Gabriele Benedetti
University of Amsterdam
From 2006 to 2011 I was an undergraduate student at Scuola Normale Superiore and at the University of Pisa (Italy).
I got my PhD at the University of Cambridge (UK) under the supervision of Gabriel P. Paternain with the thesis "The contact property for magnetic flows on surfaces".
After that, I held postdoc positions at the University of Münster and Leipzig (Germany) and at MSRI in Berkeley (USA).
Since April 2018 I have been Junior professor at the University of Heidelberg (Germany) and from September 2021 I will take up a position at the University of Amsterdam.
How would you define your field of study? What is your vision about it? Which are the topics you're most passionate about?
I study the time evolution of physical systems defined on curved spaces, or, in more precise terms, the dynamics of Hamiltonian systems on symplectic manifolds. Examples of such systems are ubiquitous in nature: from the orbits of planets in our galaxy, to the trajectories of ionized particles in the atmosphere, passing through the motions of three-dimensional rigid bodies.
My ultimate goal is to discover relationships between the shape (also known as topology) of the space and dynamical properties of the physical system (chaotic or stable motions). I am very much interested in analyzing this general circle of ideas in the concrete and fascinating model given by the motion of a charged particle on a surface under the effect of a magnetic field.
How do you expect your experience in IMM to be? Why did you accept to teach for this project?
I am really looking forward to holding the mini-course in Lahore together with Prof. Alberto Abbondandolo. We will be in strict contact with a small number of motivated students for two weeks. Thus, I expect that there will be an active and intense interaction in class. One of the main challenges will be to tailor the mini-course according to the background of the students so that they can make the most out of it.
I was highly motivated to embark in this project since teaching is one of the cornerstones of my life at university. Furthermore, I believe that establishing a network between people from different countries sharing the same passion for mathematics is a unique opportunity for the spread of knowledge and for the enrichment of the people involved in the project.
From 2006 to 2011 I was an undergraduate student at Scuola Normale Superiore and at the University of Pisa (Italy).
I got my PhD at the University of Cambridge (UK) under the supervision of Gabriel P. Paternain with the thesis "The contact property for magnetic flows on surfaces".
After that, I held postdoc positions at the University of Münster and Leipzig (Germany) and at MSRI in Berkeley (USA).
Since April 2018 I have been Junior professor at the University of Heidelberg (Germany).
What is your teaching philosophy? What would you like to transmit to your students? How do you motivate them?
In my teaching, the role of clarifying examples is extremely significant. I discuss first with the students how things work in a concrete case before venturing in proving a general statement. I also love to give the audience some notions about the origin of the questions that we study today in contemporary mathematics. To motivate students to learn a new theory, I first confront them with a particular problem that the known theory cannot solve and then see how the new theory enables us to give an answer. For instance, difficulties in treating limits with the Riemann integral are surpassed by introducing the Lebesgue integral.
Do you have one of two favorite quotes you would like to share and/or a personal "motto"?
"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" Paul Halmos
Lectures
Zoll magnetic systems on surfaces, VIII Workshop on Conservative Dynamics and Symplectic Geometry, IMPA (Rio de Janeiro), 2019
Workshop on Conservative Dynamics and Symplectic Geometry, IMPA (Rio de Janeiro), 2017
Selected Publications
On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus, with L. Asselle, Math. Z. 286, no. 3 - 4, 843 - 859, 2017.
Magnetic Katok examples on the two-sphere, Bull. Lond. Math. Soc. 48, no. 5, 855 - 865, 2016.
The contact property for symplectic magnetic fields on the 2-sphere, Ergodic Theory Dynam. Systems 36, no. 3, 682--713, 2016.
On the existence of periodic orbits for magnetic systems on the two-sphere, with K. Zehmisch, J. Mod. Dyn. 9, 141 - 146, 2015.
Infinitely many periodic orbits of non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level, with L. Asselle, Calc. Var. Partial Differential Equations 54, no. 2, 1525--1545, 2015.