Topic for Fall 2015: Symmetric functions.
Course meets: TuTh 11:40-1:00, Room 1866 East Hall.
Instructor: Sergey Fomin, 4868 East Hall, 764-6297, firstname.lastname@example.org
Grader: Benjamin Branman, email@example.com
Office hours: Tuesday 1-2, Thursday 4-6 in 4868 East Hall.
Course homepage: http://www.math.lsa.umich.edu/~fomin/665f15.html
Level: introductory graduate.
Prerequisites: none (for graduate students).
Student work expected: several problem sets.
Synopsis: This is an introduction to the foundations of the classical theory of symmetric functions from a combinatorial perspective. Core topics include Young tableaux, Schur functions, and related combinatorial algorithms and enumeration problems. The course will conclude by a survey of applications of symmetric functions to various areas of mathematics such as linear algebra, representation theory, and enumerative geometry.
|[EC2]||R. P. Stanley, Enumerative combinatorics, vol. 2, Cambridge University Press, 1999 (paperback 2001).|
|We will cover Chapter 7 (including Appendix 1).|
Contents of Chapter 7:
|[Fu]||W. Fulton, Young tableaux , Cambridge University Press, 1997.|
|[La]||A. Lascoux, Symmetric functions and combinatorial operators on polynomials, AMS, 2003.|
|[Ma]||I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd edition, Oxford University Press, 1995 (paperback 1999).|
|[Sa]||B. E. Sagan, The symmetric group, 2nd edition, Springer-Verlag, 2001.|
|[EC1]||R. P. Stanley, Enumerative combinatorics, vol. 1, 2nd edition, Cambridge University Press, 2011/2012.|