Combinatorics and interactions, thematic trimester in Institut Henri Poincaré
Combinatorics and interactions, a series of lectures in IMPAN
Examination problems
Examination problems (in Polish)
October 6, 2016, 12:15 in the room 106 of IMPAN
Lecture 1. The big plan.
Suggested leasure reading:
 Piotr Śniady. Combinatorics of asymptotic representation theory. European Congress of Mathematics, Kraków, 27 July, 2012, pp: 531545, European Mathematical Society Publishing House. Also available as arXiv:1203.6509
 Jonathan Novak, Piotr Śniady. What is... a free cumulant? AMS Notices
October 20, 2016, 12:15 in the room 105 of IMPAN
Lecture 2. Stanley character formula
Short lecture notes from Stuttgart.
Suggested nonleasure reading:

Specht modules are (supposedly) explained in the book of Fulton & Harris

Valentin Féray, Piotr Śniady.
Asymptotics of characters of symmetric groups related to Stanley character formula.
Ann. of Math. (2) 173 (2011), 887906
Also available as math/0701.5051 
S´eminaire BOURBAKI Juin 2013, 65eme annee, 20122013, no 1071
NOUVEAUX DEVELOPPEMENTS SUR LES VALEURS DES CARACTERES DES GROUPES SYMETRIQUES; METHODES COMBINATOIRES ´ [d’apres V. Feray] par Pierre CARTIER http://www.bourbaki.ens.fr/TEXTES/1071.pdf
November 3, 2016, 12:15 in the room 105 of IMPAN
Lecture 3. Consequences of Stanley character formula: asymptotics of characters
Lecture notes (preliminary version)
Reading:
 Vershik, A. M.; Kerov, S. V. Asymptotic theory of the characters of a symmetric group. Functional Anal. Appl. 15 (1981), no. 4, 246–255 (1982).
 Kerov, S., Olshanski, G. & Vershik, A. Invent. math. (2004) 158: 551.
November 10, 2016, 12:15 in the room 105 of IMPAN
Lecture 4. Partial permutations, structure constants of the symmetric group algebras, algebra of polynomial functions on the set of Young diagrams, JucysMurphy elements.
December 1, 2016, 12:15 in the room 105 of IMPAN
Lecture 5. Algebra of polynomial functions and its algebraic bases.
December 22, 2016, 12:15 in the room 105 of IMPAN
Lecture 6. Stanley coordinates.
January 5, 2017, 12:15 in the room 105 of IMPAN
Lecture 7.
January 26, 2017, 12:15 in the room 105 of IMPAN
Lecture 8.
March 2, 2017, 12:15 in the room 105 of IMPAN
Lecture 9. Cumulants
March 16, 2017, 12:15 in the room 105 of IMPAN
Lecture 10.
April 20, 2017, 16:30 in the room 321 of IMPAN
Extra lecture: Asymptotic representation theory