BIMSA Courses

Construction of Collapsing Spacetimes in Vacuum - ICBS 2024

Explore the construction of collapsing spacetimes in vacuum, featuring black hole regions and Cauchy hypersurfaces, without symmetries.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Quadratic Transform for Fractional Programs in Signal Processing and Machine Learning

Explore advanced fractional programming techniques for signal processing and machine learning, focusing on the quadratic transform method and its applications to complex optimization problems.

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

Construction of Solution Landscape for Complex Systems

Explore the novel "Solution Landscape" concept and its applications in complex systems, including nematic liquid crystals, crystalline phases, and Bose-Einstein condensates.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Reverse-Mathematical Reconsideration of Lower-Level Borel Games

Explore determinacy strength of Gale-Stewart games through Reverse Mathematics, examining collapse phenomena in boolean combinations of Fσ sets and their implications.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Neutron Spectroscopy Studies of Kitaev Quantum Magnets

Explore Kitaev quantum magnets through neutron spectroscopy, examining the Kitaev model, its realization in α-RuCl3, and extension to higher-spin systems like Na3Ni2BiO6.

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

The Global Unramified Geometric Langlands Equivalence

Explore the global unramified geometric Langlands conjecture, its history, motivation, and recent proof, along with remaining open questions in the field.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

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