# MATH230A: Differential Geometry Semester: Fall | Year offered: 2022 **Outside Link by Selena Zhang and Aayush Gupta ** \[IMPORTANT\] The syllabus is updated. Time: 10:30-11:45 pm, Tuesday-Thursday Place: Science Center 221 Instructor: Fan Ye, Science Center 505H, Course Assistant: Keeley Hoek, Science Center 333G, Office Hours: Fan Ye, SC 505H, Tuesday 1:30-3:20 pm. Keeley Hoek, SC 333G, Thursday 2:00-3:00 pm 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\_…](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. 1-8): smooth manifolds and Lie groups \[Taubes, Chapters 1-2\] - Weeks 3-4 (Sept. 13-22): vector bundles \[Taubes, Chapters 3-6\] - Weeks 5-6 (Sept. 27-Oct. 6): metrics and geodesics \[Taubes, Chapters 7-9\] - Weeks 7-8 (Oct. 11-20): de Rham cohomology and covariant derivative \[Taubes, Chapters 12\] - Weeks 9-10 (Oct. 25-Nov. 3): Levi-Civita connections and Riemann curvature tensors \[Taubes, Chapters 15, 14.1\] - Weeks 11-13 (Nov. 8-22): characteristic classes and principal bundles \[Taubes, Chapters 14, 10-11\] - Week 14 (Nov. 29-Dec. 1): Yang-Mills equation and applications. --- Attachments- [ picture\_as\_pdf syllabus\_math230a\_new2.pdf ](/sites/g/files/omnuum10216/files/fanye/files/syllabus_math230a_new2.pdf) - [ picture\_as\_pdf math230a\_notes\_week1-2.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_notes_week1-2.pdf) - [ picture\_as\_pdf assignment\_1.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_1.pdf) - [ picture\_as\_pdf math\_230a\_notes\_week3-4.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_notes_week3-4.pdf) - [ picture\_as\_pdf assignment\_2.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_2.pdf) - [ picture\_as\_pdf math\_230a\_notes\_week5-6.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_notes_week5-6.pdf) - [ picture\_as\_pdf assignment\_3.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_3.pdf) - [ picture\_as\_pdf math\_230a\_notes\_week7-8\_new.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_notes_week7-8_new.pdf) - [ picture\_as\_pdf assignment\_4.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_4.pdf) - [ picture\_as\_pdf math\_230a\_notes\_week9-10\_new.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_notes_week9-10_new.pdf) - [ picture\_as\_pdf assignment\_5\_update.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_5_update.pdf) - [ picture\_as\_pdf math230a\_oct20.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_oct20.pdf) - [ picture\_as\_pdf math230a\_oct25.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_oct25.pdf) - [ picture\_as\_pdf math230a\_oct27.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math230a_oct27.pdf) - [ picture\_as\_pdf math\_230a\_notes\_week11-14\_new.pdf ](/sites/g/files/omnuum10216/files/fanye/files/math_230a_notes_week11-14_new.pdf) - [ picture\_as\_pdf assignment\_6.pdf ](/sites/g/files/omnuum10216/files/fanye/files/assignment_6.pdf) - [ picture\_as\_pdf final\_exam.pdf ](/sites/g/files/omnuum10216/files/fanye/files/final_exam.pdf) ---