Institute for Pure & Applied Mathematics (IPAM) Courses

Support Varieties and the Tensor Product Property - Lecture

Explore support varieties in representation theory, focusing on tensor product properties and indecomposable periodic objects. Discover applications in finite groups and tensor categories.

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

G-modules: Stable Categories and Subcoalgebras - Lecture on Affine Group Scheme Representations

Explore affine group scheme representations, stable module categories, and support theory for G-modules. Discover filtrations associated with subcoalgebras of coordinate algebras in this advanced mathematics lecture.

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

Induced Functors on Drinfeld Centers via Monoidal Adjunctions

Explore induced functors on Drinfeld centers through monoidal adjunctions, examining their compatibility with braiding and preservation of commutative objects in tensor categories.

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

Chinese Remainder Theorem and Carlson's Theorem for Monoidal Triangulated Categories

Explore Carlson's connectedness theorem generalization for monoidal triangulated categories, including a Chinese remainder theorem version and Balmer support properties.

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

Stable Module Category for Finite Group Schemes over Commutative Noetherian Rings

Explore finite group schemes, tensor triangular analysis, and Balmer spectrum calculations in stable module categories, based on recent advancements in cohomology and representation theory.

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

Circuit-to-Hamiltonian from Tensor Networks and Fault Tolerance - IPAM at UCLA

Explore a novel approach to mapping quantum circuits to local Hamiltonians using tensor networks, avoiding clock registers and incorporating fault tolerance for robust quantum computation.

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