals away from optimal foraging, indicating normative conformity. Additionally, our research aims to develop process-level models of learning and decision-making, enhancing our understanding of the mechanisms underlying conformity in group foraging.

Theoretical studies from diverse areas of population biology have shown that demographic stochasticity can substantially impact evolutionary dynamics in finite populations, including scenarios where traits that are disfavored by natural selection can nevertheless increase in frequency through the course of evolution. Here, we analytically describe the eco-evolutionary dynamics of finite populations from demographic first principles. We investigate how noise-induced effects can alter the evolutionary fate of populations in which total population size may vary stochastically over time. Starting from a generic birth-death process, we derive a set of stochastic differential equations (SDEs) that describe the eco-evolutionary dynamics of a finite population of individuals bearing discrete traits. Our equations recover well-known descriptions of evolutionary dynamics, such as the replicator-mutator equation, the Price equation, and Fisher’s fundamental theorem in the infinite population limit. For finite populations, our SDEs reveal how stochasticity can predictably bias evolutionary trajectories to favor certain traits, a phenomenon we call “noise-induced biasing.” We show that noise-induced biasing acts through two distinct mechanisms, which we call the “direct” and “indirect” mechanisms. While the direct mechanism can be identified with classic bet-hedging theory, the indirect mechanism is a more subtle consequence of frequency- and density-dependent demographic stochasticity. Our equations reveal that noise-induced biasing may lead to evolution proceeding in a direction opposite to that predicted by natural selection in the infinite population limit. By extending and generalizing some standard equations of population genetics, we thus describe how demographic stochasticity appears alongside, and interacts with, the more well-understood forces of natural selection and neutral drift to determine the eco-evolutionary dynamics of finite populations of nonconstant size (ref: Bhat and Guttal, 2025, American Naturalist, doi: https://www.journals.uchicago.edu/doi/10.1086/733196)

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.

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.