Feb. 1999 - Jan. 2001: Post-doctorate fellowship at the Department of Mathematics, University of Trento; line of research: "Stochastic Partial Differential Equations and Malliavin Calculus".
Ph.D., Nov. 1998, IX Cicle, Ph.D. in Mathematics at the Faculty of Science M.F.N., University of Trento. Title of the thesis "Some Applications in Malliavin Calculus", under the supervision of professor L. Tubaro.
Master Degree in Mathematics, University of Pisa; graded magna cum laude, obtained on July 8, 1993. Title of the thesis: "Unicità forte per equazioni ellittiche", under the supervision of professor F. Colombini.
Academic career and teaching activities
In the years of service as a professor in Trento, my teaching duties may be divided in three lines.
1. An introductory course in "Probability and Statistics" for the second year of the bachelor degree in Mathematics. Previously, I gave similar courses for the bachelor degree in Informatics (from 2004 to 2014) and in Biotechnology (from 2014 to 2016). This covers the main part of my teaching effort both concerning time and number of students.
2. One advanced course for the last year of the master degree in Mathematics, "Stochastic Differential Equations". It is a free choice course, with about ten-fifteen students per year. It covers advanced topics in stochastic analysis, with some links to mathematical finance and biosystems, which are the areas of interest of the majority of students.
3. One course in the communication of science, that is compulsory for the curriculum in Teaching and Scientific Communication, that is named "Mathematical Models for the Physical, Natural and Social Sciences". In this course, that I proposed some years ago, I give some examples where mathematics is applied: for instance, Bayes theorem in trials, number theory in cryptography and sampling music, dynamical systems for biological models, graph theory in the analysis of social interactions.
December 2013, Ph.D. course on "An introduction to Malliavin calculus" during the "Italian-German training for stochastic modeling of financial crisis" at the Universtity of Wuppertal.
My research focuses on stochastic partial differential equations. Stochastics is a subfield of mathematics that deals with probability theory and statistics and stochastic equations are particularly well suited for the description of complex dynamic systems. Therefore, I can say that my research stands on the boundary between pure mathematics and applications. To better explain the last statement, it is necessary to outline the main ideas and fields that I deal with in my activity.
My Ph.D. thesis was centered on the Malliavin calculus and its applications. Let me mention the most important outcomes of the thesis: a variation of constants formula for infinite dimensional diffusion, which allows a more explicit representation of the solution, and an analysis of regularity results for diffusion processes. Later, a further application of Malliavin calculus provides a new approach to study stochastic partial differential equations with boundary noise.
During the years of study in Trento, I actively collaborated with other Ph.D. and post-doc students on various topics in stochastic analysis: on the characteristics method of solution for stochastic partial differential equations, on the study of stochastic Volterra equations, on applications of control theory to stochastic differential equations.
Active Research Fields
Infinite dimensional analysis
My research on integration by parts formulas in infinite dimensional spaces dates back to the collaboration with L. Zambotti in 2004. Recently, new results in this direction were obtained in collaboration with G. Da Prato and L. Tubaro; there are further open research lines with the same authors as well as M. Zanella (Luiss).
Stochastic integro-differential equations
My research on Volterra equation dates back to 2004 and concernes different aspects and applies different methodologies. I have a long-standing collaboration with G. W. Desch (University of Graz) on analytical methods for the solution of a class of Volterra equations.
Moreover, I established a collaboration on this topic with other worldwide known mathematicians as Giuseppe Da Prato (Scuola Normale Superiore, Pisa) and Viorel Barbu (Iasi, Romania).
Evolution Equations with Stochastic Boundary Conditions
In the last years, I actively studied problems with various kinds of boundary noise.
From a theoretical point of view, the problem can be analysed both via a variational approach (see the recent papers in collaboration with V. Barbu and L. Tubaro), via a semigroup approach (in collaboration with G. Ziglio) and through the heat kernel (both deterministic and stochastic), see the collaborations with E. Al\'os (Pompeu Fabra University, Barcelona) and the recent papers with M. Zanella (currently at Luiss, Roma).
Such problems have also relevant interest in the applications, as developed in collaboration with D. Mugnolo (currently at Fernuniversit\"at Hagen), with my former students E. Mastrogiacomo, concerning the analysis of the stochastic FitzHugh Nagumo system, and G. Ziglio on semigroup methods for solving network equations and applications. A better understanding of stochastic processes on networks may shade some light on the cellular behavior and also advance the understanding of higher brain functions that are difficult to investigate in detail. My aim is to use the theory of differential operators on networks to study FitzHugh-Nagumo systems with various kinds of stochastic dynamical boundary conditions.
Epidemics spreading in real networks
Quite recently, I was proposed to extend the analysis of diffusions on networks to study diffusion of epidemics and/or informations spreading through a community. This topic is the core of the Ph.D. thesis of my student S. Ottaviano and we actively collaborate with F. De Pellegrini (Create-Net) and P. van Mieghem (University of Delft).
Such problems depend on the social structure of the community itself, hence they are concerned with the shape of the connectivity matrix. Epidemic threshold is a critical state beyond which infections become endemic. The epidemic threshold of a graph depends fundamentally on the graph itself, in particular we focus our research on the largest eigenvalue of the adjacency matrix of the graph.
Proposal of a position of ``Visiting professor'' for prof. Delio Mugnolo (Hagen, Germany), research activity funded by Gnampa Indam, year 2016. Area: Mathematical Analysis, Probability and Applications.
