Talks

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.

The facultatively multicellular amoeba Dictyostelium discoideum is a model system for studying the transition from unicellular to multicellular organization. It is a remarkable example of microbes with aggregative life cycles, which evolved multiple times independently in distant taxa. A key feature of such cycles is that multicellular aggregates can contain cells that are genetically different, and are therefore subjected to a high degree of conflict.

I will discuss different solutions that have been proposed to account for the evolutionary persistence of such apparently paradoxical life cycles. In particular, in the light of recent experimental results, I will address the link between proximate causes, rooted in single-cell mechanics, and ultimate causation. I will also show how agent-based and eco-evolutionary models can be used to understand the role of heterogeneous motility in the evolution of aggregative life cycles.

 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.