Pagina 20

Date | Type | Start | End | Room | Speaker | From | Title |
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22/11/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Massimiliano Berti | SISSA 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. |

22/11/22 | Seminario | 14:00 | 16:00 | 1200 Biblioteca Storica | Enrico Bozzo | Università degli Studi di Udine | Sistemi 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. |

11/11/22 | Seminario | 16:00 | 17:00 | 1201 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.
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11/11/22 | Seminario | 14:30 | 15:30 | 1201 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. | |

28/10/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | 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 SL_{3} . Time permitting we will conclude discussing how this construction generalizes to higher rank. | |

28/10/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Università di Firenze | Algebra & Representation Theory Seminar (ARTS) "On character conductors"
This talk is part of the activity of the MIUR Excellence
Department Project MATH@TOV CUP E83C18000100006 N.B.: Given a character χ of a finite group G, there is a minimal positive integer f_{χ} such that all the values of χ belong to the f_{χ}-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. | |

28/10/22 | Seminario | 11:30 | 12:30 | 1201 Dal Passo | Fabio 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. |

25/10/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Roberto Feola | Università di Roma Tre | Seminario di Equazioni Differenziali Long time NLS approximation for a quasilinear Klein-gordon equation on large compact domains We consider a class of Klein-Gordon equations with quasilinear, Hamiltonian and quadratic nonlinearities posed on a large box with periodic boundary conditions.
We discuss how the cubic NLS equation can be derived to describe, approximately, the evolution of slow modulations in time and space of a spatially and temporarily oscillating wave packet.
We show that the approximation is valid over a time scale which goes beyond the natural quadratic lifespan of solutions of cubic equations. We provide error estimates in Sobolev spaces.
The proof is based on a combination of normal form techniques and energy methods.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |

14/10/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | UiT / University of Tromsø | Algebra & Representation Theory Seminar (ARTS) "Symmetries of supergeometries related to nonholonomic superdistributions" We extend the Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generating distributions on supermanifolds and their structure reductions. Several examples will be demonstrated, including distributions with at most simple Lie superalgebras as maximum symmetry. The talk is based on joint works with Andrea Santi, Dennis The and Andreu Llabres. | |

14/10/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | "Sapienza" Università di Roma | Algebra & Representation Theory Seminar (ARTS) "Moment polytopes of spherical varieties and applications to multiplicity-free Hamiltonian manifolds" Spherical varieties are a generalization of toric, symmetric and flag varieties. They are also relevant in symplectic geometry, in particular in relation with multiplicity-free Hamiltonian manifolds. In this talk we will describe how the combinatorial structures arising in this theory can be used to characterize those multiplicity-free manifolds that admit a Kähler structure, in terms of their moment polytopes. This is a joint work with Bart Van Steirteghem. |

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