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250148 VO Symmetric functions in geometry (2018S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Anton Mellit

Classes (iCal) - next class is marked with N

Thursday 01.03. 11:30 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 02.03. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 08.03. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 09.03. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 15.03. 11:30 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 22.03. 11:30 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 23.03. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 12.04. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 13.04. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 19.04. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 20.04. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 26.04. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 27.04. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 03.05. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 04.05. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Friday 11.05. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 17.05. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 18.05. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 24.05. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 25.05. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Friday 01.06. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Friday 08.06. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 14.06. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 15.06. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 21.06. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.06. 11:30 - 13:00 Hörsaal 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 28.06. 11:30 - 12:15 Hörsaal 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 29.06. 11:30 - 13:00 Hörsaal 10 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.

Lecture notes will be gradually appearing here:
https://www.dropbox.com/s/87dollku59qy6rq/symfunc.pdf?dl=0

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 12.11.2020 00:27