Graph Theory Courses

IAS | PCMI Park City Mathematics Institute

Characteristic Classes in Stable Motivic Homotopy Theory - Part 1

Delve into the foundations of characteristic classes in stable motivic homotopy theory, exploring Quillen's work extensions and modern developments in algebraic geometry and schemes.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 4

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems through expert guidance in advanced algebraic topology and geometry.

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

IAS | PCMI Park City Mathematics Institute

A1-Homotopy Theory and the Weil Conjectures - Part 4

Delve into advanced A1-homotopy theory concepts, exploring cellular homology and Weil conjectures through expert lectures, problem sets, and comprehensive mathematical analysis at the graduate level.

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

IAS | PCMI Park City Mathematics Institute

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 3

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems. Perfect for those with algebraic geometry and topology foundations.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

A1-Homotopy Theory and the Weil Conjectures - Part 3

Delve into A1-homotopy theory, exploring cellular homology and Weil conjectures through advanced mathematical concepts. Learn from expert insights on derived categories and discover new developments in algebraic topology.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 2

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems through expert guidance in advanced algebraic topology and geometry.

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

IAS | PCMI Park City Mathematics Institute

A1-Homotopy Theory and the Weil Conjectures - Part 2

Delve into advanced A1-homotopy theory, exploring cellular homology construction and Weil conjectures analogues through expert-led lectures on derived categories and modern algebraic topology concepts.

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

IAS | PCMI Park City Mathematics Institute

A¹-Algebraic Topology and Introduction to Unstable Motivic Homotopy Theory - Part 1

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and motivic spheres through expert guidance in algebraic topology and geometry fundamentals.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

A1-Homotopy Theory and the Weil Conjectures - Part 1

Delve into advanced algebraic geometry concepts through A1-homotopy theory, exploring cellular homology of Morel and Sawant while examining analogues of the Weil conjectures in modern mathematical frameworks.

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

IAS | PCMI Park City Mathematics Institute

From Matrices to Motivic Homotopy Theory

Explore the foundations of motivic homotopy theory, from matrix fundamentals to advanced concepts, with applications in algebra and algebraic geometry for graduate-level mathematicians.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

A-Upper Motives in Motivic Homotopy Theory

Delve into advanced algebraic geometry concepts focusing on motivic structures of projective homogeneous varieties and reductive groups, featuring research by Karpenko, de Clercq, and Quéguiner-Mathieu.

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

IAS | PCMI Park City Mathematics Institute

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
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

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
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

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
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

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
• Self-Paced
• Free Video