26/09/19  Seminario  12:00  13:00  1201 Dal Passo  Michael S. Floater  University of Oslo  Bivariate polynomial interpolation on interlacing rectangular grids
The question of whether polynomial interpolation in two variables is well defined, or unisolvent, depends not only on the number of points but on their positions. For polynomial degree n we need N = (n+2)(n+1)/2 points.
Two wellknown point configurations for which interpolation is unisolvent are the "principal lattice", which is a triangular grid, and the "natural lattice", which is the intersections of nonparallel lines.
In this talk I will discuss the "interlacing lattice", which is the union of two interlacing rectangular grids, one square, the other almost square. The Padua points are an example of such a lattice, with a specific spacing of the points. In this talk I will explain why the interlacing lattice is unisolvent for any spacing of the points.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. 
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 Ktheory 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 Cuntzâ€“Pimsner algebras of subproduct 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 PoissonDirichlet(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 PoissonDirichlet. (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 PoissonDirichlet distribution. This is expected to hold quite generally in
systems that consist of onedimensionall 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 AizenmanNachtergaele.

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 BrydgesFrohlichSpencer loops for more general systems). We describe
the loop models in details and explain their derivations. (Based on joint work with
C. Benassi.) 
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 computeraided 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 planewave 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 welldefined 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)

       
       