SFCA 2013FPSAC '13

25ème conférence internationale sur les séries formelles et la combinatoire algébrique.The 25th International Conference on Formal Power Series and Algebraic Combinatorics.

Paris, du 24 au 28 Juin 2013Paris, France, June 24–28, 2013


In the program below, each contribution links to the corresponding extended abstract. The complete proceedings are available here (17.5 Mo). If you find a mistake, please send an email to fpsac13[at]liafa.univ-paris-diderot.fr.

Sunday June 23

17:00–20:00 Welcome reception in le petit bain (registration mandatory)

Monday June 24

08:00–09:00 Registration and breakfast
09:00–10:00 Mireille Bousquet-Mélou
Self-avoiding walks on the honeycomb lattice
In 2010, Duminil-Copin and Smirnov proved a long standing conjecture, according to which the number of \(n\)-step self-avoiding walks (SAWs) on the honeycomb lattice grows like \(\mu^n\), up to sub-exponential factors, where \(\mu=\sqrt{2+\sqrt 2}\).
Their proof is in fact rather simple, but also very original, at least to a combinatorialist's eyes. At the heart of the proof is a remarkable identity, that relates several generating functions of SAWs \emph{evaluated at the critical point} \(1/\mu\).
We will discuss this identity and some of its extensions, with applications to SAWs interacting with a surface, and to the \(O(n)\) loop model.
10:00–10:30 Coffee break
10:30–11:00 Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel and Matteo Silimbani
Combinatorics of non-ambiguous trees (slides)
11:00–11:30 Riccardo Biagioli, Frédéric Jouhet and Philippe Nadeau
Fully commutative elements and lattice walks (slides)
11:30–12:00 Mathieu Guay-Paquet, Alejandro H. Morales and Eric Rowland
Structure and enumeration of (3+1)-free posets (slides)
12:00–14:00 Lunch Break
14:00–15:00 Grigori Olshanski
Boundaries of branching graphs
A branching graph is an infinite graded graph, sometimes with an additional structure. The boundary of such a graph describes all possible ways of escaping to infinity along "regular" monotone paths. This notion emerged about 30 years ago in the work of Vershik and Kerov on characters of the infinite symmetric group. I will survey old and new results related to boundaries of concrete graphs, and state open questions. The problems here originate from representation theory and probability theory, while the methods are mainly of combinatorial nature and rely on the theory of symmetric functions and their analogs, such as supersymmetric and quasisymmetric functions.
15:00–15:30 Vadim Gorin and Greta Panova
Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory (slides)
15:30–16:00 Coffee break
16:00–16:30 Christopher Bowman, Maud De Visscher and Rosa Orellana
The partition algebra and the Kronecker product (slides)
16:30–17:00 Marcelo Aguiar and Kyle Petersen
The module of affine descent classes of a Weyl group (slides)
17:00–19:00 Poster session A

Tuesday June 25

09:00–10:00 Bernhard Keller
Quiver mutation and combinatorial DT-invariants
A quiver is an oriented graph. Quiver mutation is an elementary operation on quivers. It appeared in physics in Seiberg duality in the nineties and in mathematics in the definition of cluster algebras by Fomin-Zelevinsky in 2002. We will show how, for large classes of quivers \(Q\), using quiver mutation and quantum dilogarithms, one can construct the combinatorial DT-invariant, a formal power series intrinsically associated with \(Q\). When defined, it coincides with the "total" Donaldson-Thomas invariant of \(Q\) (with a generic potential) provided by algebraic geometry (work of Joyce, Kontsevich-Soibelman, Szendroi and many others). We will illustrate combinatorial DT-invariants on many examples and discuss their links to quantum cluster algebras and to (infinite) generalized associahedra.
10:00–10:30 Coffee break
10:30–11:00 Cesar Ceballos and Vincent Pilaud
Denominator vectors and compatibility degrees in cluster algebras of finite types (slides)
11:00–11:30 Richard Ehrenborg, Mark Goresky and Margaret Readdy
Euler flag enumeration of Whitney stratified spaces (slides)
11:30–12:00 Kelli Talaska and Lauren Williams
Network parameterizations for the Grassmannian (slides)
12:00–14:00 Lunch break
14:00–15:00 Eric Rains
Beyond \(q\): special functions on elliptic curves
An important thread in modern representation theory (and combinatorics) is that many important objects have so- called q-analogues, generalizations depending on a parameter \(q\) which reduce to more familiar objects when \(q = 1\). For instance, the Schur functions (irreducible characters of the unitary group) have \(q,t\)-analogues, namely the famous Macdonald polynomials, and similarly the Koornwinder polynomials are six-parameter \(q\)-analogues of the characters of other classical groups. It turns out that many q-analogues extend further to elliptic analogues, in which q is replaced by a point on an elliptic curve. The Macdonald/Koornwinder polynomials are no exception; I’ll describe a relatively elementary approach to those polynomials and how to modify the approach to obtain an elliptic analogue.
15:00–15:30 Jang Soo Kim and Dennis Stanton
Moments of Askey-Wilson polynomials (slides)
15:30–16:00 Zachary Hamaker and Benjamin Young
Relating Edelman-Greene insertion to the Little map (slides)
16:00–16:30 Coffee break
16:00–18:00 Poster session B

