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DateTypeStartEndRoomSpeakerFromTitle
12/05/23Seminario14:3015:301201 Dal Passo
Thomas WEBER
Università di Torino
Algebra & Representation Theory Seminar (ARTS)
"Noncommutative differential geometry with Hopf algebra symmetry"

Abstract
  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

Abstract
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  

Abstract
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
Ernesto SPINELLI
"Sapienza" Università di Roma
Algebra & Representation Theory Seminar (ARTS)
"Hartley's Conjecture and development arising"

Abstract
  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
Abstract
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
Abstract
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
Filippo VIVIANI
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"On the Picard group of the stack of G-bundles on families of curves"

Abstract
  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
Ilaria DAMIANI
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"Quantum affine algebras: comparing two coproducts"

Abstract
  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 Uq ⊗ Uq , 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 .
13/04/23Seminario16:0017:001101 D'AntoniElias RegoShenzhenOn the shadowableness of singular flows
Abstract
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
Abstract
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.

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Procedura ad opera di Giancarlo Baglioni