Graduate courses
They will all take place in Amphitheatre Hermite at IHP, rue Pierre et Marie Curie.
For students in Paris, these courses can be validated by the doctoral schools "Physique en Ile-de-France".
The courses (except the one of Zagier) are recorded. The videos will be made available in due time on the dedicated page for the trimester on the youtube channel of IHP.
Philippe Biane (Univ. Marne-la-Vallée)
ASYMPTOTIC AND PROBABILISTIC ASPECTS OF REPRESENTATION THEORY
Keywords: Young graph, Thoma simplex, free probability, longest increasing subsequence.
Dates: Tuesday 10-12am (Jan 24th, 31st, Feb 7th, 14th) and Thursday 10-12am (Jan 26th, Feb 2nd, 9th, 16th).
Mireille Bousquet-Mélou (Labri)
ENUMERATIVE COMBINATORICS OF MAPS
Keywords: planar maps, recursive structures, bijections with trees. Maps
equipped with an additional structure (forests, self-avoiding walks, orientations...)
or with a model from statistical physics (Ising, Potts, hard particles...).
Dates: Monday 10-12am and 2-4pm (Jan 23rd, 30th, Feb 6th, 13th, 27th).
Alexey Bufetov and Vadim Gorin (MIT)
INTEGRABLE PROBABILITIES
Keywords: random tilings; interacting particle systems; Schur and Macdonald processes; representations of "big" groups.
Dates: Tuesdays 2-4pm (January 24th, 31st, February 7th, 14th)
and Wednesdays 2-4pm (January 25th, February 1st, 8th, 15th).
Nicolas Orantin (EPFL)
TOPOLOGICAL RECURSION
Keywords: combinatorics of maps; higher genus maps; spectral curve; Tutte's equations; moduli space of curves.
Dates: Tuesdays 2-4pm (February 28th, March 7th, 21st, 28th), Wednesdays 10-12am (March 1st, 8th, 22nd, 29th).
Don Zagier (MPIM Bonn)
PARTITIONS, MODULAR FORMS AND MODULI SPACES
Keywords: covering of surfaces, modular forms and quasimodular forms, Bloch-Okounkov theorem and generalizations, applications to Siegel-Veech constants and invariants of moduli space of flat surfaces.
Dates: Tuesdays 10-12am (February 28th, March 7th, 21st, 28th), Wednesdays 2-4pm (March 1st, 8th, 22nd, 29th).
Week 1 (28th February-1st March): We will discuss a very amusing space of sequences of rational numbers and give several examples of sequences arising in geometry that belong to this space, notably counting functions for graphs and the classical Hurwitz numbers counting generically ramified covers of the 2-sphere.
Week 2 (March 7-8th): We now look at the analogues of Hurwitz numbers that count generically ramified covers of the 2-torus. We explain the theorem that the corresponding generating series are quasimodular forms (whose theory will be reviewed in some detail) and the huge generalization by Bloch and Okounkov, with a very simple combinatorial proof.
My talk at the conference and in the final two weeks of the course will be about generalizations of these latter results.
Here is an ics file which includes all the courses. Here is a compact view of the trimester timeline:
| Jan. 9-13 | Jan. 16-20 | Jan. 23-27 | Jan. 30-3 | Feb. 6-10 | Feb. 13-17 | Feb. 20-24 | Feb. 27-3 | Mar. 6-10 | Mar. 13-17 | Mar. 20-24 | Mar. 27-31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Biane | S | W | X | X | X | X | W | W | ||||
| Bousquet-Mélou | S | W | X | X | X | X | W | X | W | |||
| Bufetov/Gorin | S | W | X | X | X | X | W | W | ||||
| Orantin | S | W | W | X | X | W | X | X | ||||
| Zagier | S | W | W | X | X | W | X | X |
Legend: X=course that week; S or W=school or workshop.
... and here is the weekly schedule:
Winter school courses, January 9—13 (Luminy)
In addition (and as preparation) to these courses, four introductory one-week courses have been given as part of the Introductory school.
Nicolas Curien (Orsay)THE SPATIAL MARKOV PROPERTY OF RANDOM PLANAR MAPS
Piotr Śniady (Univ. Poznán)
CHARACTERS, MAPS, FREE CUMULANTS
Béatrice de Tilière (Univ. Paris-Est)
DIMERS AND RELATED MODELS IN STATISTICAL MECHANICS
Dimitri Zvonkine (Jussieu)
HURWITZ NUMBERS
Further information (including abstracts) is available
on the introductory school webpage.
More
Mini-courses given by participants may be added at the time of the trimester.
