Speakers

Ruggero Bandiera (Sapienza Università di Roma)

Clemens Berger (Université Côte d'Azur)

Yvain Bruned  (Université de Nancy)

Angela Carnevale (University of Galway)

Adrian Celestino (Universität Münster)

Frédéric Chapoton  (Université de Strasbourg)

Bérénice Delcroix-Oger (Université de Montpellier)

Sabino Di Trani (Università degli studi de L'Aquila)

Giulia Iezzi (RPTU University Kaiserslautern-Landau) 

Mario Marietti (Università Politecnica delle Marche)

Paolo Papi (Sapienza Università di Roma)

Frédéric Patras (Université Côte d'Azur)

Viviane Pons  (Université de Paris-Saclay)

Claudio Procesi (Sapienza Università di Roma)
Mercedes Rosas (Universidad de Sevilla)

Tobias Rossmann (University of Galway)

Viola Siconolfi (Politecnico di Bari)

Sheila Sundaram (University of Minnesota)

Stephanie van Willigenburg (University of British Columbia)

Participants (Confirmed so far)

Ruggero Bandiera (Sapienza Università di Roma Italy)

Lien Cartaya Bermúdez (Talca Universidad Chile)

Clemens Berger (Université Côte d'Azur France)

Emmanuel Briand (Universidad de Sevilla Spain)

Yvain Bruned  (Université de Nancy France)

Angela Carnevale (University of Galway Ireland)

Fabrizio Caselli (Università di Bologna Italy)

Adrian Celestino (Universität Münster Germany) 

Frédéric Chapoton  (Université de Strasbourg France)

Bérénice Delcroix-Oger (Université de Montpellier France)

Sabino Di Trani (Sapienza Università di Roma Italy)

Loïc Foissy (Université du Littoral Côte d'Opale France)

Christophe Hohlweg (Université du Québec à Montréal Canada)

Giulia Iezzi (RPTU University Kaiserslautern-Landau Germany) 

Paul Laubie (Université de Lorraine France)

Claudia Malvenuto (Sapienza Università di Roma Italy)

Mario Marietti (Università Politecnica delle Marche Italy)

Jean-Christophe Novelli (Université de Marne-La-Vallée France)

Paolo Papi (Sapienza Università di Roma Italy)

Frédéric Patras (Université Côte d'Azur France)

Viviane Pons  (Université de Paris-Saclay France)

Claudio Procesi (Sapienza Università di Roma Italy)
Mercedes Rosas (Universidad de Sevilla Italy)

Tobias Rossmann (University of Galway Ireland)

Viola Siconolfi (Politecnico di Bari Italy)

Sheila Sundaram (University of Minnesota USA)

Stephanie van Willigenburg (University of British Columbia Canada)

Location

The conference will take place in Grand Hotel San Michele, Cetraro (CS, Italy). The accomodation will be a full board treatment. 

How to get there

From Rome or Naples 

From Rome or Naples, the simplest way to reach Cetraro is by train: check the schedule on https://www.trenitalia.com. On the website of Trenitalia, use "Roma Termini" for trains departing from Rome, and "Napoli centrale" for trains departing from Naples.
If you arrive in Rome Fiumicino Airport, there is a direct train going from "Fiumicino aeroporto" to "Roma Termini" (central station), it runs about every 15 minutes, lasts 32 minutes and costs 14,00 eu, you can purchase the Fiumicino Aeroporto to Roma Termini train ticket from the same website https://www.trenitalia.com.
If you arrive in Aeroporto Internazionale di Napoli, there is a bus service going to Napoli Centrale train station, called Alibus; the buses run every 15 minutes, lasts 15 minutes and should cost 5,00 eu.
The hotel has a pick-up service from both Cetraro and Paola train station:
(a) From Cetraro train station: 30 euros per ride.
(b) From Paola train station: service by Car (3 persons max., 60 euros each way) or by Minibus (8 persons max, 85 euros each way).
Both prices are for the vehicle and eventually can be shared by the passengers if more than one: in that case individual bills will be made by the Hotel.

