Institute for Pure & Applied Mathematics (IPAM) Courses

Rotating Convection at Extreme Parameters on a Logarithmic Fourier Lattice

Explore advanced numerical methods for simulating rotating convection using logarithmic Fourier lattices, focusing on efficient computation techniques and comparison with direct numerical simulations.

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

Driving and Quenching of Zonal Flows on Gas Giants

Explore the dynamics of Jupiter and Saturn's fierce winds through 3D simulations, revealing how convective flows drive zonal winds and examining the mechanisms behind their depth limitations.

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

Wall Modes in Rotating Convection - Current Understanding and Challenges

Delve into the complex dynamics of rotating Rayleigh-Bénard convection, exploring wall modes' impact on heat transport, bulk-boundary interactions, and their behavior under different container conditions.

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

Quantum Error Mitigation - Part 2

Delve into advanced quantum error mitigation techniques and strategies, exploring cutting-edge approaches for improving quantum computing reliability through IBM Research expertise.

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

Quantum Error Mitigation - Part 1

Dive into quantum error mitigation fundamentals with IBM Research expert Ewout Van den Berg, exploring key concepts and strategies for quantum computing error suppression.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Quantum Error Correction - Tutorial 2

Delve into advanced quantum error correction concepts, exploring theoretical frameworks and practical applications for quantum computing systems through expert-led technical instruction.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Quantum Error Correction - Tutorial 1

Dive into fundamental principles of quantum error correction, exploring theoretical frameworks and practical applications in quantum computing systems through expert-led instruction.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Covariance-Modulated Optimal Transport Geometry

Explore covariance-modulated optimal transport geometry, a variant of dynamical optimal transport where energy is modulated by distribution covariance matrices, with applications in ensemble Kalman methods for inverse problems.

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

Vector Valued Optimal Transport: From Dynamic to Kantorovich Formulations

Explore vector valued optimal transport theory connecting four existing notions, with applications in multispecies PDE and classification of vector valued measures, including bi-Holder equivalence and gradient flows.

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

Completely Positive Maps and the V-transform

Explore the V-transform as a tool for studying completely positive maps, its relation to quantum optimal transport, and applications in establishing subadditivity of cost in static quantum optimal transport distances.

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

Quadratic Wasserstein Distance Between Quantum Dynamical Systems

Explore the theory of Wasserstein distance between quantum dynamical systems with stationary faithful states, focusing on transport plans, modular groups, and Tomita-Takesaki modular theory of von Neumann algebras.

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

Lipschitz Cost of Quantum Channels on von Neumann Algebras

Explore a framework for quantifying the Lipschitz cost of quantum channels on von Neumann algebras, inspired by quantum optimal transport theory, with applications to gate complexities and simulation costs.

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

How Mathematical Analysis Can Help Better Understand Quantum Algorithms

Explore how mathematical analysis enhances understanding of quantum algorithms through semiclassical analysis, discrete microlocal analysis, and hypocoercivity concepts applied to quantum dynamics simulation.

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

Transport in Free Probability Theory

Explore applications of transport in free probability theory, including its relation to free entropy dimension and L^2 invariants in this mathematical lecture by Dimitri Shlyakhtenko.

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

Optimal Transport by Quantum Channels: Non-quadratic Problems, Metric Properties, and Isometries

Explore quantum mechanical optimal transport theory, focusing on non-quadratic generalizations, p-Wasserstein distances, and geometric properties of quantum channels in density operator dynamics.

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