Spring 2020 MATH 274 001 LEC
| Section | Days/Times | Location | Instructor | Class |
|---|---|---|---|---|
| 001 LEC | MoWeFr 11:00AM - 11:59AM | Evans 51 | Vivek V. Shende | 31372 |
| Units | Enrollment Status | Session |
|---|---|---|
| 4 | Open | 2020 Spring, January 21 - May 08 |
Prerequisites Consent of instructor
Description How to calculate Fukaya categories
After giving a brief introduction to the Fukaya category, we will study a sampling of celebrated results in homological mirror symmetry, drawn perhaps from
- Polischuk-Zaslow mirror symmetry for the elliptic curve
- Seidel's Lefschetz pencil methods
- Auroux-Katzarkov-Orlov on del Pezzo surfaces
- Seidel's work on the genus 2 curve and the K3 surface
- Sheridan's work on the quintic
- Abouzaid-Smith on abelian surfaces
- Fang-Liu-Treumann-Zaslow/Kuwagaki on mirror symmetry for B-model toric varieties
- Fukaya-Oh-Ohta-Ono on mirror symmetry for A-model toric varieties
Eventually we will move on to discuss local-to-global principle(s) and their use in establishing mirror symmetry. Possibly we will also discuss the Costello program for extracting higher genus curve counts from categorical information.
As per the title, the focus throughout will be on how to calculate the Fukaya category, not how to define it. Specifically, we will not enter deeply into analytic issues or foundational questions. These are subtle and important, but not the focus of this course.
Office 873
Office Hours Friday 1-4
Required Text
Recommended Reading
Grading Undergraduates taking the course for a grade will be asked to present in detail a section of a research article.
Homework
Course Webpage
