Institute for Pure & Applied Mathematics (IPAM) Courses

The Density Conjecture for Activated Random Walk

Explore self-organized criticality in activated random walk models, examining critical densities across various configurations and their implications for understanding energy release patterns in physical systems.

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

Radon-Nikodym Topography of Amenable Equivalence Relations in Acyclic Graphs

Explore the extension of Adams's dichotomy to measure-class-preserving settings, examining Radon-Nikodym cocycle behavior in acyclic graphs and its connection to global properties like amenability.

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

Interacting Polya Urns - Statistical Mechanics Beyond 2D

Explore interacting Polya urns on graphs, their asymptotic behavior, and convergence to equilibrium in this statistical mechanics presentation by Omer Angel at UCLA's IPAM workshop.

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

Perfect t-Embedding of Uniformly Weighted Hexagon

Explore perfect t-embedding of uniformly weighted hexagons in this advanced mathematics lecture, delving into vertex models and their algebraic and probabilistic aspects of universality.

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

Frozen Boundaries and Their Fluctuations in the Square-Ice Model

Explore the emptiness formation probability in the six-vertex model, focusing on frozen boundaries and fluctuations in square-ice. Discover insights into arctic curves and the GUE Tracy-Widom distribution.

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

Geometry of Dimer Models

Explore the asymptotic phenomena of random dimer coverings on large planar graphs, focusing on Aztec diamonds and their connection to Riemann surface geometry in this advanced mathematics lecture.

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

Fast Erasure Decoder for a Class of Quantum LDPC Codes - IPAM at UCLA

Explore fast erasure decoding for quantum LDPC codes, focusing on hypergraph product codes and their potential to reduce qubit count in fault-tolerant quantum computers.

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

Layer Codes - IPAM at UCLA

Explore topological defect networks in quantum error correction, focusing on a novel construction method for 3D codes with optimal scaling parameters and low-weight stabilizers.

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

High-Dimensional Sipser-Spielman Codes - IPAM at UCLA

Exploration of high-dimensional Sipser-Spielman codes, extending expander codes to cell complexes and cellular sheaves, with applications in quantum error correction and coding theory.

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

Fault Tolerant Quantum Computation Using Majorana-Based Topological Qubits

Explore fault-tolerant quantum computation using Majorana-based topological qubits, focusing on tetron qubits and scalable error correction in semiconductor-superconductor heterostructures.

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

Topological Defects in Toric Code and Sequential Quantum Circuit - IPAM at UCLA

Explore topological defects in toric code and sequential quantum circuits, focusing on the Cheshire string and its implications for understanding higher-dimensional topological orders and quantum error correction.

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

Categorical Landau Paradigm and the SymTFT - IPAM at UCLA

Explore advanced concepts in quantum physics with Oxford researcher Sakura Schafer-Nameki, focusing on the Categorical Landau Paradigm and SymTFT in relation to quantum error correction and gravity.

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

Global Unitaries and Local Measurements - IPAM at UCLA

Explore quantum cellular automata, local unitary circuits, and measurement-induced locality-preserving unitaries in this advanced talk on quantum information theory and topology.

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

Entanglement of Sections - IPAM at UCLA

Explore quantum information in parameter families through examples, presented by Microsoft Research's Michael Freedman at IPAM's workshop on topology and quantum error correction.

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

The Development of Quantum Error Correction - Green Family Lecture at IPAM at UCLA

Explore the evolution of quantum error correction with Peter Shor, overcoming the Heisenberg Uncertainty Principle to enable fault-tolerant quantum computing. Gain insights into early developments and their impact.

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