IAS | PCMI Park City Mathematics Institute Courses

Introduction to Chow Groups in Algebraic Geometry - Part 2

Delve into complex algebraic geometry through Chow groups, exploring algebraic subvarieties, divisors, and line bundles while uncovering connections to the Hodge conjecture and homotopy theory.

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

Local Systems in Arithmetic Geometry

Delve into fundamental group theory in arithmetic geometry, exploring local systems and their motivic aspects through deep conjectures and geometric obstructions in complex quasi-projective varieties.

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

Theory of Near-Term Quantum Advantage - Part 2

Delve into quantum computational advantage theory, exploring evidence for near-term quantum experiments surpassing classical computers and examining current simulation algorithms and complexity analysis.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Algorithmic Dual to the Adversary Method in Quantum Query Complexity - Part 5

Delve into quantum query complexity's algorithmic dual to the adversary method, exploring theoretical foundations and practical applications in quantum computing and algorithm development.

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

The Polynomial Method in Quantum Query Complexity - Part 2

Delve into quantum query complexity through polynomial methods, exploring fundamental lower bound techniques, compressed oracle approaches, and their role in quantum algorithm development.

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

Quantum-Inspired Algorithms: Sketching and Beyond - Part 3

Delve into quantum singular value transformation (QSVT) and polynomial approximation techniques, exploring their applications in quantum algorithm design for data analysis and machine learning.

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

Topological Aspects of Quantum Codes: Transversal Gates - Part 4

Delve into advanced quantum computing concepts, focusing on topological aspects of quantum codes, transversal gates, and surface codes with emphasis on practical applications and mathematical foundations.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Stoquastic Hamiltonians in Quantum Computing - Lecture 5

Delve into quantum Hamiltonian complexity, focusing on stoquastic systems and their computational properties. Learn to analyze ground states and simulate quantum systems with formal complexity-theoretic approaches.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Theory of Near-Term Quantum Advantage - Part 5

Delve into the theoretical foundations of near-term quantum advantage, exploring computational complexity, classical intractability, and simulation algorithms for quantum experiments.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Circuit Complexity of Code States in Topological Quantum Computing - Part 3

Delve into advanced quantum code theory, focusing on surface codes, dimensional limitations, and circuit complexity in quantum computing systems for practical applications and topological phases.

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

Theory of Near-Term Quantum Advantage - Part 4

Delve into quantum computing advantage theory, exploring experimental demonstrations, classical simulation algorithms, and computational complexity in near-term quantum devices.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Quantum Hamiltonian Complexity - Lecture 4

Delve into quantum systems' computational complexity, focusing on ground states, energy calculations, and simulation challenges in quantum Hamiltonian systems through rigorous theoretical analysis.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Theory of Near-Term Quantum Advantage - Part 3

Delve into quantum computing advantage theory, exploring experimental demonstrations, classical simulation algorithms, and the computational capabilities of near-term quantum devices.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Quantum Hamiltonian Complexity - Lecture 3

Delve into quantum Hamiltonian complexity, exploring computational challenges in quantum systems, ground states, and simulation methods through rigorous complexity-theoretic analysis.

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

Codes and Homology in Topological Quantum Computing - Part 2

Delve into quantum codes and homology, focusing on surface codes, their practical applications, and connections to topological phases of matter. Learn key theorems about code distances and logical qubits in various dimensions.

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