Universität Wien FIND

250011 VO Enumerative Geometry (2020S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik


Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").


Sprache: Englisch




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.


Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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

Mindestanforderungen und Beurteilungsmaßstab



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

Zuordnung im Vorlesungsverzeichnis


Letzte Änderung: Mo 07.09.2020 10:49