From Lamezia Terme

The nearest airport is Lamezia Terme Airport. From there are then two ways to arrive to the hotel:
(a) going to Cetraro by train from Lamezia Terme Centrale (a bus connects Lamezia airport to Lamezia centrale), then the pick-up service in Cetraro see above; again you can check the schedule on https://www.trenitalia.com.
(b) The Hotel pick-up service from Lamezia Terme Airport, by Car (3 persons max., 105 euros each way) or by Minibus (8 persons max., 137 euros each way).
Both prices are for the vehicle and so can be shared by the passengers. Individual bills will be made by the Hotel.
Please note that for night shuttle services (between 1.00 am and 5.00 am) there is a 30,00 euro supplement.
In order for us to arrange and group the pick-up service, please let us know as soon as possible (if you did not do so already) of your arrival/departure times at Cetraro (or Paola) train station, or Lamezia airport. Please feel free to write to us for any questions you may have.

Program

The final SCHEDULE AND ABSTRACTS of the Workshop is now available for downloading.

The conference will start on Monday morning, July 6 and end on Friday July 10 at 12.00. Participants are expected to arrive on Sunday July 5 and to leave on Saturday July 11.

The talks will take place in one of the Hotel Conference room. 

There will be three conferences in the morning and one by the end of the afternoon. As the goal of the conference is to enhance existing interactions and create new ones, time will be left in the afternoon for group discussions and group work: in between the talks (in the afternoon), the conference room will be available for us on the spot for working group talks.

Please note that the hotel's dress code for dinner requires gentlemen to wear long trousers in the evening.

Talks

Ruggero Bandiera (Sapienza Università di Roma) 

Titolo:  BCH product and P-partitions

Abstract: We establish a connection between Stanley's theory of P-partitions and the Baker-Campbell-Hausdorff product in a Lie algebra of finite connected posets. More precisely, we consider an operad structure on finite connected posets introduced by Fauvet, Foissy and Manchon, having several other important operads (such as the associative, left and right pre-Lie operads, as well as the operad carrying the universal formal group law) as quotients. On this operad Poset_c we can define a formal group law, and an associated morphism Lie -> Poset_c from the Lie operad. Finally, in the free Poset_c algebra generated by a totally ordered alphabet A, we can consider the BCH product of the generators, taken in increasing order, as well as the formal exponential flow generated by it. Our main result is that the latter can be explicitly described in terms of polynomials enumerating P-partitions.

Clemens Berger (Université Côte d'Azur) 

Titolo: Catalan monoids and Dold-Kan correspondence

Abstract: Abstract. To any simple graph G with vertex set {1,2,...,n} we associate a monoid C(G) with idempotent generators x_1,...,x_n and relations x_i x_j x_i=x_j x_i=x_j x_i x_j if (i,j) is an edge of G, and x_i x_j=x_j x_i if (i,j) is not an edge of G.
For the linear graph on n vertices this produces the "classical" Catalan monoid with cardinality equal to the n-th Catalan number. For the complete graph on n vertices this produces the so-called Kiselman monoids K_n studied by Kudryavtseva-Mazorchuk and shown to be finite.
The common feature of this class of monoids is a decomposition of the unit of Z[C(G)] into 2^n (non-central) idempotents. We show that this decomposition is at the heart of a classical theorem in algebraic topology, namely the so-called Dold-Kan correspondence between simplicial abelian groups and chain complexes. This is joint work with Christophe Cazanave and Ingo Waschkies.

Yvain Bruned  (Université de Nancy) 

Titolo: Algebraic structures for renormalising SPDEs

Abstract: We will introduce the main tools for describing solutions of singular SPDEs via B-series and explain the main algebraic properties that lead to the renormalised equation. We provide the renormalisation for the Regularity Structures and the Para-controlled ansatz.

Angela Carnevale (University of Galway) 

Titolo: Bruhat Order for Latin Squares

Abstract: Latin squares can be naturally viewed as three-dimensional analogues of permutations. In this talk, I will discuss an analogue of the Bruhat order for Latin squares, describing its construction, examples of the resulting posets, and current work on their structure and associated lattices. This is joint work with Cian O'Brien.

Adrian Celestino (Universität Münster Germany) 

Titolo: Antipode formulas, Schröder trees and cumulants in non-commutative probability

Abstract: In a series of recent papers, Ebrahimi-Fard and Patras developed an algebraic approach to cumulants in non-commutative probability based on a combinatorial Hopf algebra of words on words. They showed that the classical moment-cumulant relations in terms of non-crossing partitions can be recovered from fixed-point equations involving linear functionals on this Hopf algebra. In this talk, I will present a combinatorial formula for the antipode of this Hopf algebra in terms of Schröder trees and discuss applications on moment-cumulant formulas for several notions of independence. This is based on joint work with Yannic Vargas.

