Universität Wien
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250011 VO Enumerative Geometry (2020S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes

The lectures are held online using zoom (zoom.us), every Friday 15:00-16:30. Please use Meeting ID: 587 099 3495 and ask me for the password by email.


Information

Aims, contents and method of the course

Broadly speaking, enumerative geometry is about geometric questions the answer for which is a number. In practice, geometric questions are usually reduced to computations in intersection theory/K-theory. Proper treatment of the subject would be quite technical, instead we will attemt to develop a feeling of what a modern enumerative geometry is by working out some examples. Depending on the interests of participants, I will choose which examples to present.
Prerequisites: algebra, linear algebra, some familiarity with algebraic topology, manifolds, algebraic geometry will be helpful.
I will spend some time to explain the most important tools such as basics of algebraic geometry, K-theory, Chern classes, Riemann-Roch theorem.

Lecture notes will be made available here: https://mellit.xyz/teaching/enumgeo/

Assessment and permitted materials

Oral exam or a short (30-60 min) presentation on a subject of choice previously agreed with the lecturer.

Minimum requirements and assessment criteria

Examination topics

Reading list

Some of the material will be taken from:
Katz: Enumerative Geometry and String Theory
Okounkov: Lectures on K-theoretic computations in enumerative geometry (https://arxiv.org/abs/1512.07363 )
Eisenbud, Harris: 3264 & All That Intersection Theory in Algebraic Geometry (https://scholar.harvard.edu/files/joeharris/files/000-final-3264.pdf )
Fulton: Intersection theory

Association in the course directory

MGEV, MALV

Last modified: Mo 07.09.2020 10:49