BIMSA Courses

Instability and Non-Uniqueness in Fluid Dynamics

Explore instability and non-uniqueness in fluid dynamics, focusing on Leray solutions to Navier-Stokes equations and Vishik's findings on 2D Euler systems.

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

D-Modules and Singularities - Bernstein-Sato Ideals and Monodromy for Polynomial Mappings

Explore recent findings connecting D-modules with singularities, focusing on Bernstein-Sato ideals and monodromy in polynomial mappings.

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

S-duality and Lie Super-algebras

Explore geometric realization of quantum simple Lie super-algebras, S-duality, and connections to geometric Langlands correspondence and relative Langlands duality.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

A Renormalisation Group Perspective on Functional Inequalities - ICBS 2024

Explore multiscale analysis for decomposing high-dimensional measures, deriving functional inequalities using renormalization group methods in statistical physics.

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

Weyl-Strength Subconvexity for Dirichlet L-Functions

Explore Weyl-strength subconvexity for Dirichlet L-functions, examining the subconvexity problem and progress on obtaining the Weyl exponent via the method of moments.

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

Quantitative Bounds in the Polynomial Szemerédi Theorem and Related Results

Explore quantitative bounds in polynomial Szemerédi theorem and related problems in additive combinatorics, harmonic analysis, and ergodic theory.

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

Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds

Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.

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

Hilbert's Sixth Problem: From Particles to Waves

Explore Hilbert's Sixth Problem in statistical physics and kinetic theory, examining the derivation of macroscopic laws from microscopic systems in classical and quantum settings.

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

An ℓp Theory of PCA and Spectral Clustering

Explore an advanced $\ell_p$ theory of PCA, improving upon vanilla PCA for heteroscedastic noises and yielding optimal bounds for spectral clustering and community detection.

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

scverse: An Introduction to Single-Cell Data Analysis in Python

Explore Python's ecosystem for single-cell data analysis with scverse, a community-driven initiative coordinating omics data work.

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

Fixing Ambiguities in String Theory Using String Field Theory

Explore how string field theory resolves ambiguities in string theory computations, focusing on D-instanton corrections and matrix model comparisons.

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

Rigidity and Uniformity in Algebraic Dynamics

Explore connections between algebraic dynamics and arithmetic geometry, focusing on preperiodic points and torsion points in abelian varieties. Learn about recent breakthroughs in uniform bounds and conjectures.

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

AI-Assisted Automated Chemical Synthesis Planning and Execution

Explore AI-driven chemical synthesis planning integrated with robotic automation, streamlining complex molecule production for drug development and materials science.

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

How the Hilbert Space of Two-Sided Black Holes Factorizes - ICBS 2024

Explore the factorisation puzzle in AdS/CFT, examining how spacetime wormholes contribute to Hilbert space factorisation in two-sided black holes and its implications for holography.

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

Analytic and Reidemeister Torsions of Digraphs and Path Complexes

Explore Reidemeister and analytic torsions on finite digraphs using path homology theory. Learn about Hodge Laplace operators, torsion identities, and formulas for Cartesian products and joins.

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