Spring 2020 MATH 274 001 LEC

Topics in Algebra
Schedule: 
SectionDays/TimesLocationInstructorClass
001 LECMoWeFr 11:00AM - 11:59AMEvans 51Vivek V. Shende31372
UnitsEnrollment StatusSession
4Open2020 Spring, January 21 - May 08
Additional Information: 

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