Institute for Pure & Applied Mathematics (IPAM) Courses

Anomalous Dissipation for Passive Scalars

Explore anomalous dissipation in hydrodynamic turbulence for passive scalars, examining a rough divergence-free velocity field and its connections to scalar turbulence theories and inviscid mixing.

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

Heat Transport Efficiency Beyond the So-Called 'Ultimate' Regime

Explores innovative approaches to thermal convection, challenging traditional Rayleigh-Bénard models with radiative heating techniques to achieve more efficient heat transport in turbulent flows.

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

Transportation Engineering for Connected and Automated Vehicles

Explore the impact of connected and automated vehicles on transportation engineering, focusing on mathematical challenges and opportunities in this emerging field.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Basic Traffic Models and Traffic Waves

Explore fundamental traffic models and wave phenomena in vehicular flow, examining mathematical concepts crucial for understanding and optimizing autonomous vehicle systems.

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

Triangular Ice Combinatorics

Explores Alternating Phase Matrices, a generalization of Alternating Sign Matrices, in the context of triangular lattice ice models. Discusses connections to domino tilings and presents enumeration formulas and limit shape results.

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

Positivity for Symmetric Functions and Vertex Models

Explore connections between symmetric function homomorphisms and stochastic six-vertex model positivity, linking to RSK correspondence in algebraic combinatorics.

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

Polymer Partition Functions and the Geometric RSK Correspondence

Explore geometric RSK correspondence, polymer partition functions, and their connections to discrete Gibbs fields in this advanced mathematics lecture by Ivan Corwin.

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

Nonconvex Homogenization for 1D Controlled Brownian Motion in a Random Potential

Explores stochastic control of Brownian motion in random potentials, analyzing optimal payoff growth and Bellman equation homogenization. Discusses effective Hamiltonians and distinct control regimes.

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

A General Theory for Discrete-Time Mean-Field Games

Comprehensive theory of discrete-time mean-field games, covering perfect and imperfect information structures, existence of equilibria, and extensions to risk-sensitive scenarios and hierarchies.

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

Computational Methods for Mean-Field Games

Explore computational methods for mean-field game systems, including finite-difference, convex optimization, Lagrangian, and machine-learning techniques for solving high-dimensional Hamilton-Jacobi PDEs.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Towards Real-Time Reachability

Explore advanced techniques in real-time reachability analysis for high-dimensional systems, focusing on Hamilton-Jacobi PDEs and their applications in control and safety verification.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Gradient Descent, Stochastic Gradient Descent, and Acceleration - Part 2

Explore advanced gradient-based optimization methods for large-scale machine learning, including stochastic gradient descent and accelerated versions, with convergence analysis and ODE connections.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Sample-Based Learning Model Predictive Control

Explores learning predictive control for autonomous systems, focusing on sample-based LMPC for constrained uncertain linear systems. Discusses safe set design, value function, and data-driven approximations, with applications in autonomous cars and solar…

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

Curbing Our Enthusiasm - Constraining Decision Policies Learned from the Past to Ensure Good Futures

Explore batch off-policy reinforcement learning challenges and solutions, including structural minimization for future performance and algorithms for personalized policies using historical data.

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

Trying to Make Sense of Control from Pixels

Explores challenges in merging machine learning with control systems, focusing on autonomous vehicles using vision. Discusses uncertainty quantification, robust controller design, and performance guarantees.

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