Graph Theory Courses

Institute for Pure & Applied Mathematics (IPAM)

Stochastic Density Functional Theory - IPAM at UCLA

Explore stochastic density functional theory for efficient ground-state calculations in extended materials, including noise reduction techniques and applications in warm dense matter at elevated temperatures.

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

Institute for Pure & Applied Mathematics (IPAM)

Recent Results in Density Functional Theory - IPAM at UCLA

Explore recent advancements in Density Functional Theory, including the Lieb-Oxford bound and Local Density Approximation, presented by Mathieu Lewin at IPAM's workshop on Model Reduction in Quantum Mechanics.

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

Institute for Pure & Applied Mathematics (IPAM)

Quantum Impurity and Quantum Embedding Theory - IPAM at UCLA

Explore quantum impurity and embedding theories, from non-interacting systems to advanced concepts like DMET and DMFT, enhancing understanding of quantum many-body problems.

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

Institute for Pure & Applied Mathematics (IPAM)

Theory of Molecular Interactions - IPAM at UCLA

Explore advanced quantum mechanics concepts, focusing on molecular interactions, perturbation theory, and frequency-dependent properties in this in-depth tutorial by Alexandre Tkatchenko.

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

Institute for Pure & Applied Mathematics (IPAM)

Many-Body Perturbation Theory and Green's Function Methods - IPAM at UCLA

Explore Green's functions and many-body perturbation theory in quantum physics, covering Feynman diagrams, self-energy, and applications like GW method and DMFT. Gain insights into mathematical structures and open problems.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

A Mathematical Introduction to Quantum Embedding Theory - IPAM at UCLA

Explore quantum embedding methods for strongly-correlated materials, focusing on computational challenges at the single-particle level and recent optimization approaches.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Many-Body Perturbation Theory and Wavefunction Methods: A Physics Perspective

Explore many-body perturbation theory and wavefunction methods from a physics perspective, covering applications, multiscale modeling, and advanced quantum mechanics concepts.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Machine Learning and Game Theory for Social Impact

Explore machine learning and game theory applications in security, sustainability, and food rescue, featuring real-world deployments and innovative solutions for societal challenges.

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

Institute for Pure & Applied Mathematics (IPAM)

Binary Black Hole Mergers in Cubic Horndeski Theory - IPAM at UCLA

Explore binary black hole mergers in cubic Horndeski gravity, examining non-linear effects and comparing results to general relativity. Gain insights into alternative gravity theories and their implications for astrophysical phenomena.

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

Institute for Pure & Applied Mathematics (IPAM)

Quantum Field Theory of Exotic Systems - IPAM at UCLA

Explore quantum field theory of exotic systems, focusing on fracton phases and their challenges to conventional understanding. Delve into subsystem symmetries, tensor gauge theories, and peculiar UV/IR mixing phenomena.

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

Institute for Pure & Applied Mathematics (IPAM)

Task Structure and Generalization in Graph Neural Networks

Explore graph neural networks' generalization properties, focusing on the interplay between task structure and architectural biases for improved learning and performance in algorithmic tasks.

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

Institute for Pure & Applied Mathematics (IPAM)

A Framework for Differentiable Discovery of Graph Algorithms

Explore graph algorithm discovery using deep learning and tree decomposition. Learn effective techniques for NP-complete problems with interpretable results and expanded search space.

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

Michael Penn

An Algebra for String Theory - The Virasoro Algebra

Explore the Virasoro algebra, a fundamental concept in string theory, and its applications in theoretical physics and mathematics.

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

Michael Penn

Difference at Distance 1 - Number Theory

Explore number theory concepts focusing on difference 2 at distance 1, with examples, proofs, and generating functions to deepen understanding of this mathematical topic.

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

Michael Penn

Ramanujan's Famous Mod 5 Congruence - Number Theory

Explore Ramanujan's famous (mod 5) congruence in number theory, delving into its mathematical significance and applications. Gain insights into this intriguing concept through clear explanations and examples.

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