31/05/22  Seminario  16:00  17:00  1201 Dal Passo  Anna Chiara Lai  Sapienza, Università di Roma  Seminario di Equazioni Differenziali
Converse Lyapunov theorems and optimal stabilizability for unbounded control systems
(MS Teams link for the streaming at the end of the abstract)
We review some recent results on the stabilizability of a wide class of control systems with unbounded inputs, including those with a polynomial dependence on the controls.
We present an extension to these unbounded control systems of the wellknown relations between the global asymptotic controllability, the sample stabilizability, and the existence of a control Lyapunov function. The results are based on a reparameterization technique commonly adopted in optimal impulsive control, and in particular, on showing that the unbounded setting can be equivalently recasted in terms of a related, extended control problem with bounded controls.
Finally, we briefly discuss an integral cost associated to the control system and we establish sufficient conditions for the sample stabilizability of the system with regulated cost.
This talk is based on a joint work with Monica Motta, Università di Padova.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 
27/05/22  Seminario  16:00  17:00  1200 Biblioteca Storica  Kasun Fernando  SNS Pisa  Mathematical Physics Seminar "A bootstrap technique for dynamical systems"
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using statistical methods. When measuring the uncertainty of such parameter estimation, the bootstrap stands out as a simple but powerful technique. In this talk, I will introduce a bootstrap technique for dynamical systems and discuss its consistency and secondorder efficiency using a novel continuous Edgeworth expansions for dynamical systems. This is a joint work with Nan Zou (Macquarie University). 
27/05/22  Seminario  14:30  15:30  1201 Dal Passo  Francesco BRENTI  Università di Roma "Tor Vergata" 
Algebra & Representation Theory Seminar (ARTS)
"Graphs, stable permutations, and Cuntz algebra automorphisms"
 in live & streaming mode 
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Stable permutations are a class of permutations that arises in the study of the automorphism group of the Cuntz algebra. In this talk, after introducing the Cuntz algebra and surveying the main known results about stable permutations, I will present a characterization of stable permutations in terms of certain associated graphs. As a consequence of this characterization we prove a conjecture in [Advances in Math. 381 (2021) 107590], namely that almost all permutations are not stable, and we characterize explicitly stable 4 and 5cycles.
This is a joint work with Roberto Conti and Gleb Nenashev.
N.B.: please click HERE to attend the talk in streaming.

27/05/22  Seminario  14:30  15:30  1200 Biblioteca Storica  Matteo Tanzi  Courant Institute of Mathematical Sciences  Mathematical Physics Seminar "Selfsustaining measures for highdimensional coupled maps with and without noise"
I will describe the evolution of measures for coupled dynamical systems with/without noise where the number of coupled units is large, but finite. I will compare the evolution for the finite dimensional system with its thermodynamic limit, which is described by a nonlinear selfconsistent transfer operator. In particular, I will give sufficient conditions for the equilibrium states of the thermodynamic limit to be “selfsustaining” for the finite dimensional system: These states are characterized by being “almost” invariant for the finite system, and although might be far from any stationary state, they describe the statistical behavior of the system for long transients whose duration scales exponentially with the number of coupled units. 
24/05/22  Seminario  16:00  17:00  1201 Dal Passo  Marta Calanchi  Università degli studi di Milano  Bifurcation of positive solution for a Neumann problem with indefinite weights
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We consider eigenvalue problems and bifurcation of positive solutions for elliptic equations with indefinite weights and with Neumann boundary conditions. We give complete results concerning the existence and non existence of positive solutions for the superlinear coercive and noncoercive problems, showing a surprising complementarity of the respective results.
Joint work with Bernhard Ruf (Università degli Studi di Milano).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

