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.

Lecture notes.

Suggested leasure reading:

• Piotr Śniady. Combinatorics of asymptotic representation theory. European Congress of Mathematics, Kraków, 2-7 July, 2012, pp: 531-545, 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.

Complete lecture notes.

Suggested non-leasure 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), 887-906
  Also available as math/0701.5051

• S´eminaire BOURBAKI Juin 2013, 65eme annee, 2012-2013, 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, Jucys-Murphy elements.

Lecture notes, part 1

Lecture notes, part 2

December 1, 2016, 12:15 in the room 105 of IMPAN

Lecture 5. Algebra of polynomial functions and its algebraic bases. 

Lecture notes

December 22, 2016, 12:15 in the room 105 of IMPAN

Lecture 6. Stanley coordinates.

Lecture notes

 

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

Lecture notes

 

March 16, 2017, 12:15 in the room 105 of IMPAN

Lecture 10.

Lecture notes

April 20, 2017, 16:30 in the room 321 of IMPAN

Extra lecture:   Asymptotic representation theory