# Math230A: Differential Geometry 2023 Semester: Fall | Year offered: 2023 **Outside Link by Selena Zhang and Aayush Gupta ** **\[Syllabus updated\]** Time: 3:00-4:15 pm, Monday-Wednesday Place: Science Center 113 Instructor: Fan Ye, Science Center 505H, Course Assistant: Keeley Hoek, Office Hours: Fan Ye, SC 505H, 4:20-5:20 pm, M-W. Keeley Hoek, SC 333G 1:30-2:30pm Tuesday. Main References: Differential Geometry: Bundles, Connections, Metrics and Curvature, Chapters 1-16, by Clifford H. Taubes Other suggested references: - An Introduction to Differentiable Manifolds and Riemannian Geometry, William M. Boothby: [https://books.google.com/books/about/An\_Introduction\_to\_Differentiable\_M...](https://books.google.com/books/about/An_Introduction_to_Differentiable_Manifo.html?id=oWLJ6zaSwyIC) - Fundations of differentiable manifolds and Lie groups, Frank W. Warner: - Differential forms in algebraic geometry, Raoul Bott and Loring W. Tu: - Vector bundles & K-theory, Allen Hatcher Prerequisites: An undergraduate-level understanding of manifolds. An undergraduate may look at the first chapter of Cliff's book for preparation. Tentative Course Outline: Notes will be posted on the course page after the classes. - Weeks 1-2 (Sept. 6-13): smooth manifolds and Lie groups \[Taubes, Chapters 1-2\] - Weeks 3-4 (Sept. 18-27): vector bundles \[Taubes, Chapters 3-6\] - Weeks 5-6 (Oct. 2-11, with holiday on Oct. 9): metrics and geodesics \[Taubes, Chapters 7-9\] - Weeks 7-8 (Oct. 16-25): de Rham cohomology and covariant derivative \[Taubes, Chapters 12\] - Weeks 9-10 (Oct. 30-Nov. 8): Levi-Civita connections and Riemann curvature tensors \[Taubes, Chapters 15, 14.1\] - Weeks 11-13 (Nov. 13-20, with holidays on Nov. 22-26): characteristic classes and principal bundles \[Taubes, Chapters 14, 10-11\] - Week 14 (Nov. 27-Dec. 4): Yang-Mills equation and applications. --- Attachments- [ picture\_as\_pdf syllabus\_math230a\_01.pdf ](/sites/g/files/omnuum10216/files/fanye/files/syllabus_math230a_01.pdf) - [ picture\_as\_pdf assignment01.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment01.pdf) - [ picture\_as\_pdf math230a\_part\_i.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_part_i.pdf) - [ picture\_as\_pdf assignment02.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment02.pdf) - [ picture\_as\_pdf math\_230a\_part\_ii.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_part_ii.pdf) - [ picture\_as\_pdf assignment03.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment03.pdf) - [ picture\_as\_pdf math\_230a\_part\_iii.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_part_iii.pdf) - [ picture\_as\_pdf math230a\_week7.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_week7.pdf) - [ picture\_as\_pdf math230a\_week\_8.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_week_8.pdf) - [ picture\_as\_pdf assignment\_5\_updated\_01.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_5_updated_01.pdf) - [ picture\_as\_pdf math230a\_week\_10.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_week_10.pdf) - [ picture\_as\_pdf assignment\_4\_updated.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_4_updated.pdf) - [ picture\_as\_pdf assignment\_06\_updated.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_06_updated.pdf) - [ picture\_as\_pdf math230a\_week11.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_week11.pdf) - [ picture\_as\_pdf math230a\_week12.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_week12.pdf) - [ picture\_as\_pdf math230aweek13.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230aweek13.pdf) - [ picture\_as\_pdf final\_exam2023.pdf ](/sites/g/files/omnuum10216/files/fanye/files/final_exam2023.pdf) ---