Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
27/06/22	Seminario	11:00	12:00	1201 Dal Passo	Benedikt Wegener	Tor Vergata	Esame finale di dottorato Gauge Inequivalence, Energy Inequalities and Entanglement in Algebraic Quantum Field Theory". In streaming mode - link in the abstract Abstract Teams Link
13/06/22	Seminario	15:00	16:00	1201 Dal Passo	Davide Bianchi	Harbin Institute of Technology	Asymptotic spectra of large graphs with a uniform local structure Abstract We are concerned with sequences of graphs with a uniform local structure. The underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. We discuss different applications and provide numerical examples in order to underline the practical use of the developed theory. In particular, we show how the knowledge of the symbol f can benefit iterative methods to solve Poisson equations on large graphs and provides insight on the recurrence/transience property of random walks on graphs. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
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) 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 well-known 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" Abstract 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 second-order 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 - ( click HERE* to attend the talk in streaming )* Abstract 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 5-cycles. 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 "Self-sustaining measures for high-dimensional coupled maps with and without noise" Abstract 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 self-consistent transfer operator. In particular, I will give sufficient conditions for the equilibrium states of the thermodynamic limit to be “self-sustaining” 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 ( MS Teams Link for the streaming ) Abstract 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 non-coercive 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 Calogero-Moser cells in type A" - in live & streaming mode - ( please click HERE* to attend the talk in streaming )* N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 Abstract A few years ago, Bonnafé-Rouquier defined 'Calogero-Moser 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 Kazhdan-Lusztig cells. In other words, conjecturally 'Calogero-Moser cells' generalise Kazhdan-Lusztig 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 - ( please click HERE* to attend the talk in streaming )* Abstract 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 2-cocycle deformation - of Drinfeld's celebrated QUEA U_h(g). In this talk I will introduce a new, far-reaching 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 2-cocycles (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 C¹ simplex spline basis for the Alfeld split Abstract 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 Clough-Tocher split of a triangle. Simplex splines with arbitrary knots are the natural generalization of univariate B-splines to several variables. We consider degrees d = 2s-1 in dimension s and construct a partition of unity basis for the space S¹_2s-1;s on the Alfeld split, consisting of simplex-splines. We also show a Marsden like identity for s ≤ 5. Joint work with Jean-Louis Merrien. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.