Frédéric Chapoton  (Université de Strasbourg) 

Title: On some polytopes attached to preorders

Abstract: We will introduce the class of preorder polytopes, defined from preorders on finite sets. These are lattice polytopes, defined by simple inequalities using order ideals. They also have a clean description as Minkowski sums of simplices. This was initially motivated by some numerical coincidences with lattices of torsion classes in finite dimensional algebras. We obtain an amusing duality exchanging the Ehrhart polynomial with the zeta polynomial of the natural partial order on lattice points. If time permit, we will explain how reflexive polytopes enter the picture when adding one more Minkowski summand. (joint work with Christos A. Athanasiadis)

Bérénice Delcroix-Oger (Université de Montpellier) 

Titolo: Generalised flip order

Abstract: Two well-known posets, the Tamari lattice and the Weak order, can be realised as the partial order on the vertices of the associahedron and the permutohedron respectively, whose covering relation is given by edges of these polytopes. These orders were extended to orders on faces of each of these polytopes by  Krob-Latapy-Novelli-Phan-Schwer and Palacios-Ronco. In this talk, I will introduce an order on faces of hypergraph polytopes/nestohedra, extending on one side the order on faces of associahedra and permutohedra, and on the other side, Barnard-McConville's flip order on vertices of graph associahedra. This order is deeply linked with the shuffle/tridendriform products introduced in our previous work. This is a joint work in collaboration with Pierre-Louis Curien and Jovana Obradovic.

Sabino Di Trani (Università degli Studi de L'Aquila) 

Titolo: Nil Hecke Actions on the Cohomology of Cyclic Quiver Grassmannians

Abstract: In 2023, Lanini and Pütz defined a permutation action on the equivariant cohomology of certain varieties arising from the representation theory of cyclic quivers. Using this action, one can define an action of certain divided difference operators on the cohomology, analogous to the well-studied action defined for classical flag varieties. This leads to a representation of a nilHecke algebra on the equivariant cohomology ring, which can be explicitly described using a suitable basis, the Knutson-Tao basis. In this talk, we will provide a criterion for the faithfulness of this representation—which can be verified by examining certain partitions—and discuss when the cohomology ring is a cyclic module. These results will be the subject of a forthcoming preprint with V. Siconolfi.

Giulia Iezzi (Aachen University) 

Titolo: Linear degenerations of Schubert varieties via quiver Grassmannians

Abstract: Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. For instance, this method was used to study linear degenerations of flag varieties, obtaining characterizations of flatness, irreducibility and normality via rank tuples. We realise Schubert varieties as quiver
Grassmannians and define their linear degenerations, giving a combinatorial description of the correspondence between their isomorphism classes and the B-orbits of certain quiver representations.

Mario Marietti (Università Politecnica delle Marche) 

Titolo: Flipclasses and the Combinatorial Invariance Conjecture

Abstract: The Combinatorial Invariance Conjecture predicts that Kazhdan--Lusztig polynomials depend only on the isomorphism type of Bruhat intervals. We investigate a novel approach to this conjecture based on flipclasses. This leads to a proof of the combinatorial invariance of Kazhdan-Lusztig \widetilde{R}-polynomials of Weyl groups modulo q^7, and of Kazhdan-Lusztig \widetilde{R}-polynomials of type A modulo q^8. As a consequence, the Combinatorial Invariance Conjecture holds for all Bruhat intervals of length at most 8 in Weyl groups and of length at most 10 in type A.  (Joint work with Francesco Esposito and Salvatore Stella.)

Paolo Papi (Sapienza Università di Roma) 

Titolo: On algebras of braids and ties 

Abstract: Recently, Ivan Marin introduced an extension C_W of the Iwahori-Hecke algebra of a Coxeter system (W,S) and built up a family of generically surjective morphisms  k[B_W]→C_W (here B_W is the Artin braid group attached to W). When W is of type A_{n−1}, it turns out that C_W is Aicardi-Juyumaya's algebra of braids and ties,  which has been extensively studied for its connections with link invariants.

We proceed along the lines of Marin's work  at a more abstract level, in order to  produce in a unified way all the “braids and ties” algebras available in literature and new ones. Based on joint works with F. Aicardi-J. Juyumaya and R. Fasano-D. Fiorenza.

