## Flanders’ theorem for many matrices under commutativity assumptions – Fernando De Terán (Universidad Carlos III de Madrid)

Given two matrices $A \in C^{m \times n}$ and $B \in C^{n \times m}$ , it is known [1] that theJordan canonical form of AB and BA can only differ in the sizes of theJordan blocks associated with the eigenvalue zero, and the difference in thesize of…

## A bio-inspired optimization tool, the Dynamic Monge-Kantorovich model. Numerical solutions and applications – Enrico Facca (Scuola Normale Superiore, Pisa)

In this talk I will present the DynamicalMonge-Kantorovich model, a PDE system coupling an ellipticequation with a diffusion coefficient that change in timeaccording to a non-linear dynamics. The steady state of this system has been related to…

## Handling the conditioning of extreme-scale matrices – Massimiliano Fasi (Department of Mathematics, The University of Manchester)

In order to assess experimentally the stability of algorithms for the solution of systems of linear equations, it is typically desirable to have a certain degree of control over the condition number of the test matrices being used. If the tests are…

## Crouzeix Conjecture – Michael L. Overton (Courant Institute of Mathematical Sciences, New York University)

Crouzeix’s conjecture is among the most intriguing developments in matrix theory in recent years. Made in 2004 by Michel Crouzeix, it postulates that, for any polynomial p and any matrix A, ||p(A)|| <= 2 max(|p(z)|: z in W(A)), where the norm is the…

## MATLAB Tools for Large-Scale Linear Inverse Problems – James Nagy (Department of Mathematics, Emory University)

Inverse problems arise in a variety of applications: image processing, finance, mathematical biology, and more. Mathematical models for these applications may involve integral equations, partial differential equations, and dynamical systems, and…

## Neural networks for image understanding: methods, limitations, and new frontiers – Fabio Carrara (ISTI-CNR, Pisa)

Vision is natural and easy for living beings, while it is incredibly complex to be replicated in machines. In the last 40 years, a lot of work in Computer Vision has been spent trying to model and implement visual perception manually, with slow…

## Low-rank tensor methods for PDE-constrained optimization under uncertainty – Peter Benner (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany)

We discuss optimization and control of unsteady partial differential equations (PDEs), where some coefficient of the PDE as well as the control may be uncertain. This may be due to the lack of knowledge about the exact physical parameters, like…

## Matrices in companion rings and their Smith forms, with applications to group theory and algebraic topology – Vanni Noferini (University of Essex and Aalto University)

In group theory, various properties of the abelianization of a cyclically presented group can be deduced by the Smith normal form of an integer circulant matrix. Motivated by this fact, we present a number of results on the Smith form of matrices…

## Embedding properties of network realizations of reduced order models with applications to inverse scattering and data science – Vladimir Druskin (Worcester Polytechnic Institute)

Continued fractions are known since antiquity as the most compact representations of numbers. At the end of the 19th century Stieltjes connected them with physics. This connection gave rise to network syntheses in the first half of the 20th century…

## Computing dependability-oriented measures on Markov chains by means of matrix functions – Giulio Masetti (ISTI-CNR)

In the context of computing and communication system, dependability is defined as the ability to deliver service that can justifiably be trusted. Dependability is then an umbrella term that encompasses several attributes, such as: availability,…

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