Wednesday June 26

09:00–10:00 Olivier Bernardi
A unified bijective framework for planar maps
Planar maps are connected planar graphs embedded in the sphere (considered up continuous deformations). Planar maps have been actively studied in combinatorics ever since the seminal work of William Tutte in the sixties. Along the years, deep connections have been fruitfully exploited between planar maps and subjects as diverse as the combinatorics of the symmetric group, graph drawing algorithms, random matrix theory, statistical mechanics, and 2D quantum gravity.
In the last decade, following the work of Cori, Vauquelin and Schaeffer, many bijections have been discovered between classes of maps (e.g. triangulations, bipartite maps) and classes of trees. These bijections provide the ''proofs from the Book'' for the many simple-looking counting formulas discovered by Tutte and his followers. Moreover they proved to be invaluable tools in order to study the metric properties of maps, finding algorithms for maps, and solving statistical mechanics models on maps.
In this talk, I will explain some of the aforementioned motivations for studying maps. I will then describe a bijective framework, developed jointly with Eric Fusy, which unifies and extends almost all the known bijections for planar maps. This framework relies on two ingredients: the existence of certain canonical orientations for planar maps, and a master bijection for oriented maps.
10:00–10:30 Wenjie Fang
A generalization of the quadrangulation relation to constellations and hypermaps (slides)
10:30–11:00 Coffee break
11:00–11:30 Michael Chmutov
Type A molecules are Kazhdan-Lusztig (slides)
11:30–12:00 Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling and Mark Shimozono
A uniform model for Kirillov-Reshetikhin crystals (slides)
12:00–12:30 Sara Billey and Brendan Pawlowski
Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence (slides)
12:30–12:45   Group photo 
12:45– Free afternoon
15:00–17:00 Guided walking tour in Le Marais (registration mandatory)

