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Brain connectivity inference methods, focusing on directed connectivity inference in the frequency domain. Multivariate autoregressive methods, such as partial directed coherence (PDC) and variants, directed transfer function (DTF), and related estimators, recover directed connectivity networks from neural signals (EEG, fMRI, MEG). From these inferred networks, we go beyond pairwise graphs toward multiway, multilayer, temporal, and dynamic representations that capture directed, higher-order neural interactions through hypergraphs, simplicial complexes, and digraph-based complexes. We characterize these structures through discrete geometry (Ollivier–Ricci and Forman–Ricci curvatures, finite geometries, and combinatorial invariants) and through graph theoretic and topological data analysis (TDA) (persistent homology, filtration-based descriptors, Q-analysis, and network summary statistics), quantifying structural and functional organization across scales.

Analysis of neural population activity through low-dimensional neural manifolds. Investigating the geometric and topological organization of neural and artificial latent representations, and determining how manifold structure encodes cognitive maps, learned world models, and behavioral states.

• Topological and Geometric Deep Learning for Neuroscience: Development and application of geometric, topological, and manifold-aware learning architectures (graph, hypergraph, simplicial, and sheaf neural networks, and manifold-valued models, adapted to the structure of neural and connectomic data). The goal is to build models whose inductive biases respect the higher-order, geometric, and topological nature of brain data, improving both predictive performance and interpretability relative to generic deep learning approaches.
• AI Systems for Neuroscience Research: Investigating specialized AI systems for neuroscience research, including specialized small language models (SSLMs), domain adaptation, scientific reasoning, research assistance, and automated analysis. A particular focus is understanding the trade-offs between model scale, domain specialization, generality, reliability, and computational efficiency across neuroscience research workflows.

Brain-inspired AI algorithms, encompassing spiking neural networks (SNNs), stochastic SNNs, ultra-LIF SNNs, and oscillatory neural networks (ONNs), together with biologically grounded learning rules such as dopaminergic reinforcement learning and neuromodulated synaptic plasticity.

• Categorical Approaches to Consciousness and Cognition: Application of category theory and higher-category methods to consciousness science, with a focus on developing compositional and relational mathematical frameworks for cognitive processes. Investigating how categorical structures can formalize relationships between perception, embodiment, self-modeling, agency, and conscious experience, as well as their integration within 4E cognition and cognitive multi-agent systems.
• Computational Philosophy of Mind and Consciousness: Developing mathematical and computational frameworks for formalizing, simulating, and comparing theories of mind and consciousness. This work investigates how philosophical positions such as functionalism, emergentism, physicalism, dualism, and Integrated Information Theory (IIT) can be expressed as computational models, evaluated through common formal criteria, and integrated into unified frameworks for studying cognition and consciousness.

Investigating how complex collective behaviors arise from interactions among cognitive agents with different cognitive architectures and environments, including MARL-trained, ethology-based animal agents; LLM-based multi-agent systems of human behavior; and LLM-based opinion dynamics systems. A central focus is the emergence and evolution of interaction-network topology, using graph theory and applied algebraic topology to identify structural signatures of phenomena such as cooperation, hierarchy, social organization, consensus, polarization, and fragmentation, and to understand the feedback between cognitive architectures, environments, network topology, and collective behavior.