|24/09/19||Seminario||16:00||17:00||1201 Dal Passo||Francesca Arici||Leiden University||Circle and sphere bundles in noncommutative geometry
In this talk I will recall how Pimsner algebras of self Morita equivalences can be thought of as total spaces of quantum circle bundles, and the associated six term exact sequence in K-theory can be interpreted as an operator algebraic version of the classical Gysin sequence for circle bundles. After reviewing some results in this
direction, I will report on work in progress concerning the construction of higher dimensional quantum sphere bundles in terms of Cuntz–Pimsner algebras of sub-product systems. Based on (ongoing) joint work with G. Landi and J. Kaad.
|23/09/19||Seminario||15:00||16:30||1201 Dal Passo||D. Ueltschi||University of Warwick||The random interchange model on the complete graph|
This model involves random permutations given by the product of random transpositions.
The joint distribution of the lengths of the cycles is given by Poisson-Dirichlet(1) (Schramm,
2005). We consider variants of this model with weights such as 2^# cycles. These variants
are related to quantum spin systems (Toth, 1993). We give a partial characterisation of the
joint distribution of cycle lengths, that is compatible with Poisson-Dirichlet. (Joint work with
J. Bjornberg and J. Frohlich.)
|20/09/19||Seminario||15:00||16:30||1201 Dal Passo||D. Ueltschi||University of Warwick||Universal behaviour of loop soups in dimensions 3 and higher|
It was recently understood that the joint distribution of the lengths of the loops is
given by a Poisson-Dirichlet distribution. This is expected to hold quite generally in
systems that consist of one-dimensionall loops living in space of dimensions three
and higher. The conjecture will be explained in details, and some results will be presented.
|18/09/19||Seminario||15:00||16:30||1201 Dal Passo||D. Ueltschi||University of Warwick||Quantum spin systems and their loop representations
We introduce quantum spin systems such as XY and quantum Heisenberg. We describe their loop representations due to Toth and Aizenman-Nachtergaele.
|17/09/19||Seminario||15:00||16:30||1201 Dal Passo||D. Ueltschi||University of Warwick||Classical spin systems and their loop representations|
We introduce classical spin systems such as Ising, XY, Heisenberg. They can
be represented with the help of loop models (Aizenman random currents for
Ising, and Brydges-Frohlich-Spencer loops for more general systems). We describe
the loop models in details and explain their derivations. (Based on joint work with
|12/09/19||Seminario||14:30||15:30||1201 Dal Passo||Rida T. Farouki||University of California Davis||The Bernstein polynomial basis: a centennial retrospective
The Bernstein polynomial basis, introduced in 1912 to provide a constructive proof of the Weierstrass approximation theorem, attracted little interest for practical computations until the advent of the novel field of computer-aided geometric design in the 1960s and 1970s. Through the work of Paul de Casteljau at Citroen and Pierre Bezier at Renault, the remarkable properties and elegant algorithms associated with this representation for polynomials over finite domains became more widely appreciated. Apart from offering useful geometrical insight into the behavior of polynomials, the Bernstein form is an intrinsically very stable representation with an attractive hierarchical structure in the multivariate context, and in recent decades it has enjoyed an increasingly diverse repertoire of applications. This talk will provide a brief perspective on the historical evolution of the Bernstein form, and a synopsis of the current state of associated algorithms and applications.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
|11/09/19||Seminario||16:00||17:00||1201 Dal Passo||Daniela Cadamuro||Leipzig University||Curing the infrared problem in nonrelativistic QED|
In nonrelativistic QED, the electron as an infraparticle exhibits
velocity superselection, namely plane-wave configurations of the
electron with different velocities give rise to inequivalent
representations of the algebra of the asymptotic electromagnetic
field. Moreover, as another feature of the infrared problem, the
Hamiltonian has no well-defined ground state in this realm. These
properties make the construction of scattering states of electrons a
difficult task. In a model of one spinless electron interacting with
the quantized electromagnetic field, we approach these problems in
two different ways: On the one hand, by viewing the electron on a
new background state, the infravacuum state, which generates a new
class of representations; on the other hand, by restricting the
algebra to the future light cone. In both cases, our construction
leads to the absence of velocity superselection.
(Joint project with W. Dybalski)
|23/07/19||Seminario||14:00||15:00||1201 Dal Passo||Florin Radulecu||Univ. Tor Vergata||Transferring unitary representations from PSL(2,R) to PSL(2,Q_p)- an operator algebra approach
We use an operator algebra approach in transferring unitary representations in the discrete series of PSL(2,R) to PSL(2,Q_p). This is related to finite Murray von Neumann dimension of the von Neumann algebra obtained by restriction to PSL(2,Z). In the case of infinite dimension, we construct a "double representation" (by left and right multiplication operators) that we can control modulo compact operators.
|23/07/19||Seminario||12:00||13:00||1201 Dal Passo||Yongjie Jessica Zhang||Carnegie Mellon University||Image-based mesh generation and volumetric spline modeling for isogeometric analysis with engineering applications
In this talk, I will highlight our research on image-based mesh generation for complicated domains, trivariate spline modeling for isogeometric analysis (IGA), as well as biomedical, materials science and engineering applications. I will first present advances and challenges in image-based geometric modeling and meshing along with a comprehensive computational framework, which integrates image processing, geometric modeling and mesh generation with multi-scale analysis at molecular, cellular, tissue and organ scales. Then, I will present a centroidal Voronoi tessellation (CVT) based surface segmentation method to build polycubes, which are used to generate volumetric control meshes via parametric mapping. After that, truncated hierarchical spline basis functions are derived to enable partition of unity and linear independence. Furthermore, blended B-spline and hybrid nonuniform subdivision approaches are developed to construct basis functions around extraordinary nodes, achieving an optimal convergence rate of IGA. The developed platforms have been incorporated into Rhino, Abaqus and LS-DYNA for engineering applications.
This talk is in the frame of the MIUR Excellence Department Project CUP E83C18000100006 and of the Oberwolfach Simons Visiting Professors Program.
|16/07/19||Seminario||16:30||17:30||1101 D'Antoni||Yen-Chi Chen ||University of Washington||Analyzing GPS data using density ranking|
A common approach for analyzing a point cloud is based on estimating the underlying probability density function. However, in complex datasets such as GPS data, the underlying distribution function is singular so the usual density function no longer exist. To analyze this type of data, we introduce a statistical model for GPS data in the form of a mixture model with different dimensions. To derive a meaningful surrogate of the probability density, we propose a quantity called density ranking. Density ranking is a quantity representing the intensity of observations around a given point that can be defined in a singular measure. We then show that one can consistently estimate the density ranking using a kernel density estimator even in a singular distribution such as the GPS data. We apply density ranking to GPS datasets to analyze activity spaces of individuals.