Thursday June 27

09:00–10:00 Andrea Sportiello
Razumov-Stroganov–type Correspondences in the 6-Vertex and O(1) Dense Loop Model
Razumov and Stroganov conjectured in 2001 a correspondence between the enumerations of Fully-Packed Loops (FPL) on a square domain (a version of the 6-Vertex Model), refined according to the link pattern, and the ground-state components of the Hamiltonian in the periodic XXZ Quantum Spin Chain at \(\Delta = -1/2\), a realisation of the O(1) Dense Loop Model (DLM) on a cylinder. Extensions have been considered later on. In particular, Di Francesco in 2004 suggested a one-parameter generalization: on the `DLM side', the ground state of the Hamiltonian H is replaced by the one of the Scattering Matrix, S(t) on the `FPL side', one also considers the refinement on the last row. Similar conjectures existed for two large families of domains: those with a `hidden dihedral symmetry', or with `vertical symmetry', respectively. Both the basic and extended conjectures have been proven, in the dihedral case, by L. Cantini and the speaker, while the vertical cases are open. We present the subject, its implications on Algebraic Combinatorics and Statistical Mechanics, and how the forementioned conjectures have been proven.
10:00–10:30 Coffee break
10:30–11:00 Daniel Bragg and Nathaniel Thiem
Rainbow supercharacters and poset analogue to q-binomial coefficients (slides)
11:00–11:30 Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano and Mike Zabrocki
The immaculate basis of the non-commutative symmetric functions (slides)
11:30–12:00 Nicholas Loehr, Luis Serrano and Gregory Warrington
Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials (slides)
12:00–14:00 Lunch break
14:00–15:00 Patricia Hersh
Topological combinatorics of Bruhat order and total positivity
This talk will focus on the rich interplay of combinatorics, topology, and representation theory arising in the theory of total positivity and in particular in the study of the totally nonnegative part of a matrix Schubert variety. Along the way, we will survey what combinatorics of a closure poset can and what it cannot tell us about the topology of a stratified space. Braid moves on reduced and nonreduced words in the associated 0-Hecke algebra are interpreted topologically, yielding information about the possible relations among (exponentiated) Chevalley generators of a Lie group. The subword complexes introduced by Allen Knutson and Ezra Miller also play a role in this story, giving the face poset structure for the fibers of a map \(f_{(i_1,\dots ,i_d)}\) suggested in work of Lusztig where \(f_{(i_1,\dots , i_d)}\) is given by a product of exponentiated Chevalley generators. Sergey Fomin and Michael Shapiro conjectured that totally nonnegative spaces arising as images of these maps, or equivalently as the Bruhat decompositions of the totally nonnegative part of matrix Schubert varieties, together with the links of their cells, are regular CW complexes homeomorphic to balls having the intervals of Bruhat order as their closure posets. We will discuss the new combinatorics and topology which the proof of this conjecture revealed.
15:00–15:30 Richard Kenyon and Robin Pemantle
Double-dimers, the Ising model and the hexahedron recurrence (slides)
15:30–16:00 David B Rush and XiaoLin Shi
On Orbits of Order Ideals of Minuscule Posets (slides)
16:00–16:30 Coffee break
16:00–18:00 Poster session C
19:30– Conference dinner in restaurant Le moulin vert(registration mandatory)

Friday June 28

09:00–10:00 Svante Linusson
Particles jumping on a cycle, a process on permutations and words
I will describe recent research regarding the so called TASEP on a cycle. It describes permutations (or more generally words) on a cycle, where a small number may jump over a larger number. This process has been studied both for probabilistic and algebraic combinatorics reasons. It exhibits a number of very nice structural and enumerative properties, several of which are still unproved.
10:00–10:30 Coffee break
10:30–11:00 Martin Rubey, Bruce Sagan and Bruce Westbury
Descent sets for oscillating tableaux (slides)
11:00–11:30 Mireille Bousquet-Mélou and Julien Courtiel
Spanning forests in regular planar maps (slides)
11:30–12:00 Art Duval, Caroline Klivans and Jeremy Martin
Cuts and Flows of Cell Complexes (slides)
12:00–14:00 Lunch break
14:00–15:00 Francisco Santos
Recent Progress on the Diameter of Polyhedra and Simplicial Complexes
We review several recent results on the diameter of polytopes, polyhedra and simplicial complexes, motivated by the (now disproved, but not quite solved) Hirsch Conjecture.
15:00–15:30 Lionel Pournin
A combinatorial method to find sharp lower bounds on flip distances (slides)
15:30–15:45 Coffee break
15:45–16:15 Alex Fink and Luca Moci
Matroids over a ring (slides)
16:15–16:45 Satoshi Murai and Eran Nevo
On \(r\)-stacked triangulated manifolds (slides)
16:45–17:00 Best paper awards -- sponsored by Elsevier
  • Best paper: A combinatorial method to find sharp lower bounds on flip distances, by Lionel Pournin
  • Best student paper: Type A molecules are Kazhdan-Lusztig, by Michael Chmutov
17:00–18:00 Closing goûter

Program of poster sessions

Poster session A (Monday 24, 17:00–19:00)

Chair: Marie Albenque

Room D15

Room D16

Room D17

Poster session B (Tuesday 25, 16:00–18:00)

Chair: Anne Micheli

Room D15

Room D16

Room D17

Poster session C (Thursday 27, 16:00–18:00)

Chair: Guillaume Chapuy

Room D15

Room D16

Room D17

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