| 21/09/22 | Seminario | 15:00 | 16:00 | 1201 Dal Passo | Karl-Henning Rehren | University of Göttingen | LV formalism in perturbative AQFT
pAQFT defines nets of local algebras by a limiting construction with
relative S-matrices. The latter can be constructed perturbatively from an interaction
Lagrangian. In many instances, the construction can be improved by adding a total
derivative to the interaction Lagrangian (which would have no effect in classical
field theory).
The LV formalism controls whether and how this modification affects the
(relative) S-matrices and provides a tool to identify the local observables of the
model. |
| 07/07/22 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Tommaso de Fernex | University of Utah (USA) | ALGEBRAIC GEOMETRY SEMINAR
Local geometry of spaces of arcs
The arc space of a variety is an infinite dimensional scheme whose geometric structure captures, in a way that is not yet fully understood, certain features of the singularities of the variety. Focusing on its local rings and invariants of these rings such as embedding dimension and codimension, we explore the local structure of arc spaces. Our main tools rely on a formula for the sheaf of differentials on arc spaces and some recent finiteness results on the fibers of the map induced at the level of arc spaces from an arbitrary morphism of schemes over a field. The talk is based on joint work with Christopher Chiu and Roi Docampo.
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| 30/06/22 | Seminario | 15:00 | 16:30 | 1201 Dal Passo | H. Bostelmann and D. Cadamuro | H.B University of York, D.C. University of Leipzig |
Joint seminar
Fermionic integrable models and graded Borchers triples
The operator-algebraic construction of 1+1-dimensional integrable quantum field theories has received substantial attention over the past decade. These models are characterized by their asymptotic particle spectrum and their two-particle scattering matrix; so far, those particles have been bosonic. By contrast, we consider the case of asymptotic fermions. Abstractly, they arise from a grading of the underlying operator algebraic structures (Borchers triples); more concretely, one replaces the generating quantum fields fulfilling wedge-local commutation relations with a variant fulfilling anticommutation relations. Many of the technical methods required can be carried over from the bosonic case; most importantly, existing results on the technically hard part of the construction (i.e., establishing the modular nuclearity condition) do not require modification. Thus we are lead to a new family of rigorously constructed quantum field theories which are physically distinct from the bosonic case (with a different net of local algebras). Haag-Ruelle scattering theory confirms that they indeed describe fermions. Also, their local operators fulfill a modified version of the form factor axioms, consistent with the physics literature. |
| 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
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| 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
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)
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"
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 )
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.
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| 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"
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 )
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
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