Graph Theory Courses

Institute for Pure & Applied Mathematics (IPAM)

Basis-Set Correction Based on Density-Functional Theory - IPAM at UCLA

Rigorous framework for basis-set correction in quantum mechanics using density-functional theory, explored through a one-dimensional model with delta-potential interactions for systematic analysis.

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

Institute for Pure & Applied Mathematics (IPAM)

Beyond Density Functional Approximations by Lessons From Density Functional Theory

Exploring alternatives to density functional approximations in quantum mechanics, focusing on extrapolating model families and generalizing Kato's cusp condition for improved accuracy in electronic systems.

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

Institute for Pure & Applied Mathematics (IPAM)

Fast Algorithm for the Strong-Interaction Limit of Density Functional Theory

Explore a novel algorithm for computing the strong-interaction limit in density functional theory, enhancing accuracy in modeling strongly correlated systems and overcoming computational challenges.

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

Institute for Pure & Applied Mathematics (IPAM)

Field Theory Methods for Multiscale Description of Quantum Systems - IPAM at UCLA

Explore quantum field theory's role in multiscale phenomena, from fundamental interactions to condensed matter physics and biology. Learn about inequivalent Hilbert space representations and their applications.

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

Institute for Pure & Applied Mathematics (IPAM)

Quantum Field Theory of Exotic Systems - IPAM at UCLA

Explores quantum field theory for exotic systems, focusing on fracton phases and subsystem symmetries. Discusses challenges to traditional beliefs and examines novel approaches in 2+1 and 3+1 dimensions.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes

Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.

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

Institute for Pure & Applied Mathematics (IPAM)

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
• Self-Paced
• Free Video

IMSA

Gauge Theory and Low Dimensional Topology - Conference Lecture

Explore gauge theory and low-dimensional topology with expert insights from Paul Feehan in this engaging 48-minute conference talk at the University of Miami.

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

IMSA

Gauge Theory and Low Dimensional Topology

Explore gauge theory and low-dimensional topology with insights from MIT expert Tom Mrowka in this conference talk at the University of Miami.

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

IMSA

Periods, Shafarevich Maps and Applications - Nodal Surfaces and Coding Theory

Explore nodal surfaces and coding theory in K3 geometry. Learn about period maps, Torelli theorem, and binary codes in relation to polarized nodal K3 surfaces and their components.

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

IMSA

Homological Mirror Symmetry - Floer Homotopy Theory

Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with expert Mohammed Abouzaid.

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

IMSA

Homological Mirror Symmetry - Mohammed Abouzaid - Floer Homotopy Theory Pt. II

Explore recent advancements in Floer generalized homology groups, their applications, and ongoing research on curvature in this context with Mohammed Abouzaid.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

IMSA

Homological Mirror Symmetry - Floer Homotopy Theory

Explore recent developments in Floer generalized homology groups, their applications, and ongoing research on curvature in Floer homotopy theory with Mohammed Abouzaid.

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

IMSA

Homological Mirror Symmetry - Coulomb Branches & Rozansky-Witten Theory Pt. II

Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact and infinite-dimensional target spaces.

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

IMSA

Homological Mirror Symmetry - Coulomb Branches and Rozansky-Witten Theory

Explore Rozansky-Witten theory and its connection to homological mirror symmetry, from basics to modern developments involving non-compact spaces and ongoing research.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video