|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.
|12/07/19||Seminario||16:30||17:30||1101 D'Antoni||Marianna Pensky||University of Central Florida||Estimation and Clustering in Popularity Adjusted Stochastic Block Model
Stochastic networks in general and stochastic block models in particular attracted a lot of attention in the last decade. The talk considers the Popularity Adjusted Block model (PABM) which generalizes the Stochastic Block model and the Degree Corrected Block Model by allowing more flexibility for block probabilities. We argue that the main appeal of the PABM is its less rigid spectral structure which makes the PABM an attractive choice for modeling networks that appear in biological sciences. Based on a joint work with Majid Noroozi and Ramchandra Rimal.
|03/07/19||Seminario||16:00||17:00||1201 Dal Passo||James Tener||Australian National University||Chiral Segal CFTs from conformal nets|
In this talk I will describe joint work in progress with Andre Henriques to construct functorial chiral conformal field theories from the data of a conformal net. The key idea is the use of "thin cobordisms", which can also be used to connect conformal nets to vertex operator algebras. I will introduce the idea of thin cobordisms and explain how they give a geometric description of a conformal net.
|02/07/19||Seminario||14:30||15:30||1201 Dal Passo||Hugo Tavares||Universit' di Lisbona||Least energy solutions of Hamiltonian elliptic systems with Neumann boundary conditions|
In this talk we will discuss existence and qualitative properties of solutions to a class of Hamiltonian elliptic systems with Neumann boundary conditions ,both in the sublinear and superlinear problems, in the subcritical regime. In balls and annuli we show that least energy solutions (l.e.s.) are not radial functions, but only partially symmetric (namely foliated Schwarz symmetric). A key element in the proof is a new L^t-norm-preserving transformation, which combines a suitable flipping with a decreasing rearrangement. This combination allows us to treat annular domains, sign-changing functions, and Neumann problems, which are non-standard settings to use rearrangements and symmetrizations. Our theorems also apply to the scalar associated model, where our approach provides new results as well as alternative proofs of known facts.
This is a joint work with Alberto Saldaña.
|27/06/19||Seminario||16:00||17:30||1101 D'Antoni||Valentina Cammarota||Sapienza University of Rome||Two Point Function for Critical Points of a Random Plane Wave |
Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemannian manifolds. This is known to be true on average. In the present paper we discuss one of important geometric observable: critical points. We first compute one-point function for the critical point process, in particular we compute the expected number of critical points inside any open set. After that we compute the short-range asymptotic behaviour of the two-point function. This gives an unexpected result that the second factorial moment of the number of critical points in a small disc scales as the fourth power of the radius. Joint work with Dmitry Beliaev and Igor Wigman.
|27/06/19||Seminario||14:00||17:00||1201 Dal Passo||Barbara Bolognese||University of Sheffield||Stabilità di Bridgeland|
Ultima lezione del II CICLO di Corso per Dottorato di Ricerca in Matematica -
nell'ambito del PROGETTO ECCELLENZA MIUR "Math@Tov". ORGANIZZATORE SCIENTIFICO: C. Ciliberto.
GIUGNO: giorno 27 - Aula Dal Passo - 14:00-17:00 (pausa di 30 minuti)
Gli argomenti trattati saranno i seguenti: richiami di stabilità per fasci e spazi di moduli,
categorie triangolate e derivate,
condizioni di stabilità su categorie triangolate, la varietà di stabilità, il caso delle curve ellittiche e
curve in generale, superficie in generale e in particolare superficie K3, risultati di Bayer e Macrì sulla
classe di divisori nef sullo spazio dei moduli dei complessi stabili, superficie regolari ed altri esempi.
|25/06/19||Seminario||14:30||15:30||1201 Dal Passo||Matteo Tanzi||University of Victoria||Heterogeneously Coupled Maps: Rigorous Mean Field Reduction and Dynamics Reconstruction
A graph with heterogeneous degrees has most of its nodes making a small number of connections, while the remaining nodes, called hubs, have very high degree. This type of graph is ubiquitously found in models of natural and artificial systems made of interacting components such as, among others, neuronal networks, gene-regulatory networks, and power grids. I will report results addressing the ergodic theoretical properties of uniformly expanding maps coupled on such graphs, focusing the attention on the case where the number of nodes in the graph is very large.
The results justify the emergence of macroscopic behaviour such as coherence of dynamics among hubs with the same number of connections. They also suggest an algorithm to reconstruct the network structure and dynamical features from observations of the dynamics at every node. Tested on computer simulations, the algorithm is able to effectively recover the degree distribution of the network, community structures, local dynamics and effective coupling.
|21/06/19||Seminario||14:30||15:30||1201 Dal Passo||Eric Bedford||Stony Brook||Ueda Theory of semi-attracting fixed points for automorphisms of C^2|