Pagina 20

25/11/22Seminario16:0017:001201 Dal Passo
Alessandro IRACI
Università di Pisa
Algebra & Representation Theory Seminar (ARTS)
"Delta and Theta operators expansions"
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  Delta and Theta operators are two families of operators on symmetric functions that show remarkable combinatorial properties. Delta operators generalise the famous nabla operator by Bergeron and Garsia, and have been used to state the Delta conjecture, an extension of the famous shuffle theorem proved by Carlsson and Mellit. Theta operators have been introduced in order to state a compositional version of the Delta conjecture, with the idea, later proved successful, that this would have led to a proof via the Carlsson-Mellit Dyck path algebra. We are going to give an explicit expansion of certain instances of Delta and Theta operators when t=1 in terms of what we call gamma Dyck paths, generalising several results including the Delta conjecture itself, using interesting combinatorial properties of the forgotten basis of the symmetric functions.
25/11/22Seminario14:3015:301201 Dal Passo
Giovanni GAIFFI
Università di Pisa
Algebra & Representation Theory Seminar (ARTS)
"Combinatorial aspects of the cohomology of compactifications of toric arrangements"
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  I will describe how to construct monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. In particular, I will focus on the case of the toric arrangements associated with root systems of type A. Here the combinatorial description of these basis offers a geometrical point of view on the relation between some eulerian statistics on the symmetric group.
  This is a joint work with Oscar Papini and Viola Siconolfi.
22/11/22Seminario16:0018:001200 Biblioteca StoricaDario FasinoUniversità degli Studi di UdineMetodi matriciali nell'analisi di reti complesse

Breve panoramica sulla scienza delle reti. Concetti classici di centralità basati su cammini minimi. Misure di centralità, somiglianza e distanza tra nodi basate su tecniche spettrali e funzioni di matrici. Catene di Markov a tempo discreto: Percorsi casuali classici e non-retrocedenti. Tecniche matriciali per la localizzazione di clusters, strutture core-periphery o quasi-bipartite. Introduzione ai percorsi casuali del secondo ordine: Tensori stocastici, PageRank nonlineare. Il seminario fa parte delle attività del Progetto MIUR Dipartimento d'Eccellenza CUP E83C18000100006 e del centro RoMaDS.
22/11/22Seminario16:0017:001201 Dal PassoMassimiliano BertiSISSA Trieste
Seminario di Equazioni Differenziali
Benjamin-Feir instability of Stokes waves

A classical subject in fluid mechanics regards the spectral instability of traveling periodic water waves, called Stokes waves. Benjamin, Feir, Whitam and Zhakarov predicted, through experiments and formal arguments, that Stokes waves in sufficiently deep water are unstable, finding unstable eigenvalues near the origin of the complex plane, corresponding to small Floquet exponents $mu$ or equivalently to long-wave perturbations. The first rigorous mathematical results have been given by Bridges-Mielke (’95) in finite depth and by Nguyen-Strauss (’20) in infinite depth. On the other hand, it has been found numerically that when the Floquet number $mu$ varies, two eigenvalues trace an entire figure-eight. I will present a novel approach to prove this conjecture fully describing the unstable spectrum. This is joint work with A. Maspero and P. Ventura.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006.
22/11/22Seminario14:0016:001200 Biblioteca StoricaEnrico BozzoUniversità degli Studi di UdineSistemi dinamici lineari su grafi

Argomenti: Grafi e matrici: concetti di connettività, matrice di adiacenza, matrici non negative, matrici primitive, teoria di Perron-Frobenius. Matrici stocastiche e substocastiche, problema del consenso. Matrici Laplaciane e di Metzler, punti di equilibrio e consenso nel caso continuo, cenno ai sistemi compartimentali. Il seminario fa parte delle attività del Progetto MIUR Dipartimento d'Eccellenza CUP E83C18000100006 e del centro RoMaDS.
11/11/22Seminario16:0017:001201 Dal Passo
Università di Trento
Algebra & Representation Theory Seminar (ARTS)
"Smoothness Criteria for T-Fixed Points in Flat Linear Degenerations of the Flag Variety"

  Linear Degenerations of the Flag Variety arise as very natural generalizations of the Complete Flag Variety and their geometrical properties very often appear to be linked with interesting combinatorial patterns.
  The talk will focus on a special class of linear degenerations, the Flat Degenerations, that have the remarkable property of being equidimensional algebraic varieties of the same dimension as the Complete Flag Variety. In some very recent works of M. Lanini and A. Pütz it is proved that Linear Degenerations of the Flag Variety can be endowed with a structure of GKM variety, under the action of a suitable algebraic torus T.
  The aim of the talk is to show how GKM Theory can be applied in this setting to prove some new results about the smooth locus in Flat Degenerations, generalizing a smoothness criterion proved by G. Cerulli Irelli, E. Feigin and M. Reineke for Feigin Degeneration.
  Finally, we provide a different combinatorial criterion, linking the smoothness property of a T-fixed point to the complete graph and to its orientations.
11/11/22Seminario14:3015:301201 Dal Passo
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Categorification of skew-symmetrizable cluster algebras through symmetric quivers"

  I will present my attempt to categorify cluster algebras of type B and C using the theory of symmetric quivers in the sense of Derksen and Weyman.
28/10/22Seminario16:0017:001201 Dal Passo
Salvatore STELLA
Università de L'Aquila
Algebra & Representation Theory Seminar (ARTS)
"Dominance order and pointed bases for cluster algebras"

  Cluster algebras are a class of commutative rings endowed with a partial canonical basis whose elements are called cluster monomials. They are defined recursively through the combinatorial machinery of seeds and mutations. Cluster monomials have a particularly nice property: they are pointed, i.e. they can be written as the product of a Laurent monomial with a monic polynomial with respect to any seed.
  One of the main problems in the theory has been to extend the set of cluster monomials to a full basis consisting only of pointed elements. This has been achieved in a variety of generalities using approaches deriving, for example, from representation of associative algebras, Teichmüller theory, and mirror symmetry. Recently Qin introduced a dominance order on the tropical points of the associated cluster variety and showed that this order can be used to parametrize all possible pointed bases.
  In this talk we will explicitly describe the dominance order in rank two using a simple geometric construction. We will then connect it to certain representations of SL3 . Time permitting we will conclude discussing how this construction generalizes to higher rank.
28/10/22Seminario14:3015:301201 Dal Passo
Università di Firenze
Algebra & Representation Theory Seminar (ARTS)
"On character conductors"
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  Given a character χ of a finite group G, there is a minimal positive integer fχ such that all the values of χ belong to the fχ-th cyclotomic field over the rationals. This number is often referred to as the conductor of χ. I will discuss some features of irreducible character conductors and their behavior with respect to factor groups.
28/10/22Seminario11:3012:301201 Dal PassoFabio Cipriani Politecnico di Milano Spectral triples, Dirichlet spaces, and discrete groups.

We study natural conditions on extended spectral triples $(A,h,D)$ by which the quantum differentials $da$ of elements $a in A$, belong to the ideal generated by the line element $ds = D^{-1}$. We also study upper and lower bounds on the singular values of the $da$'s to form a conformally invariant energy functional. We apply the general framework to study natural spectral triples of Dirichlet spaces and in particular those on duals of discrete groups arising on negative definite functions.

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