20/05/22  Seminario  16:00  17:00  1201 Dal Passo  Iain GORDON  University of Edinburgh 
Algebra & Representation Theory Seminar (ARTS)
"Gaudin algebras, RSK and CalogeroMoser cells in type A"
 in live & streaming mode 
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N.B.: This talk is part of the activity of the MIUR Excellence
Department Project MATH@TOV CUP E83C18000100006
A few years ago, BonnaféRouquier defined 'CalogeroMoser cells' through the representation theory of rational Cherednik algebras. These cells partition the elements of a complex reflection group G, but are currently difficult to calculate except in small rank examples. In the special case when G is a finite Coxeter group, the cells are conjectured to be the same as KazhdanLusztig cells. In other words, conjecturally 'CalogeroMoser cells' generalise KazhdanLusztig cell theory from Coxeter groups to complex reflection groups. I will discuss a confirmation of this conjecture for G being the symmetric group. The proof uses ideas from integrable systems (Gaudin algebras), algebraic geometry (moduli of points on genus zero curves), and combinatorics (crystals).
This is joint work with A.Brochier and N.White.
N.B.: please click HERE to attend the talk in streaming.

20/05/22  Seminario  14:30  15:30  1201 Dal Passo  Fabio GAVARINI  Università di Roma "Tor Vergata" 
Algebra & Representation Theory Seminar (ARTS)
"Multiparameter quantum groups: a unifying approach"
 in live & streaming mode 
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The original quantum groups  in particular, quantized universal enveloping algebras, in short QUEA's  have been introduced as depending on just one "continuous" parameter. Later on, multiparameter quantum groups  in particular, multiparameter QUEA's  have been introduced in differente ways, with the new, "discrete" parameters either affecting the coalgebra structure or the algebra structure (while leaving the dual structure unchanged). Both cases can be realized as special type deformations  namely, either by twist, or by 2cocycle deformation  of Drinfeld's celebrated QUEA U_{h}( g). In this talk I will introduce a new, farreaching family of multiparameter QUEA's that encompasses and generalizes the previous ones, while also being stable with respect to both deformation by twists and deformations by cocycles. Taking semiclassical limits, these new multiparameter QUEA's give rise to a new family of multiparameter Lie bialgebras, that in turn is stable under both by twist and deformations by 2cocycles (in the Lie bialgebraic sense).
This is a joint work with Gastón Andrés García  cf. arXiv:2203.11023 (2022).
N.B.: please click HERE to attend the talk in streaming.

18/05/22  Seminario  14:00  15:00  2001  Tom Lyche  University of Oslo  A C^{1} simplex spline basis for the Alfeld split
Piecewise polynomials over triangles and tetrahedrons have applications in several branches ranging from finite element analysis, surfaces in computer aided design... The smoothness on tetrahedrons is obtained either by high degrees of polynomials or using smaller degrees when splitting the tetraehedron into smaller pieces. Here we consider the Alfeld split which generalizes the CloughTocher split of a triangle. Simplex splines with arbitrary knots are the natural generalization of univariate Bsplines to several variables. We consider degrees d = 2s1 in dimension s and construct a partition of unity basis for the space S^{1}_{2s1;s} on the Alfeld split, consisting of simplexsplines. We also show a Marsden like identity for s ≤ 5.
Joint work with JeanLouis Merrien.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. 
17/05/22  Seminario  16:00  17:00  1201 Dal Passo  Chaona Zhu  Chinese Academy of Sciences and Roma "Tor Vergata"  Prescribing scalar curvatures: the negative case
( MS Teams Link for the streaming )
The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant, Rauzy (Trans. Amer. Math. Soc. 1995) showed solvability, if the function to be prescribed is not too positive, as quantified by AubinBismuth (J. Funct. Anal. 1997) later on. In this talk we will review these results variationally and shed some light on the case, when Rauzy’s conditions fail. This talk is joint work with Martin Mayer.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

13/05/22  Colloquium  15:00  16:00  1201 Dal Passo  Michela Procesi  Università di Roma Tre  May12: Celebrating Women in Maths
Order and chaos and wave dynamics
(Opening address by Gabriella Tarantello)
(MS Teams link for the streaming at the end of the abstract)
Many physical phenomena are well described as the propagation of waves: the motion of the sea, the transmission of sound, electromagnetic waves (light, radio waves). Their mathematical description is often extremely complicated, and characterized by the coexistence of stable and chaotic behaviors. I will discuss some models of wave propagation by nonlinear Partial Differential Equations illustrating briefly the main difficulties as well as some mathematical methods used to study them.
A small refreshment will be served at the end of the colloquium.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 