09/05/23  Seminario  16:00  17:00  1201 Dal Passo  Giuseppe Pipoli  Università dell'Aquila  Seminario di Equazioni Differenziali
Constant mean curvature hypersurfaces in H^n x R
with small planar boundary
Denoting with H^n the ndimensional 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
halfspaces 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

02/05/23  Seminario  14:30  15:30  1201 Dal Passo  Veronica Tora  Università di Roma "Tor Vergata"  Seminario di Equazioni Differenziali
Reactiondiffusion 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 (20232027) 
28/04/23  Seminario  14:30  15:30  1201 Dal Passo  Ernesto SPINELLI  "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. 
20/04/23  Seminario  17:00  18:00  1201 Dal Passo  Stefano Luzzatto  ICTP  Existence and nonexistence of Physical Measures for doubly intermittent interval maps
We introduce a class of onedimensional 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. 
20/04/23  Seminario  16:00  17:00  1201 Dal Passo  Hamza Ounesli  SISSA  Existence 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 Diniintegrable. 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. 
14/04/23  Seminario  16:00  17:00  1201 Dal Passo  Filippo VIVIANI  Università di Roma "Tor Vergata" 
Algebra & Representation Theory Seminar (ARTS)
"On the Picard group of the stack of Gbundles 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 Gbundles on the family.
This is a joint work with Roberto Fringuelli. 
14/04/23  Seminario  14:30  15:30  1201 Dal Passo  Ilaria DAMIANI  Università di Roma "Tor Vergata" 
Algebra & Representation Theory Seminar (ARTS)
"Quantum affine algebras: comparing two coproducts"
The quantum affine algebras U_{q} are Hopf algebras with the coproduct Δ defined by Drinfeld and Jimbo; but they have also a "coproduct" Δ_{v} with values in a completion of U_{q} ⊗ U_{q} , 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 Rmatrix, Δ_{v} is by construction equivariant with respect to the action of the weight lattice.
In this talk I will show that Δ_{v} can be obtained as "equivariant limit" of Δ .

13/04/23  Seminario  16:00  17:00  1101 D'Antoni  Elias Rego  Shenzhen  On 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 nonhyperbolic 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 nonshadowableness 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. 
05/04/23  Seminario  14:00  15:00  1101 D'Antoni  Bernardo Carvalho  Federal University of Minas Gerais / Tor Vergata / UFMG  Chaos 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, cwexpansiveness, cwhyperbolicity and firsttime sensitivity. 
04/04/23  Seminario  14:30  15:30  1201 Dal Passo  Marco Pozza  Università di Roma "Tor Vergata"  Seminario di Equazioni Differenziali
Large Time Behavior of Solutions to HamiltonJacobi Equations on Networks
Starting from Namah, Roquejoffre (1999) and Fathi (1998), the large time asymptotic behavior of solutions to HamiltonJacobi equations has been extensively investigated by many authors, mostly on smooth compact manifolds or the Ndimensional 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 HamiltonJacobi problem on networks. 