BIMSA Courses

Learning Manifold-Structured Data Using Deep Neural Networks - Theory and Applications

Explore deep neural networks' ability to learn geometric data structures using multi-chart latent spaces and Chart Auto-Encoders, with theoretical foundations and practical applications.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Second Order Interior Estimates of Monge-Ampere Type Equations

Explore interior second order derivative estimates for Monge-Ampere type equations, focusing on partial structure cases using Pogorelov estimates and Legendre transforms.

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

3D Kinetic Couette Flow via the Boltzmann Equation in the Diffusive Limit

Explore the rigorous connection between incompressible Couette flow and the Boltzmann equation through novel anisotropic estimates in the Wiener algebra function space.

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

Large Values of Zeta and Dirichlet L-Functions - ICBS 2024

Explore large values of Riemann zeta and Dirichlet L-functions on the critical line, uncovering key insights in analytic number theory.

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

Particle and Game Theoretic Methods for Multi-scale and High Dimensional Problems

Explore Lagrangian and game theoretic approaches for solving complex PDEs, including front speed computation, high-dimensional entropy production, and turbulent combustion analysis.

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

Geometric Principle in Wave Scattering and Applications

Explore a geometric principle bridging micro and macro scales in wave scattering theory, with applications in super-resolution imaging and invisibility cloaking.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Analyticity in Spin and Causality Constraints in Conformal Bootstrap - ICBS 2024

Explore analyticity in spin and causality constraints in conformal bootstrap, including applications to operator spectrum and AdS/CFT duality.

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

Generalized Spin-Statistics Theorem for Loop Excitations

Explore an extended spin-statistics theorem for loops using Klein bottle representation. Examine new solvable lattice models for topological phases and fermionic loop excitations in higher dimensions.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Symplectic Singularities Arising from Algebras of Symmetric Tensors

Explore symplectic singularities from symmetric tensor algebras, their construction, and relation to existing methods in algebraic geometry and representation theory.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Degeneration of Singular Circle Patterns

Explore singular Euclidean circle patterns, cone-angle maps, and degeneration schemes. Analyze the structure of cone-angle polytopes and their relationship to admissible partial edge orientations.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Summation for Two Sets in Hyperbolic Space - ICBS 2024

Explore hyperbolic summation and its application in developing Brunn-Minkowski theory for hyperbolic space geometry, extending classical Euclidean concepts.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Certifying Bipartite Pure Quantum States Efficiently Using Untrusted Devices

Explore efficient certification of bipartite pure quantum states using untrusted devices, requiring fewer measurements while maintaining reliability in quantum experiments.

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

Multipollutant Traceability via Dynamic CGO Solutions

Explore a novel inversion framework using dynamic CGO solutions for precise identification of multiple pollution sources in environmental systems, addressing complex pollutant interactions.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Bayesian Quantile Joint Modeling of Multivariate Longitudinal and Time-to-Event Data

Explore Bayesian quantile joint modeling for multivariate longitudinal and time-to-event data, focusing on non-Gaussian outcomes and time-varying covariates in medical research applications.

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

Computational Quantum Mechanics in Phase Space - An Attempt to Break the Curse of Dimensionality

Explore computational quantum mechanics in phase space, focusing on breaking the curse of dimensionality through grid-based and particle-based methods for high-dimensional Wigner quantum dynamics simulations.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video