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Bayesian Inference and Uncertainty Quantification for AI: Posterior Learning, Predictive Guarantees, Calibration, Reliable Decisions

Discrete Structures and Combinatorics for AI: Graphs, Symmetry, Relaxation, the Limits of Learned Algorithms

Computational Linear Algebra and Tensor Methods for AI: Stability, Randomization, Low-Rank Structure, Scalable Computation

Logical and Compositional Foundations of AI: Proof, Semantics, Composition, Verifiable Machine Reasoning

Sequential Decision Making for AI: Interaction, Learning, Memory, and Control

Training-Time Optimization of AI: Data, Dynamics, Scaling, and Post-Training

Causal Inference and Learning for AI: Interventions, Identification, Counterfactuals, Decisions

Geometric Foundations of AI (II): Data Manifolds, Symmetry, and Learned Representations

Resilience of AI Systems: Detection, Containment, Recovery, and Re-entry

Geometric Foundations of AI (I): Parameter Spaces, Statistical Manifolds, and Optimization

Scalable Oversight of AI Systems: Verification, Discriminating Power, and Safety Assurance

Deployment-Time Optimization of AI: Robustness, Compression, Evaluation, Inference, and Adaptive Environments

Operator and Spectral Theory for AI: Operators, Spectra, Resolvents, Semigroups, Infinite-Dimensional Learning

Algebraic Statistics and Singular Models for AI: Polynomial Models, Identifiability, Learning, Latent Geometry

Safety of Embodied AI and Autonomous Systems: Control, Safe Learning, Verification, Runtime Assurance

Stochastic Dynamics for AI: Continuous-Time Methods Learning, Sampling, Generation, and Control

Privacy Mathematics for AI Systems: Differential Privacy, Information Leakage, Memorization, Auditing, and Assurance

Information Theory for AI: Compression, Representation, and the Limits of Machine Knowledge

Approximation Theory for AI: Function Classes, Resource Trade-offs, and the Limits of Learnability

Statistical Physics of Learning and AI: Disorder, Free Energy, Phase Transitions, Neural...

Dynamics, Stability, and Generative Flows for AI: State-Space Lyapunov Stochastic Evolution, Transport

High-Dimensional Statistics for AI: Probability, Geometry, Spectra, and the Limits of Learning-Theoretic Transfer

Topological Data Analysis and Learning: Persistent Homology, Stability, Differentiable Topology, Multiscale Learning...

Games, Incentives, and Mechanism Design for AI Agents: Strategic Interaction, Contracts, Markets,...

Quantum Information and Tensor Networks for AI: Entanglement, Structured Representations, Learning, Classical...

AI Safety and Risk Management - A Quantitative Approach

Computation and Complexity for AI: Algorithms, Lower Bounds, Resource Trade-offs

Embodied Intelligence: Geometry, Mechanics, and Sensorimotor Control (Mathematics of Intelligent Systems)

Optimal Transport for AI: Theory, Computation, and Applications

AI Control and Assurance: Safety Under Imperfect Alignment