Pagina 16

16/05/23Seminario14:3015:301201 Dal PassoRoberta BianchiniIAC - CNR
Seminario di Equazioni Differenziali
     Mathematical analysis of stably stratified fluids  

We will be interested in the analysis of a system of PDEs modeling continuously stratified fluids under the influence of gravity. The system is obtained by a linearization of the equations of incompressible non-homogeneous fluids (non-homogeneous Euler equations) around a background density profile that increases with depth (spectrally stable density profile). I will present some mathematical problems related to (asymptotic) stability and long-time dynamics.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
12/05/23Seminario16:0017:001201 Dal Passo
Emanuele LATINI
Università di Bologna
Algebra & Representation Theory Seminar (ARTS)
"Higher conformal Yang-Mills equation"

  On a pseudo Riemannian manifold consider a 2-form taking value in the adjoint representation of some (semisimple) Lie algebra. It is well known that the corresponding Yang-Mills functional is conformally invariant just in four dimensions. A natural question is whether there are natural replacements of the Yang-Mills functional that are conformally invariant.
  In the first part of the talk we will describe the main tools needed to answer this question, namely conformal defining densities for conformally compact manifolds and the (adjoint) tractor bundle; then we will show how to set up and to formally solve the Yang-Mills boundary problem on conformally compact manifolds. In general, smooth solutions are obstructed by an invariant of boundary connections. Specializing to Poincaré-Einstein manifolds with even boundary dimension parity, this obstruction is a conformal invariant of boundary Yang-Mills connections. This yields conformally invariant, higher order generalizations of the Yang-Mills equations and their corresponding energy functionals.
12/05/23Seminario14:3015:301201 Dal Passo
Thomas WEBER
Università di Torino
Algebra & Representation Theory Seminar (ARTS)
"Noncommutative differential geometry with Hopf algebra symmetry"

  While in classical differential geometry one is given a unique differential structure, the de Rham calculus, such a canonical choice does not exist in noncommutative geometry. Moreover, while the de Rham differential is equivariant with respect to a given Lie group action, a noncommutative calculus might not be compatible with a corresponding Hopf algebra symmetry.
  We give a gentle introduction to noncommutative differential geometry, reviewing seminal work of Woronowicz (covariant calculi on Hopf algebras) and Hermisson (covariant calculi on quantum homogeneous spaces). The latter invokes the notion of faithful flatness and Takeuchi/Schneider equivalence. Afterwards we discuss an original construction of a canonical equivariant calculus for algebras in symmetric monoidal categories, with main examples including algebras with (co)triangular Hopf algebra symmetry, particularly Drinfel’d twisted (star product) algebras. The approach relies on and is essentially dual to the concept of ‘braided derivations’ and we show that the corresponding braided Gerstenhaber algebra of multi-vector fields combines with the noncommutative calculus, forming a braided Cartan calculus. If time permits we illustrate how to formulate Riemannian geometry in this framework, proving that for every equivariant braided metric there is a unique quantum Levi-Civita connection. The second half of the talk is based on the thesis of the speaker.
09/05/23Seminario16:0017:001201 Dal PassoGiuseppe PipoliUniversità dell'Aquila
Seminario di Equazioni Differenziali
Constant mean curvature hypersurfaces in H^n x R with small planar boundary

Denoting with H^n the n-dimensional hyperbolic space, we show that constant mean curvature hypersurfaces in H^n x R with small boundary contained in a horizontal slice P are topological disks, provided they are contained in one of the two half-spaces determined by P. This is the analogous in H^n x R of a result in R^3 by A. Ros and H. Rosenberg. The proof is based on geometric and analytic methods : from one side the constant mean curvature equation is a quasilinear elliptic PDE on manifolds, to the other the specific geometry of the ambient space produces some peculiar phenomena. This talk is based on a joint work with Barbara Nelli.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
02/05/23Seminario14:3015:301201 Dal PassoVeronica ToraUniversità di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
     Reaction-diffusion equations on graphs for the modelling of the formation of large protein aggregates in Alzheimer’s disease  

Link to the abstract

Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
28/04/23Seminario14:3015:301201 Dal Passo
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Hartley's Conjecture and development arising"

  In the 80s Bryan Hartley conjectured that if the unit group a torsion group algebra FG satisfies a group identity, then FG satisfies a polynomial identity. In this talk we aim to review the most relevant results that arose from its solution and to discuss some recent developments concerning group identities for the set of symmetric units of FG.
20/04/23Seminario17:0018:001201 Dal PassoStefano LuzzattoICTPExistence and non-existence of Physical Measures for doubly intermittent interval maps

We introduce a class of one-dimensional full branch maps which may admit up to two neutral fixed points as well as critical points and/or singularities with unbounded derivative. We give a complete classification of the possible physical measures which may appear (or not), study some other statistical properties, and show that different behaviour can be quite intermingled in parameter space. This is joint work with Douglas Coates and Muhammad Mubarak.
20/04/23Seminario16:0017:001201 Dal PassoHamza OunesliSISSAExistence of invariant measures for circle expanding maps of low regularity

It is well known that uniformly expanding circle maps whose derivative is Holder continuous have a unique ergodic invariant probability measure absolutely continuous with respect to Lebesgue. This result was extended by Fan and Jiang in 2001 to maps whose derivative is Dini-integrable. However, there exist counterexamples, both to the existence and to the uniqueness, for C^1 maps for which the derivative is less regular. We show that nevertheless, for any given modulus of continuity, there is a C^1 uniformly expanding map of the circle whose derivative has that modulus of continuity and has an invariant probability measure equivalent to Lebesgue.
14/04/23Seminario16:0017:001201 Dal Passo
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"On the Picard group of the stack of G-bundles on families of curves"

  Given a family of smooth projective curves and an arbitrary connected linear algebraic group G, we investigate the Picard group of the stack of relative G-bundles on the family.
  This is a joint work with Roberto Fringuelli.
14/04/23Seminario14:3015:301201 Dal Passo
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"Quantum affine algebras: comparing two coproducts"

  The quantum affine algebras Uq are Hopf algebras with the coproduct Δ defined by Drinfeld and Jimbo; but they have also a "coproduct" Δv with values in a completion of UqUq , introduced by Drinfeld for quantm affinizations. While the relation between Δ and the action of the braid group (and also of the weight lattice, which is a subgroup of the braid group) is complicated and involves the R-matrix, Δv is by construction equivariant with respect to the action of the weight lattice.
  In this talk I will show that Δv can be obtained as "equivariant limit" of Δ .

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