188,689 research outputs found
Factorization in generalized Calogero-Moser spaces
Get PDFUsing a recent construction of Bezrukavnikov and Etingof we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = S_n, this confirms a conjecture of Etingof and Ginzburg
On singular Calogero-Moser spaces
Get PDFUsing combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter c if and only if the group is different from the wreath product and the binary tetrahedral group. This result and a theorem of Ginzburg and Kaledin imply that there does not exist a symplectic resolution of the singular symplectic variety h+h*/W outside of these cases; conversely we show that there exists a symplectic resolution for the binary tetrahedral group (Hilbert schemes provide resolutions for the wreath product case)
Periodic Solutions of a System of Complex ODEs. II. Higher Periods
No full textIn a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers, while the independent variable t ("time") is real. In that context it was proven that there exists, in the phase space of the initial data zn(0), zn(0), an open domain having infinite measure, such that all trajectories emerging from it are completely periodic with period 2, zn(t + 2) = zn(t). In this paper we investigate, both by analytcal techniques and via the display of numerical simulations, the remaining solutions, and in particular we show that there exist many -- emerging out of sets of initial data having nonvanishing measures in the phase space of such data -- that are also completely periodic but with periods which are integer multiples of 2. We also elcidate the mechanism that yields nonperiodic solutions, including those characterized by a "chaotic" behavior, namely those associated, in the context of the initial-value problem, with a sensitive dependence on the initial data
Una fede resiliente: il religioso dopo il tramonto della religione
No full textIl contributo è la postafazione alla riedizione della classica traduzione di Guido Calogero di "A Common Faith" (1934) di John Dewey. Nel testo mostro l'attualità del messaggio di Dewey in un'epoca in cui la fede comune nella capacità umana di cambiare in meglio sé stessi e il mondo può fungere da antidoto al disincanto
Presentazione
No full textNuovi approcci ascrivibili all’ambito dei visual studies sembrano avere soppiantato quelli della storia dell’arte, che resta invece strumento fondamentale anche per indagare tematiche più trasversali, come l’arcano rapporto
che lega l’immagine e la parola. In questa prospettiva, la storia dell’arte può
liberarsi dai suoi vincoli tradizionali e aprirsi all’esplorazione di altri domini culturali, da quello letterario a quello filosofico, per analizzare le immagini “latenti”, ossia le traduzioni verbali di oggetti figurativi o la sublimazione in termini
letterari e poetici di opere visuali già prodotte. I contributi contenuti in questo
volume tentano perciò di indagare, da diversi punti di vista, come i meccanismi
propri del visivo possano influenzare o determinare le forme verbali, ma anche
i modi in cui queste ultime riescono talvolta ad accostarsi e tradurre il contenuto ineffabile delle immagini artistiche
Introduzione
No full textIntroduzione
ReUso Roma 2021
In Roma, Capitale d’Italia 150 anni dopo,
volume primo. a cura di Calogero Bellanca e Susana Mora Alonso Munoyerro
Roma, Artemide 2021, pp. 23-25
Si auspica di contribuire a infondere fiducia per il nostro futuro e di indirizzare con un appropriato approccio metodologico il corretto uso compatibile dei beni architettonici, nella difesa dei nostri valori, senza continuare , come alcuni anni addietro, a “istrapazzar le sostanze”. Roma è la città ideale per riflettere ancora una volta su queste tematiche. L’obiettivo di questi convegni è stato sempre quello di far confluire le diverse discipline dell’architettura verso una costante attenzione agli organismi preesistenti con articolate proposte rivolte all’Uso delle nostre architetture, ai siti archeologici, ai centri storici e al paesaggio. Si p cercato di fornire spunti per allargare gli orizzonti disciplinari e attuativi. Credo che si possa concordare con il termine ragione che sottolinea l’autentica visione di un nuovo Umanesimo, oggi più che mai necessario, con il valore centrale dell’uomo, insieme ai diversi valori espresso dalle preesistenze
The quantum angular Calogero-Moser model
Get PDFThe rational Calogero–Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the ‘angular Calogero–Moser model’ on the sphere S^{n-1}. We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a ‘relative angular Calogero–Moser model’, which is analyzed in parallel. We generalize our considerations to the Calogero–Moser models associated with Coxeter
groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin–Calogero system
From real fields to complex Calogero particles
No full textWe provide a novel procedure to obtain complex PT-symmetric multi-particle Calogero systems. Instead of extending or deforming real Calogero systems, we explore here the possibilities for complex systems to arise from real nonlinear field equations. We exemplify this procedure for the Boussinesq equation and demonstrate how singularities in real-valued wave solutions can be interpreted as N complex particles scattering amongst each other. We analyse this phenomenon in more detail for the two- and three-particle cases. Particular attention is paid to the implementation of PT-symmetry for the complex multi-particle systems. New complex PT-symmetric Calogero systems together with their classical solutions are derived
Calogero–Moser eigenfunctions modulo ps
Get PDFIn this note we use the Matsuo–Cherednik duality between the solutions to the Knizhnik–Zamolodchikov (KZ) equations and eigenfunctions of Calogero–Moser Hamiltonians to get the polynomial p8-truncation of the Calogero–Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The s→∞ limit to the pure p-adic case has been analyzed in the n=2 case
Periodic Solutions of a Many-Rotator Problem in the Plane. II. Analysis of Various Motions
No full textVarious solutions are displayed and analyzed (both analytically and numerically) of a recently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling constants); in paticular the origin of certain periodic behaviors is explained. The light thereby shone on the connection among integrability and analyticity in (complex) time, as well as on the emergence of a chaotic behavior (in the guise of a sensitive dependance on the initial data) not associated with any local exponential divergence of trajectories in phase space, might illuminate interesting phenomena of more general validity than for the particular model considered herein
- …
