Topics in J-holomorphic maps and gauge theory
Topics in J-holomorphic maps and gauge theory
Class Meets by live Zoom
Tuesday & Thursdays 10:20 - 11:10
Fridays 11:30 -- 12:20.
Professor: T. ParkerOffice: D-216 Wells Hall parker@math.msu.edu
Office hours: Monday 2-3 Tuesday 3-4Friday 1-2 or by appointment.
Office hours: Monday 2-3 Tuesday 3-4Friday 1-2 or by appointment.
Format: This class will be entirely online. Lectures will be live via Zoom at the hours listed above. Zoom passcode: 853510.
Goals: This course will begin with an introduction to gauge theory, followed by some symplectic geometry and topology. We will then shift focus to the theory of $J$-holomorphic maps. It will develop both the geometric intuition and the analytic tools of the subject. One goal is to include new approaches to the issues of compactness and ``virtual fundamental classes''. Course Syllabus
Prerequisites: A working knowledge of (i) Riemannian geometry and (ii) elliptic PDE at the level of Evans' Chapters 5 and 6. Some knowledge of Riemannian Geometry, elliptic PDE, algebraic geometry, and algebraic topology will help.
Textbook: Holomorphic Curves in Low Dimensions by Chris Wendl. Further references are listed on the Additional Resources page. Reference: J-holomorphic curves and symplectic topology ([MS] ``big book'')
Exams and grades: Course grades will be based on homework assignments and on team projects. The nature of the projects will be explained in class.
Goals: This course will begin with an introduction to gauge theory, followed by some symplectic geometry and topology. We will then shift focus to the theory of $J$-holomorphic maps. It will develop both the geometric intuition and the analytic tools of the subject. One goal is to include new approaches to the issues of compactness and ``virtual fundamental classes''. Course Syllabus
Prerequisites: A working knowledge of (i) Riemannian geometry and (ii) elliptic PDE at the level of Evans' Chapters 5 and 6. Some knowledge of Riemannian Geometry, elliptic PDE, algebraic geometry, and algebraic topology will help.
Textbook: Holomorphic Curves in Low Dimensions by Chris Wendl. Further references are listed on the Additional Resources page. Reference: J-holomorphic curves and symplectic topology ([MS] ``big book'')
Exams and grades: Course grades will be based on homework assignments and on team projects. The nature of the projects will be explained in class.