Marco Abate
Professor of Geometry - University of Pisa
Marco Abate got a Ph.D. in Mathematics from the Scuola Normale Superiore, Pisa, Italy, in 1988. He is full professor of Geometry since 1994, and from 2001 he teaches in the University of Pisa, Italy, where he is now Vice-Rector for Teaching.
He has visited, giving talks and courses, many universities and research centres in all five continents. He has written nine mathematical books and published about one hundred scientific papers, in some of the most prestigious international mathematical journals.
His main interests include holomorphic dynamical systems, geometric function theory, complex differential geometry, writing (comics and short stories), photography, origami and travelling (having already visited Antarctica his next destination will be the Moon).
What is your teaching philosophy? What would you like to transmit to your students? How do you motivate them?
My goal in teaching is to make the students able to appreciate and internalise the ideas, the techniques and the way of thinking about the specific problems the course is about. I try and make them to become mathematically autonomous, able to understand, use and possibly expand by themselves the ideas discussed in the course.
The techniques that I use to motivate the students depend very much on the kind of students I’m teaching and on the content of the course. In an advanced mathematical course to Ph.D. students in mathematics I try and show how exciting and novel and interesting by itself the topic of the course is; in a basic calculus course for biology students I try and show how mathematical ideas and tools can be useful in real life, in all kind of science and in biology too, and that they can also be, why not, beautiful.
How would you define your field of study? What is your vision about it? Which are the topics you're most passionate about?
My field of study is complex analysis and complex geometry. More specifically I have worked on geometric function theory in several complex variables, on complex differential geometry and on holomorphic dynamical systems.
I like these topics because they are strongly interdisciplinary, relying on ideas and techniques coming from analysis, algebra, geometry, topology, number theory, mathematical physics and so on — and, of course, on ideas and techniques originated specifically in these areas — with a very fruitful and exciting mixing of thoughts and arguments leading to new results and new theories.
How do you expect your experience in IMM to be? Why did you accept to teach for this project?
I strongly believe that mathematics should be shared, and should be shared worldwide, without any boundary of any kind (geographic, political, or gender, religion, ethnicity, etc.).
Furthermore, mathematics (and the way of thinking which is the fundamental basis of mathematics) is becoming more and more important for understanding and living in the contemporary digital world.
For these reasons I have decided to do my part and to help in sharing and teaching mathematics around the world, and in particular in countries less in contact (for whatever reason) with the more recent developments of mathematics. It also is a wonderful way to meet and know different cultures and different ways of living and thinking — and to learn from people I meet.
It is always a two-way exchange, and the things I discover, the people I have conversations with, the experiences I have make me a better mathematicians and, I hope, a better person. So thank you for giving me this opportunity.
Lectures
Fatou flowers and parabolic curves, ICTP (Trieste), 2016
Selected publications
M. Abate, J. Raissy: Backward iteration in strongly convex domains. Adv. Math. 228 (2011), 2837-2854.
M. Abate, F. Tovena: Poincare’-Bendixson theorems for meromorphic connections and holomorphic homogeneous vector fields. J. Diff. Equations, 251 (2011), 2612-2684.
M. Abate, F. Bracci, F. Tovena: Embedding of submanifolds and normal bundles. Adv. Math. 220 (2009), 620-656.
M. Abate, F. Bracci, F. Tovena: Index theorems for holomorphic self-maps. Ann. Math. 159 (2004), 819-864.
M. Abate: The residual index and the dynamics of holomorphic maps tangent to the identity. Duke Math. J. 107 (2001), 173-207.
M. Abate: Diagonalization of non-diagonalizable discrete holomorphic dynamical systems. Amer. J. Math. 122 (2000), 757-781.
M. Abate, P. Heinzner: Holomorphic actions on contractible domains without fixed points. Math. Z. 211 (1992), 547-555.
M. Abate: The Lindelof principle and the angular derivative in strongly convex domains. J. Anal. Math. 154 (1990), 189-228.
M. Abate: Common fixed points of commuting holomorphic maps. Math. Ann. 283 (1989), 645-655.
M. Abate: Horospheres and iterates of holomorphic maps. Math. Z. 198 (1988), 225-238.
Appointments and Awards
- Benedetto Sciarra prize for the year 1985.
- Giuseppe Bartolozzi prize 1991, awarded by the Unione Matematica Italiana.
- 04.10.2008-19.09.2013: coordinator of the National Committee of directors of degree courses in Mathematics
- 01.01.2009-30.06.2015: member of the Scientific Committee of the Unione Matematica Italiana
- 01.02.2013-today: member elected of the Italian National University Council (Consiglio Universitario Nazionale)
- 02.01.2015-05.31.2019: coordinator of the Didactic Committee of the National University Council
- 09.01.2015-01.31.2017: coordinator of the Group of Experts in Evaluation of the Area 01 (Mathematics and Computer Science) for the VQR 2011-2014