Universität Wien
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250057 VO Selcted topics in Combinatorics (2014S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 13.03. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.03. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.03. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.04. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.04. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.05. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.05. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.05. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.06. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.06. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.06. 10:15 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The topic of this course will be the so-called
"k-Schur functions". These form a special class of
symmetric functions, of which - after their Introduction
by Lapointe, Lascoux, and Morse in connection with a
conjecture on Macdonald polynomials, an enormously
important class of symmetric functions - it was
realised over time that they appear in various different
algebraic contexts and play a significant role there.

I shall start with a brief introduction into the "classical"
theory of symmetric functions, which will present the
description of the importat bases of the space of symmetric
functions - elementary symmetric functions, complete
homogeneous symmetric functions, monomial symmetric
functions, power symmetric functions, Schur functions,
together with the combinatorial theory, which is tied
with them.

Then I shall enter the fascinating theory of these
"k-Schur functions", which contains many analogues to
the "classical" theory of symmetric functions, but
at the same time many surprising twists and open
problems.

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

Examination topics

Reading list

The course will be based on the book
"k-Schur functions and affine Schubert
calculus" by Thomas Lam, Luc Lapointe, Jennifer Morse,
Anne Schilling, Mark Shimozono, and Mike Zabrocki.
It is available at http://arxiv.org/abs/1301.3569.

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40