Frédéric Patras (Université Côte d'Azur) 

Titolo: Matrix symmetric functions 

Abstract: A fundamental result by L. Solomon in algebraic combinatorics and representation theory states that Mackey formulas for products of characters of a symmetric group, or equivalently the computation of tensor products of representations thereof, can be lifted to the corresponding Solomon's descent algebra, a subalgebra of the group algebra with a very rich structure. Motivated by the structure of the product formula in these algebras and by other results and ideas in the field, we introduce and investigate in the present article a two dimensional analogue of descent algebras based on packed integer matrices that inherits most of their fundamental properties. One of the various bialgebra structures we introduce on packed integer matrices identifies with a bialgebra recently introduced by J. Diehl and L. Schmitz to define a two dimensional generalisation of Chen's iterated integrals signatures. Joint work with L. Foissy and C. Malvenuto.

Viviane Pons  (Université de Paris-Saclay) 

Titolo: Permutree Sorting

Abstract: Permutrees define combinatorial families interpolating between permutations, binary trees and binary sequences. They also correspond to certain congruence classes of the weak order lattice on permutations. In this talk, we present the Permutree sorting algorithm which attempts to sort permutations following certain constraints, succeeding only when the permutation is minimal inside its permutree congruence class. In this sense, it is a generalization of the well known stack sorting from Knuth and the c-sorting related to Cambrian lattices defined by Reading. (joint work with D. Tamayo and V. Pilaud)

Claudio Procesi (Sapienza Università di Roma) 

Titolo: Invariant theory of fermionic matrices

Abstract: In some models  of theroretical physics matrices over Grassmann algebra play a role. I will discuss old and new results  about the invariant theory of m-tuples of matrices with entries Grassmann variables, under conjugation.

Mercedes Rosas (Universidad de Sevilla) 

Title: The Priority Lattice

Abstract We introduce the priority lattice, a structure arising from the priority search algorithm on rooted trees and forests. We prove bijectively that its maximal chains are labeled by parking functions, and that the maximal chains of its principal ideals are labeled by partial parking functions. We establish that it is a graded lattice and compute its Möbius function and characteristic polynomials.   A preliminary version of this work can be found at https://arxiv.org/abs/2603.28905. This is joint work with Adrián Lillo.

Tobias Rossmann (University of Galway) 

Titolo: Enumerating orbits of unipotent groups

Abstract: This talk revolves around generating functions arising from the enumeration of linear orbits and conjugacy classes of unipotent groups. Following a linearisation step, the study of these generating functions gives rise to an unexpected blend of algebra, combinatorics, and geometry. I will discuss selected aspects of this connection.

Viola Siconolfi (Politecnico di Bari) 

Titolo: Chromatic symmetric functions, interval orders and increasing forests

Abstract: The chromatic quasi-symmetric (csf) function is  a generalization  of the cromatic symmetric function

of a graph introduced by Shareshian and Wachs. A known fact about csf is that it is symmetric for graphs

associated to interval unit orders. This case has therefore attracted a lot of attention. Here, we are going to

 talk about csf associated to the larger class of  graphs associated to interval orders. In this case the csf is not necessarily symmetric. In particular we focus on writing these chromatic symmetric functions as sums of certain quasi symmetric functions associated to spanning trees and generalize an identity for chromatic functions in terms of LLT symmetric functions.

Based on a joint work with M. D'Adderio and R. Riccardi

Sheila Sundaram (University of Minnesota) 

Titolo: Results and conjectures surrounding a curious variant of Lie(n) 

Abstract:  Fundamental work of Reutenauer and Garsia (1980s-1990s) launched a renewed interest and vast literature on the  representation Lie(n) of the symmetric group S_n on the multilinear component of the free Lie algebra on n generators.

This talk will discuss a curious variant Lie(n,2) of the celebrated representation Lie(n). Introduced a few years ago by the speaker, the variant Lie(n,2)  satisfies the analogue of almost every known property of Lie(n). As one example, the exterior powers of the variant Lie(n,2) decompose the regular representation of S_n. The classical free Lie algebra counterpart of this result is the 1942 theorem of Robert Thrall which also follows from the earlier Poincaré-Birkhoff-Witt theorem: it is the well-known decomposition of the regular representation given by the symmetrised powers of the representations Lie(n) (the higher Lie modules). There are tantalising hints of analogies with the homology groups associated to the partition lattice as well.

Stephanie van Willigenburg (University of British Columbia) 

Title: Schur functions in noncommuting variables

Abstract: In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the classical Schur functions, in the algebra of symmetric functions, Sym. In this talk we answer this by introducing Schur functions in noncommuting variables, which naturally refine Rosas-Sagan Schur functions, in addition to having many analogous classical properties that we will discuss. This is joint work with Farid Aliniaeifard and Shu Xiao Li and requires no prior knowledge.