Talks

 In this era of omnipresent social media, social contagions are becoming a growing matter of interest. Our work integrates insights from systematic survey data, the tool of choice for social opinion exploration, with computational models to demonstrate a novel framework for deriving compartmental models from open-ended questions. By analyzing free-form survey responses and qualitative narratives, we systematically map individual opinions and behaviors into discrete compartments that mirror the stages of influence and adoption observed in various peer influenced dynamics, like public health and marketing campaigns. In the vaccine perception domain, respondents’ descriptions of peer interactions and protective behavior are classified into states analogous to susceptible, influenced, and resistant, capturing the dynamics of opinion formation and behavioral change. Similarly, in the referral marketing scenario, open-ended responses reveal latent engagement stages that inform a compartmental structure reflective of awareness, participation, and advocacy. Our quantitative treatment shows that these data-driven compartments can be effectively incorporated into dynamical systems models, giving rise to interesting opinion diffusion patterns. The proposed framework not only bridges qualitative insights with rigorous mathematical modeling but also highlights the broader applicability of compartmental approaches in deciphering complex social processes from open-ended inquiry.

The study of multi-agent systems (MAS) and related control architectures is becoming increasingly popular in emerging engineering systems such as power grids, multi-robot systems, IoT (Internet of Things) systems, and sensor networks. These systems are large-scale and characterized by multiple interdependent decision-making entities, or agents, that are networked and heterogeneous.

This work focuses on the distributed control of networked MAS with linear time-invariant dynamics and quadratic performance measures. Since the MAS is networked, each agent has access only to the state information of its neighbors, also referred to as the local or output feedback information structure. Consequently, full-state feedback controllers are not implementable.

Using a game-theoretic framework, we model the distributed control problem as a networked differential game. We illustrate that verifying the existence of an output feedback Nash equilibrium is challenging due to structural constraints imposed by the network topology. To address this, we develop the notion of an output feedback guaranteed cost equilibrium. These equilibrium controllers ensure an upper bound on individual agent costs while maintaining an equilibrium property.

We derive several properties of these equilibrium strategies and provide linear matrix inequality-based conditions for their existence, along with an algorithm for synthesizing them. Finally, we demonstrate the performance of the proposed equilibrium strategies through numerical experiments.

(joint work with Aniruddha Roy).

Biological communities are endowed with properties, such as diversity, primary production, or total biomass, that have ecological relevance. The possibility that such properties are shaped by natural selection has been tested by experimentally selecting microbial communities based on some collective function.

I will discuss different models for artificial community selection and discuss in particular its effect on species traits, notably on the interaction parameters.

Collective functions are typically evaluated at the level of groups of agents, and group structure is important for understanding the impact of heterogeneity-induced conflicts. If mathematical models often assume that group form independently of the agents' strategies, in nature group formation and group function commonly depend on the same set of traits.

In this lecture, I will address different models where the ecological and evolutionary dynamics are coupled through the process of group formation, and discuss their relevance to the evolution of aggregative multicellularity.

Expanding beyond traditional evolutionary games, this lecture discusses higher-order interactions in ecology and their connection to evolutionary dynamics. The mathematical connection between Lotka-Volterra dynamics and replicator equations is explored, illustrating how ecological and evolutionary processes interlink even in higher dimensions. Moving to social systems, we discuss the evolution of collective beliefs and trust, providing insights into the role of MEGs in shaping human social structures.

These lectures underscore the versatility of MEGs in explaining the complex nature of both natural selection and cultural evolution.

Widespread exploitation of biological resources raises concerns about the emergence of tipping points characterizing abrupt ecosystem collapse. Mitigating these tipping points is crucial for the sustainability of our being. However, our understanding of how the feedback loop between human exploitation strategies and the environment influences the mechanisms governing these tipping points remains elusive. This study employs an eco-evolutionary game-theoretic framework to explore the coupled dynamics of a renewable resource undergoing a sudden collapse. We investigate the co-evolution of strategic interactions and environmental dynamics using six possible game combinations representing diverse social dilemmas.

We find that, depending on the choice of environment-dependent payoff structure, the tipping point can be shifted or even completely eluded. Additionally, this study emphasizes the impact of monitoring and punishment mechanisms against high-effort exploitation strategists on the system’s resilience. Our results unveil a rich spectrum of dynamics, spanning from multistability to oscillation, thereby presenting formidable challenges to resource management. While addressing the tragedy of the commons resulting from heightened harvesting efforts, targeted penalties for high-effort strategists emerge as a mitigating factor. Overall, our study highlights the interplay between ecological tipping points, individual decision-making, and external control mechanisms within the realm of resource management.

The 2021 WHO Malaria Report revealed that most Sub-Saharan African countries fell short of the 2020 Global Technical Strategy (GTS) targets, largely due to inconsistent use of insecticide-treated nets (ITNs) driven by various socioeconomic factors.

This research talk leverages data from 38 SSA countries and game-theoretic models to uncover key patterns and emerging trends in malaria control. By analyzing historical data and generating optimized projections, the study identifies critical barriers—including economic constraints, behavioural resistance, and declining ITN efficacy—that contributed to these shortfalls. It also provides country-specific recommendations on the likelihood of achieving the GTS 2025 and 2030 goals.

Simulated intervention scenarios highlight actionable strategies, particularly the role of public-sector engagement in subsidizing ITN distribution to mitigate financial barriers for vulnerable populations. Additionally, using the Cobb-Douglas production model, the study demonstrates how integrated strategies can enhance donor-funded efforts and promote long-term economic sustainability within malaria elimination programs.

This talk will emphasize the necessity of aligning public health interventions with economic policies to sustain high ITN coverage and accelerate progress toward malaria eradication.

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.