Systems Core Courses

Institute for Pure & Applied Mathematics (IPAM)

Convergence of the Planewave Approximations for Quantum Incommensurate Systems

Explore quantum incommensurate systems through rigorous analysis of Schrödinger operators' spectrum distribution, focusing on density of states characterization and planewave approximation methods with novel energy cutoffs.

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

Institute for Pure & Applied Mathematics (IPAM)

Finite-Size Error and Its Correction in Energy Calculations for Periodic Systems

Explore finite-size errors in periodic systems, focusing on Hartree-Fock and MP2 theories. Learn about convergence rates, Madelung-constant correction, and the staggered mesh method for improved calculations.

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

Institute for Pure & Applied Mathematics (IPAM)

Local Response in Bulk-Gapped Interacting Systems - IPAM at UCLA

Explore quantum Hall effect in thin Hall bars, interacting fermion systems' response to local perturbations, and adiabatic theorems for extended many-body systems with bulk gaps.

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

Institute for Pure & Applied Mathematics (IPAM)

Message Passing Neural Networks for Atomistic Systems - Materials - IPAM at UCLA

Explore message passing neural networks for atomistic systems, focusing on thermal transport simulations and diffusion in materials science, with practical examples and convergence tests.

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

Institute for Pure & Applied Mathematics (IPAM)

Taming the Dynamical Sign Problem in Diagrammatic Algorithms for Open Quantum Systems

Explore diagrammatic algorithms for open quantum systems, focusing on balancing dynamical sign problems and error amplification in numerical integration through partial resummation techniques.

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

International Mathematical Union

Mean-Field Limits for Quantum Systems and Nonlinear Gibbs Measures

Explore quantum systems, Bose-Einstein condensation, and nonlinear Gibbs measures in this advanced mathematics lecture on mean-field limits and symmetry-induced independence.

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

International Mathematical Union

Structure-Preserving Model Order Reduction of Hamiltonian Systems

Explore structure-preserving model order reduction for Hamiltonian systems, focusing on symplectic geometry and reduced basis algorithms. Learn about extensions to nonlinear problems and applications in plasma physics.

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

Institute for Pure & Applied Mathematics (IPAM)

Mesoscale Models and Many-Body Systems - IPAM at UCLA

Explores mesoscale structures in many-body systems, explaining the autonomy of continuum equations and their connection to lower-scale physics, with implications for deep neural networks.

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

Institute for Pure & Applied Mathematics (IPAM)

Optimal Scaling Quantum Linear Systems Solver via Discrete Adiabatic Theorem

Explore optimal quantum linear systems solver using discrete adiabatic theorem, achieving linear complexity in condition number and precision, with simplified implementation and constant factor analysis.

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

Institute for Pure & Applied Mathematics (IPAM)

The Quantum Linear Systems Problem - IPAM at UCLA

Explore quantum algorithms for solving linear systems, including improved methods and complexity analysis, with a focus on potential exponential speedups and verification challenges.

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

International Mathematical Union

Tamas Hausel - Enhanced Mirror Symmetry for Langlands Dual Hitchin Systems

Explore enhanced mirror symmetry for Langlands dual Hitchin systems, covering topics from SYZ mirror symmetry to equivariant cohomology and Kirillov algebras.

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

North Carolina School of Science and Mathematics

Linear Data Analysis for Math Common Core Standards - Part 3

Explore linear functions for real-world data modeling, focusing on slope and intercept interpretation, linear regression, and residual analysis using interactive tools and practical examples.

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

North Carolina School of Science and Mathematics

Ratio and Proportion Leading to Slope - Part 2 of NCSSM Common Core Math Series

Explore real-world applications of ratio and proportion, focusing on NCSSM materials. Learn to analyze relationships, create tables, and graph data to understand proportional concepts and develop slope understanding.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

North Carolina School of Science and Mathematics

Not Your Grandfather's Electricity - Physics and Future of Electrical Systems

Explore the evolution of electricity, from historical debates to modern smart grids, covering physics, circuits, renewable energy, and future technologies in this engaging seminar.

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

Applied Algebraic Topology Network

Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.

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