BIMSA Courses

Pseudo-Isotopy and Diffeomorphisms of 4-Manifolds

Explore recent advancements in pseudo-isotopy theory and its applications to studying diffeomorphisms of 4-manifolds with David Gabai.

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

Lensless Imaging: Overview, Opportunities, and Challenges

Explore lensless imaging advancements, principles, and applications in 3D reconstruction, discussing challenges and future opportunities in camera design and computational algorithms.

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

Growth in Tensor Powers

Explore tensor power decomposition in group representations, focusing on asymptotic behavior and non-negligible summands using symmetric tensor category theory.

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

Educability: Defining and Simulating Human Capabilities - ICBS 2024

Explore "educability" as a defining human capability, synthesizing learning from experience and others to explain humanity's achievements and guide future technology development.

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

The Ricci Flow - Lecture by Richard Hamilton

Explore the Ricci flow equation, its applications in geometry, and its role in understanding manifold curvature evolution. Gain insights into singularities and geometric analysis.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Chaos and Black Holes: From Butterfly Effect to Event Horizons - ICBS 2024

Explore chaos theory, quantum systems, and black holes, examining their interconnections and the fascinating implications for understanding event horizons.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

A Proof of the Erdos-Faber-Lovasz Conjecture

Explore the recent proof of the Erdos-Faber-Lovasz conjecture and its generalization, delving into linear hypergraphs and chromatic index concepts.

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

Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps

Explore sharp rectifiability results for singular sets of minimizing harmonic maps, with uniform Minkowski bounds and integrability. Analyze quantitative stratification and dimension-reduction techniques.

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

Ball Quotients and Algebraic Geometry - ICBS 2024

Explore ball quotients in algebraic geometry, focusing on moduli spaces, Kaehler metrics, and their connections to sporadic finite simple groups. Examine known examples and recent progress on the Allcock ball quotient.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Global Convergence in Stochastic Optimization - ICBS 2024

Explore stochastic optimization algorithms with adaptive variance for non-convex functions, featuring provable convergence rates and numerical examples.

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

Reconstructing Reality: From Physical World to Virtual Environments

Explore data-driven modeling techniques integrating classical methods and statistical learning to reconstruct reality in virtual environments, from traffic flow to crowd behaviors and deformation estimation.

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

Cartan Geometry and Infinite-Dimensional Kempf-Ness Theory

Explore Cartan geometry and infinite-dimensional Kempf-Ness theory, focusing on novel approaches to generalize concepts to infinite dimensions and applications in Kähler geometry, deformation quantization, and gauge theory.

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

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