BIMSA Courses

Analysis on Metric Spaces and Walk Dimension

Explore Analysis on Ahlfors-regular metric spaces, focusing on Hausdorff and walk dimensions. Gain insights into integral and differential calculus on fractals and regular metric spaces.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Non-linearities and Gravitational Signals from Black Hole Spacetimes

Explore non-linear behavior of perturbed black holes and its implications for gravitational wave detection and new physics in mergers.

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

Operator Algebras, Tensor Categories and Tensor Networks in Topological Order

Explore tensor networks in topological order using operator algebra techniques. Discover quantum symmetries and their mathematical representation through tensor categories.

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

Derived Approach to Highest Weight Categories

Explore highest weight categories in Representation Theory, examining their interpretation through exact categories, abelian envelops, and exceptional collections in derived categories.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

When and Why Do Efficient Algorithms Exist for Constraint Satisfaction and Beyond

Explore the mathematical structures behind efficient algorithms for constraint satisfaction problems and beyond, focusing on polymorphisms and their role in computational complexity.

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

Hermitian Yang-Mills Connections on Log Terminal Kahler Spaces

Explore Hermitian Yang-Mills theory on mildly singular spaces, focusing on recent results for sheaves and log terminal Kähler spaces.

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

Approximation of Non-Linear Hyperbolic Problems and Conservation Properties

Explore advanced numerical methods for non-linear hyperbolic problems, focusing on conservation properties and flux formulations in various schemes like finite volume and discontinuous Galerkin.

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

Optimal Immersions in the Calculus of Variations of Surfaces

Explore innovative minmax techniques for optimal surface immersions, including recent progress on Yau, Willmore, and 16π conjectures in calculus of variations.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Graph Limits and Homomorphism Density Inequalities

Explore graph limits theory, homomorphism density inequalities, and their applications in extremal combinatorics. Gain insights into undecidability and randomness in graph theory.

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

A Nonlinear Least-squares Finite Element Method for the Monge-Ampere Equation

Explore a nonlinear least-squares finite element method for solving the Monge-Ampere equation, focusing on smooth convex solutions and innovative degrees of freedom.

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

Higher Representation Theory and Low-Dimensional Topology

Explore higher representation theory's role in geometric representation and its connection to 4D topology, focusing on Heegaard-Floer invariants.

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

A Morse Model for Stable Homotopy - ICBS 2024

Explore stable homotopy groups, framed bordism, and Morse theory in topological spaces. Gain insights into Floer homotopy foundations and the Pontryagin-Thom construction.

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

Filling Radius, Positive Scalar Curvature and Quantitative Operator K-Theory

Explore techniques in quantitative operator theory to estimate filling radius, connecting positive scalar curvature and asymptotic dimension in large-scale geometry.

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

Geometry of Dimer Models - ICBS 2024

Explore asymptotic phenomena in random dimer coverings, focusing on Aztec diamonds and their connection to Riemann surface geometry.

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

Representations of Simple Affine Vertex Algebras at Elliptic Levels and Affine Springer Fibres

Explore connections between affine vertex algebras and elliptic affine Springer fibres, delving into representation theory and geometric insights.

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