Exchange CDLab/LIAM! Jianhong Wu will visit Udine on July 26-27, 2018. I will visit York University late this August. More on here, here and here.

Utrecht once more, april 2017. Another short visit to Odo Diekmann, and Davide Liessi spending three months at UU. This time also enjoyed the lectures by Sjoerd Verduyn Lunel on bounded operators and relevant characteristic matrices, very intriguing with a lot of inspiration for future developments.

One day in Trento, november 2016, enjoining again the collaboration with Andrea Pugliese and Mimmo Iannelli, trying to finalize the final submission of a paper (now #31 in the publication list), and revisiting codes for some tests to be included in the last Mimmo’s effort, a fresh upcoming Springer monograph on age-structured populations, co-authored with Fabio Milner.

Back in Utrecht again! A short visit to Odo Diekmann together with Rossana Vermiglio and Davide Liessi, as well as Francesca Scarabel and Mats Gyllenberg from Helsinki and Hans Metz from Leiden. An absorbing week on several aspects about structured populations, from modeling ones to advanced numerics. The first outcome is the paper #30 in the publication list: ever seen a period doubling cascade for renewal equations?

A short visit to Naples (february 29 – march 2, 2016), invited by Bruno Buonomo. I’ll give a seminar on the recent activity on numerical methods for dynamical systems generated by complex functional equations of retarded type, with applications to physiologically structured populations. We will have also time to discuss about our recently submitted PRIN proposal, jointly with the universities of Trento, Pisa and Roma Tor Vergata.

Julia Sánchez Sanz is again at DiMI at UNIUD, from september till november 2014. We are completing the codes for the eigenvalues of the real Daphnia model and proving the convergence of the numerical scheme.

Odo Diekmann briefly visited DiMI at UNIUD in april 2014. We keep on working together on Daphnia models, see 11 below.

Julia Sánchez Sanz visited DiMI at UNIUD in september 2013. We started to collaborate on Daphnia models. These are systems of coupled renewal and delay differential equations. We wish to extend the computation of the eigenvalues through the discretization of the infinitesimal generator by pseudospectral methods. The final aim is to study stability and bifurcation of equilibria.

In march 2012 I visited Odo Diekmann in Utrecht (NL). We are interested in studying the approximation of nonlinear delay equations by systems of ordinary differential equations. The practical aim is at using the ODEs as input to standard, efficient and, above all, available bifurcation tools (e.g., Matcont, Auto, etc.). But I have to say that the use of pseudospectral methods in this context reveals a lot of intriguing details on the dynamics of delay systems. In the occasion I also gave the seminar Computing Lyapunov exponents for systems with delay.

In may 2011 I visited Erik Van Vleck at Lawrence (KS-USA). This to complete our research line on the numerical approximation of Lyapunov exponents for retarded functional differential equations. There I gave the seminar Numerics for stability analysis of delay systems and population dynamics.

In november 2010 Odo Diekmann, from Utrecht University, visited DiMI at UNIUD. We started to consolidate a strong collaboration on models of population dynamics fromulated as delay equations, either differential or integro-differential.

In june 2010 I first met Alexandre Ern. He was visiting UNIUD at the Department of Economics and Statistics. We had a very nice exchange on several mathematical problems (Alexandre comes back to Udine several times actually!).

In april 2010 Bernd Krauskopf, from Bristol University, visited DiMI at UNIUD. He gave the advanced course Dynamical systems and numerical analysis and the plenary seminar The mystery of chaos in the Lorenz equations.

In november 2008 I made a research trip to USA. I first visited Erik Van Vleck at Lawrence (KS) and then Luca Dieci in Atlanta (GA). This to start a new investigation, for which I got a GNCS “young researchers” grant. I am interested in the numerical computation of Lyapunov exponents for delay differential equations, and they are experts on the same problem for ODEs. At Lawrence I gave the seminar On computing the spectrum of mixed type functional differential equations.

In september 2006 Tony Humphries, from McGill University in Montreal, visited DiMI at UNIUD. Basically we continued our collaboration on delay and retarded-advanced equations started in 2005.

In june 2006 Gabor Stépan, from the Budapest University of Technology and Economics, visited DiMI at UNIUD. We spoke a lot about time delay systems and he gave the advanced course Delay induced vibrations in engineering.

Autumn in Connecticut: what colors! In september 2005 I visited the ALARM lab at UCONN, directed by Nejat Olgac. I was invited to share my knowledge on pseudospectral techniques to compute the characteristic roots of time delay systems. And to learn their speciality: the cluster treatment of characteristic roots (CTCR). A great exchange! There I gave the seminars Linear time delay systems: from characteristic roots to stability charts and Pseudospectral approximation of eigenvalues of derivative operators with nonlocal boundary conditions.

In april 2005 I visited Tony Humphries at McGill University in Montreal. We spent around a week talking about numerics for delay systems, and also about some interesting models in real applications. There I gave the seminars Linear time delay systems: from characteristic roots to stability charts and Pseudospectral approximation of eigenvalues of derivative operators with nonlocal boundary conditions.

I spent august 2003 at KU Leuven (B), visiting Dirk Roose and Wim Michiels. Their research group created DDE-BIFTOOL, a Matlab package for the bifurcation analysis of delay differential equations. What a better place to exchange opinions on the computation of characteristic roots, my PhD thesis subject! There I gave the seminars Infinitesimal generator approximation for the computation of characteristic roots for DDEs and Use of pseudospectral differencing methods for the discretization of the solution operator semigroup of linear DDEs.