Institute for Pure & Applied Mathematics (IPAM) Courses

Collective Intelligence for Deep Learning - A Survey of Recent Developments

Survey of recent developments in collective intelligence for deep learning, exploring self-organization, emergent behavior, and cellular systems to address robustness and adaptability issues in neural networks.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Physical Computation in Insect Swarms - IPAM at UCLA

Explore physical computation in insect swarms, focusing on firefly visual signals and bee pheromone communication. Discover how swarm intelligence emerges from individual interactions.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Multi-Agent Common Sense - IPAM at UCLA

Explore multi-agent common sense through mathematical frameworks combining Bayesian learning and game theory. Discover insights into human collaboration, joint intentions, and cultural knowledge acquisition.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

Categories - The Mathematics of Connection - IPAM at UCLA

Explore the mathematics of connection through category theory, focusing on open systems, their interfaces, and composition. Learn how this approach applies to various fields and collective intelligence.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Learning via Conjectural Variations - IPAM at UCLA

Explore learning via conjectural variations, including challenges, equilibrium concepts, experiments, and applications in collective intelligence mathematics.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Collective Intelligence as Collective Computation - Future Directions

Explore collective intelligence as computation, examining principles of information processing, dimension reduction, and emergent phenomena in biological and social systems.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Waists, Widths and Symplectic Embeddings

Explore geometric measures of manifolds and their applications to symplectic embeddings. Discover area estimates for minimal submanifolds and quantitative symplectic camels in this advanced mathematics talk.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Large Deviations for Triangle Densities

Explore large deviations for triangle densities in graphs, including Borell's inequality, Gaussian noise stability, and applications to quantum ground states approximation.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Volume of P-Zonoids and Inequalities for Determinants

Explore new inequalities for 2-zonoid volumes, potential extensions to p-zonoids, and related determinant inequalities. Delve into Minkowski sums, projections, and support functions in this advanced mathematics lecture.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

The Brownian Transport Map - IPAM at UCLA

Explore Lipschitz transport maps between probability measures, focusing on the Brownian transport map's construction, properties, and applications to Euclidean functional inequalities.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Topological Properties of Hypersurfaces with Low Entropy - IPAM at UCLA

Explore topological properties of hypersurfaces with low entropy, focusing on Colding-Minicozzi entropy, mean curvature flow, and closed hypersurfaces in this advanced mathematics lecture.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

The Log-Minkowski Problem - IPAM at UCLA

Explore the log-Minkowski problem and recent progress in convex geometry, including uniqueness of self-similar solutions and isomorphic resolution, with applications to centro-affine differential geometry.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Singularities and Diffeomorphism - IPAM at UCLA

Explore singularities and diffeomorphism in calculus of variations, covering special cases, classification, and applications in probability and geometry.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Training Quantum Neural Networks with an Unbounded Loss Function - IPAM at UCLA

Explore quantum neural networks, unbounded loss functions, and techniques to overcome barren plateaus in quantum machine learning, with applications in thermal state and Hamiltonian learning.

• YouTube
• 32 minutes
• Self-Paced
• Free Video