Local coordinator of ``Deterministic and stochastic evolution equations'', coordinated by professor Alessandra Lunardi. Research activity funded by M.I.U.R. Ministero dell'Università e della Ricerca, year 2016. Area: 01 - Scienze matematiche e informatiche.
Member of ``Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni'', coordinated by professor Marco A. Fuhrman. Research activity funded by M.U.R. Ministero dell'Università e della Ricerca, year 2010-11. Area: 01 - Scienze matematiche e informatiche.
Coordinator of ``Equazioni integro-differenziali stocastiche in dimensione infinita". Research activity funded by Gnampa Indam, year 2010. Area: Mathematical Analysis, Probability and Applications.
Member of ``Equazioni di Kolmogorov'', coordinated by professor Alessandra Lunardi. Research activity funded by M.U.R. Ministero dell'Università e della Ricerca, year 2008. Area: 01 - Scienze matematiche e informatiche.
Member of ``Neurobiologia stocastica'' (NEST), coordinated by professor Sergio Albeverio. Research activity funded by P.A.T. Provincia Autonoma di Trento, 2008-2010. Research topic: Biomathematics.
Member of ``Equazioni di Kolmogorov'', coordinated by professor Giuseppe Da Prato. Research activity funded by M.U.R. Ministero dell'Università e della Ricerca, year 2006. Area: 01 - Scienze matematiche e informatiche.
Member of ``EPIdemics description and COntrol'' (EPICO), coordinated by professor Mimmo Iannelli. Research activity funded by P.A.T. Provincia Autonoma di Trento, 2005-2008. Research topic: Biomathematics.
Member of ``Equazioni di Kolmogorov'', coordinated by professor Giuseppe Da Prato. Research activity funded by M.I.U.R. Ministero dell'Istruzione, dell'Università e della Ricerca, year 2004. Area: 01 - Scienze matematiche.
Member of ```Equazioni di Kolmogorov'', coordinated by professor Giuseppe Da Prato. Research activity funded by M.I.U.R. Ministero dell'Istruzione, dell'Università e della Ricerca, year 2002. Area: 01 - Scienze matematiche.
Conferences and lectures
Sept. 25, 2017: organizer of the "Workshop in Honour of Luciano Tubaro" at the University of Trento.
May 29-Jun. 4, 2016: organizer of the conference "Stochastic Partial Differential Equations and Applications, 10th International Meeting", joint with A. Debussche (Rennes), F. Flandoli (Pisa), M. Roeckner (Bielefeld); held at the Grand Hotel Bellavista, Levico Terme.
Jan. 6-11, 2014: local organizer of the conference "Stochastic Partial Differential Equations and Applications, 9th International Meeting"; held at the Grand Hotel Bellavista, Levico Terme.
Nov. 26-27, 2012: Organizer of the workshop "Evolution equations: deterministic and stochastic models and applications" at the University of Trento.
Dec. 17-19, 2009: Organizer of the workshop "White workshop on Mathematical Biology" at the University of Trento.
Nov. 24-28, 2008: Organizer of the workshop "Equazioni di Kolmogorov in dimensione infinita e applicazioni" at the Department of Mathematics, University of Trento.
Oct. 2006 -- June 2007: joint organizer, with Enrico Priola (University of Torino), of the X edition of Internet Seminar, on the topic ``From Brownian Motion to Kolmogorov's equations''. We prepared 15 lectures, containing both theory and exercises, spread worldwide on the internet to about 150 partecipants. The final part of the course consisted of a final workshop, (which have taken place at the Grand Hotel Bellavista, Levico Terme, June 10-15, 2007) which was attended byseveral students and other experts.
Lectures (last 5 years)
16 October 2018, "Some notes on Malliavin calculus, surface integrals and integration by parts formulae in infinite dimensional spaces'', Department of Mathematics, University of Ferrara, Italy.
17-20 September 2018, "Optimal control for stochastic Volterra equations driven by L ́evy noise (joint with Fulvia Confortola)'', during the ``SIMAI UMI PMT Joint Meeting", Wroclaw, Poland.
2-6 July 2018, "Some notes on stochastic functional differential equations'', during the ``14th Viennese Conference on Optimal Control and Dynamic Games'', TU Wien, Austria.
25 September 2017, "Stochastic Characteristics'', during the workshop ``Workshop in Honour of Luciano Tubaro'', Trento, Italy.
4-6 September 2017, "A Probabilistic Representation for Solutions to High Order Heat-type Equations'', during the workshop ``Deterministic and stochastic evolution equations'', Parma, Italy.
19-22 June 2017, "Some notes on stochastic functional differential equations'', during the conference ``1st Italian Meeting on Probability and Mathematical Statistics'', Torino, Italy.
21-22 January 2016, "Some notes on stochastic diffusion equations for neurons'', during the conference ``Stochastic Models and Related Topics'', Salerno, Italy.
26-30 January 2015, "A probabilistic representation for solutions of high-order heat-type equations'', during the conference ``Interacting Particle Systems in Thermodynamic Models'', L'Aquila, Italy.
6-11 January 2014, "Equations with boundary noise'', during the conference ``9th International Meeting on Stochastic Partial Differential Equations and Applications'', Levico Terme, Italy.
5-6 December, 2013, "Equations with boundary noise'', during the conference ``Problemi differenziali di evoluzione'', Politecnico di Milano, Italy.
17-19 June 2013, "Evolution equation on networks with stochastic inputs'', during the workshop ``Congas Meeting'', Delft, Netherlands.