Conference GSI Courses

Can Generalized Divergences Help for Invariant Neural Networks?

Explore the potential of generalised divergences in enhancing invariant neural networks, examining their impact on network performance and robustness.

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

Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks

Explore PDE-G-CNNs: equivariant networks with geometric symmetries, data efficiency, and extendability. Discover their functional properties and applications in image processing and deep learning.

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

Algebraic Statistics and Gibbs Manifolds

Explore Gibbs manifolds and their applications in optimization, statistics, and quantum physics, extending toric geometry concepts through an Algebraic Statistics lens.

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

A Non-Formal Formula for the Rankin Cohen Deformation Quantization

Explore the Rankin-Cohen deformation quantization, its connections to modular forms and foliations, and discover a new oscillatory integral formula for Zagier's UDF.

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

Unitarity Excess in Schwarzschild Metric

Explore eigenvalues in Gordon Klein equation with Schwarzschild metric, examining implications for black hole information paradox and eternal black holes.

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

Souriau's Geometric Principles for Quantum Mechanics

Explore geometric principles bridging classical and quantum mechanics, examining symmetries, Planck's constant, and prequantization to determine quantum states through inequalities.

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

Geometric Quantum States and Lagrangian Polar Duality - Quantum Mechanics without Wavefunctions

Explore geometric formulation of quantum states using Lagrangian polar duality, challenging traditional uncertainty principle interpretations and quantum mechanics concepts.

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

Can Cencov Meet Petz - Unifying Classical and Quantum Information Geometry

Explore the unification of Cencov's and Petz's theorems through W*-algebra formulations of classical and quantum information geometry.

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

Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising

Explore scalar curvature monotonicity in quantum exponential family for transverse-field Ising chains, examining finite-size effects and implications for Petz conjecture.

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

Statistical Methods for Medical Image Processing and Reconstruction

Explore statistical methods for medical image processing and reconstruction, from basic to advanced Bayesian approaches, across various imaging modalities.

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

TRANSVERSE POISSON STRUCTURES TO ADJOINT ORBITS IN A COMPLEX SEMI-SIMPLE LIE ALGEBRA

Explore transverse Poisson structures in complex semi-simple Lie algebras, focusing on adjoint orbits and their nilpotent cases. Discover determinantal formulas and quasihomogeneous polynomials in this advanced mathematical topic.

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

Information Theory with Kernel Methods

Explore entropy estimation in data science using kernel methods and quantum information theory for covariance matrices.

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

From Alan Turing to Contact Geometry: Towards a Fluid Computer

Explore the intersection of hydrodynamics, computation, and contact geometry. Discover how fluid dynamics can simulate universal Turing machines and its implications for undecidable fluid paths and celestial mechanics.

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

Variational Gaussian Approximation of the Kushner Optimal Filter

Explore the Variational Gaussian approximation technique for optimizing the Kushner filter, enhancing signal processing and estimation capabilities.

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

On the f-Divergences Between Hyperboloid Models

Explore f-divergences between hyperboloid models in this concise conference talk, delving into mathematical concepts and their applications in geometric analysis.

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