Definitions: stable curves, moduli spaces, quantum cohomology.
Skills: Getting familiarity with modern techniques in enumerative geometry including moduli compactifcations, Gromov-Witten invariants, quantum products. A more detailed list will be available at the end of the course, reflecting the students' previous knowledge and their interests.
Necessary: basic algebraic geometry (schemes, quasi-coherent sheaves)
We will mostly follow the book "An invitation to Quantum cohomology": we will introduce stable curves, stable maps, Gromov-Witten invariants, and Quantum Cohomology. If time allows, we will discuss in some additional detail stacks, and the algebraic structure of quantum cohomology
Blackboard lectures; occasionally the students might be asked to present a topic which is relevant for the course.
Oral exam, more precisely a short talk (20-30 minutes) on a topic chosen
together by student and teacher: among the possibilities are topics
treated in class, exercises proposed during the course (both those that
were solved in class and those that weren’t) or any other topic
which is coherent with the course’s content and methods, as long as it is
agreed to by the teacher but keeping into strong account the student’s
taste and interest.
It is strongly advised to be present at the first lecture.
we will follow the text "Introduction to quantum cohomology." Additional reference will be provided as the course progresses