BIMSA Courses

Critical Points of Eisenstein Series and Spectrum of the Lame Operator

Explore critical points of Eisenstein series E2, E4, E6 and their applications to the Lame operator's spectrum in this advanced mathematics lecture.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Higher Condensation Theory in Topological Orders

Explore a unified mathematical theory of defect condensations in topological orders across all dimensions, based on higher categories, algebras, and representations.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Stacking Group Structure of 't Hooft Anomalies and Fermionic Topological Phases

Explore 't Hooft anomalies in quantum field theory and their connection to fermionic topological phases, focusing on the Abelian group structure in lower dimensions.

• YouTube
• 1 hour
• On-Demand
• Free Video

Recent Progress on Self-Expanders of Mean Curvature Flow and Applications

Explore recent advancements in self-expanders of mean curvature flow, their role in modeling singularities, and applications in geometric analysis.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Large N of Chern-Simons Matrix Model and Conformal Field Theory

Explore the emergence of 1+1D conformal field theory from large N limit of 2+1D Chern-Simons matrix models, including Kac-Moody algebra and holographic duality.

• YouTube
• 46 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video