Pagina 17

13/04/23Seminario16:0017:001101 D'AntoniElias RegoShenzhenOn the shadowableness of singular flows

The shadowing property is a landmark of the dynamical systems theory which is deeply related to stability phenomena. Hyperbolicity is a famous source of systems with the shadowing property. Nevertheless, the shadowing property does not hold for systems beyond the hyperbolic ones. Indeed, the Lorenz attractor is a paradigmatic example of non-hyperbolic flow which reassembles several properties of the hyperbolic ones, although it does not satisfy the shadowing property, as it was showed by M. Komuro. Several years later L. Wen and X. Wen extended Komuro's results and proved that a sectional hyperbolic set does not satisfy the shadowing property, unless it is hyperbolic. In this talk, we will push further this discussion and ask whether the non-shadowableness of singular flows is due to the sectional hyperbolicity or it is, in fact, a consequence of existence of attached singulaties. This is a joint work with A. Arbieto, A Lopez and Y. Sanchez.
05/04/23Seminario14:0015:001101 D'AntoniBernardo CarvalhoFederal University of Minas Gerais / Tor Vergata / UFMGChaos theory and hyperbolic dynamics

In this talk I will discuss relations between chaotic and hyperbolic systems. More specifically, how we can obtain known results from hyperbolic dynamics using stronger notions of sensitivity to initial conditions. I will briefly explain expansiveness, topological hyperbolicity, cw-expansiveness, cw-hyperbolicity and first-time sensitivity.
04/04/23Seminario14:3015:301201 Dal PassoMarco PozzaUniversità di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
     Large Time Behavior of Solutions to Hamilton-Jacobi Equations on Networks  

Starting from Namah, Roquejoffre (1999) and Fathi (1998), the large time asymptotic behavior of solutions to Hamilton-Jacobi equations has been extensively investigated by many authors, mostly on smooth compact manifolds or the N-dimensional torus. Following recent development due to Pozza, Siconolfi (to appear), we extended this asymptotic analysis to time dependent problems on networks. The main difference between this and more traditional settings is that, for the well posedness of the evolutive problem on networks, the equation must be coupled with a ”flux limiter”, that is the choice of appropriate constants on each vertex of the network. These constants, among other things, bond from above the time derivatives of any subsolution on the vertices. In this talk we will show how this new condition impact the asymptotic behavior of the solutions to the Hamilton-Jacobi problem on networks.
31/03/23Seminario16:0017:001201 Dal Passo
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Fundamental Superalgebras in PI Theory"

  Fundamental superalgebras are special finite-dimensional superalgebras over an alge-braically closed field of characteristic zero defined in terms of certain multialternating graded polynomials. They play a key role in Kemer's Representability Theorem. In the present talk we provide new examples of fundamental superalgebras. Finally, if time allows, we shall give a characterization of fundamental superalgebras in terms of the representation theory of the hyperoctahedral group.
  This is based on a joint work with Antonio Giambruno and Ernesto Spinelli.
31/03/23Seminario14:3015:301201 Dal Passo
Giulia IEZZI
Università di Roma "Tor Vergata" & RWTH Aachen University
Algebra & Representation Theory Seminar (ARTS)
"A realisation of some Schubert varieties as quiver Grassmannians"

  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 give a construction for smooth quiver Grassmannians of a specific wild quiver, realising a class of Schubert varieties inside flag varieties. This allows for a definition of linear degenerations of Schubert varieties.
29/03/23Seminario16:0017:001201 Dal PassoKarl-Hermann NeebFAU Erlangen-Nürnberg
Operator Algebras Seminar
Causal symmetric spaces and nets of operator algebras

In the theory of local observables in Algebraic Quantum Field Theory (AQFT) modular theory creates a one-parameter group of modular automorphisms from a single state and this group often has a geometric implementation. If modular groups are contained in finite-dimensional Lie groups, they naturally lead to gradings of the Lie algebra and further to causal symmetric spaces. Conversely, we explain how nets of local observables (resp. of standard subspaces) on causal symmetric spaces can be constructed for all irreducible unitary representations of simple Lie groups which are either linear or locally isomorphic to SL(2,R). This is joint work with Jan Frahm (Aarhus), Gestur Olafsson (Baton Rouge) and Vincenzo Morinelli (Rome)
28/03/23Seminario14:3015:301201 Dal PassoFrancesca OronzioUniversità di Roma
Seminario di Equazioni Differenziali
ADM mass and potential theory

In this talk, we describe some monotonicity formulas holding along the regular level sets of suitable p-harmonic functions in asymptotically flat Riemannian 3-manifolds with a single end, with or without boundary, having nonnegative scalar curvature. Using such formulas, we obtain some geometric inequalities, including the positive mass inequality and the Riemannian Penrose inequality.
21/03/23Seminario16:3017:301201 Dal PassoWael BahsounLoughboroughLinear response due to singularities

It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tent-like family with a cusp at the turning point, we recover the linear response. This is a joint work with Stefano Galatolo.
17/03/23Seminario16:0017:001201 Dal Passo
Université Libre de Bruxelles
Algebra & Representation Theory Seminar (ARTS)
"Glimpses from truss theory"

  Trusses are like affine rings: as a ring is an abelian group with a compatible multiplica-tion, a truss is a torsor (over an abelian group) with a compatible multiplication. Introduced by Brzeziński in 2017 to unify the classical theory of rings with the modern theory of braces, trusses unexpectedly revealed the existence of a previously uncharted territory, whose exploration is not just leading to fascinating discoveries, but it is also shedding new light on groups and rings themselves. This talk would like to be a brief walk in the world of ternary operations to meet heaps, trusses, their modules and their novel heaps of modules.
17/03/23Seminario14:3015:301201 Dal Passo
Università de L'Aquila
Algebra & Representation Theory Seminar (ARTS)
"A taste of polynomial identities"

  A polynomial identity of an algebra A is a polynomial (in non-commuting variables) vanishing under all evaluations in A. Algebras satisfying at least one of these non-trivial relations are called PI-algebras. The first goal of this talk is to show how it is possible to characterize PI-algebras by means of numerical invariants related to their identities. Along the way we will highlight the combinatorial and analytical aspects of the theory, its connection with invariant theory, representation theory and growth problems. In the last part, we will look at some of the latest developments in this area, when it comes to algebras with additional structure.

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