BIMSA Courses

Higher Genus Meanders and Masur-Veech Volumes

Explore higher genus meanders, their asymptotics, and connections to moduli spaces of Abelian and quadratic differentials. Gain insights into complex mathematical concepts and recent advances in geometry.

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

Algebraic Renormalisation of Regularity Structures

Explore canonical renormalisation of singular stochastic PDEs through regularity structures, bialgebras of decorated forests, and algebraic Birkhoff factorisation.

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

Polynomial Bounds on Reidemeister Moves in Knot Theory

Explore polynomial bounds on Reidemeister moves in knot theory, examining algorithms for trivial knot recognition and the relationship between diagram complexity and move sequences.

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

Variational Approximations for Bayesian and Semi-Bayesian Inferences

Explore variational approximations in Bayesian inference, focusing on group-variable selection and heteroscedastic Gaussian processes. Learn efficient parameter estimation and process forecasting techniques.

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

Graph Theory for Exploration of Material Genes and Structural Chemistry of Li-ion Batteries

Explore graph theory's application in material genes and structural chemistry of Li-ion batteries. Uncover new paradigms for advancing critical battery materials through interdisciplinary research methods.

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

Accelerating Materials Design with Crystal Graph Neural Networks

Explore Crystal Graph Convolutional Neural Networks for predicting material properties and their impact on graph neural networks and transformers in materials design.

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

Sparsity of Rational Points on Curves - What is Known and What is Expected

Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.

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

The Emergent String Conjecture in Quantum Gravity

Explore the Emergent String Conjecture in quantum gravity, its origins, implications, and recent developments in theoretical physics and string theory.

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

Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds

Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.

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

Moduli of Curves and Moduli of Sheaves - Relationships and Correspondences

Explore relationships between moduli spaces of curves, maps, and sheaves, from GW/DT correspondence to connections with K3 surfaces and abelian varieties moduli.

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

On the Direct Summand Conjecture and Beyond

Explore the direct summand conjecture's history, proof, and impact on commutative algebra and mixed characteristic birational geometry.

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

Gravity as a Double Copy of Gauge Theory

Explore the gravitational double copy framework, connecting gravity to Yang-Mills theory and enabling advanced quantum computations and classical general relativity studies.

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

Heuristics for the Arithmetic of Elliptic Curves and Abelian Varieties

Explore probabilistic models for elliptic curve arithmetic, examining theoretical evidence and predictions for higher-dimensional abelian varieties.

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

The Higgs Boson and the Possible Instability in Its Potential

Explore the Higgs boson's discovery, its implications, and potential instability in ultra-high energy scenarios with insights from LHC findings.

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

Understanding the Visual World Through Object Intrinsics

Explore neuro-symbolic approaches to scene and object understanding, focusing on intrinsic structures and their role in visual data interpretation and generalization.

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