Differential Equations in Algebraic GeometryCharles Doran (University of Alberta)
Sep 1, 2021 — Dec 31, 2021
About the course
What can differential equations tell us about the solutions to systems of algebraic equations? Conversely, what are the special properties of differential equations, and their solutions, that “come from geometry”?
In this course, we will combine tools from both algebra and analysis in our concrete introduction to transcendental algebraic geometry. This includes the theory of differential forms and integration on families of algebraic curves, complex surfaces, and even Calabi-Yau threefolds. Along the way we will present the general theory of Fuchsian differential equations, their isomonodromic deformations, and associated completely integrable Pfaffian systems. Techniques of computation will be emphasized along with the theory.
This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.
- Course Name
- Differential Equations in Algebraic Geometry
- Sep 1, 2021 — Dec 31, 2021
- Course Number
- Math 676 - Topics in Geometry I
- Section Number
- Section Code
University of Alberta
For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website