Universität Wien
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250089 VO Symmetric Functions in Geometry (2023W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 06.10. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 13.10. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 20.10. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 27.10. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 03.11. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 10.11. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 17.11. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 24.11. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 01.12. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 15.12. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 12.01. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 19.01. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 26.01. 13:15 - 15:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course is about computations of various geometric invariants with a particular stress on the use of symmetric functions. The course assumes knowledge of basic linear algebra (matrices) and algebra (groups, polynomials). All the background from algebraic geometry and algebraic topology will be explained during the course.
In particular we are going to cover the following topics: symmetric functions, representations of symmetric and general linear groups, Schur-Weyl duality, geometry of Grassmannians and flag manifolds, vector bundles, K-theory, characteristic classes, Hirzebruch-Riemann-Roch theorem, Borel-Weil-Bott theorem.

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Linear algebra, algebra

Examination topics

Reading list

Some of the topics are covered in the following books, some of which are quite advanced, so during the course we will attempt to give a more accessible presentation:
Macdonald "Symmetric functions and Hall polynomials"
Fulton, Harris "Representation Theory: A First Course"
Fulton "Young tableaux"
Milnor, Stasheff "Characteristic classes"

Association in the course directory

MALV; MGEV

Last modified: Th 29.02.2024 07:26