2026.09.10 Colloquia Seminars
| Speaker |
Prof. Joris van der Hoeven, CNRS, Ecole Polytechnique, France |
| Title |
Asymptotic differential algebra |
| Time |
2026.09.15 10:00-11:00 |
| Venue |
N219 |
| Abstract |
Asymptotic differential algebra aims at studying the asymptotic behavior of solutions to differential equations using techniques from differential algebra and valuation theory.
One central concept is that of an H-field: a differential field with an ordering that satisfies natural compatibility conditions with respect to the derivation. Natural examples of H-fields are
Hardy fields and the field of transseries. It turns out that both the field of transseries and maximal Hardy fields are "H-closed" and their first order theory is now well understood.
In our talk, we will survey these and some other results, which are the fruits of a long collaboration with Matthias Aschenbrenner and Lou van den Dries. |
| Biography |
Joris van der Hoeven is a Dutch mathematician and computer scientist. He is currently a Research Director at the French National Centre for Scientific Research and also heads the Symbolic Computation team in the Department of Computer Science at École Polytechnique in Paris. His main research areas are differential algebra, asymptotic analysis and computer algebra, especially transseries (a generalization of formal power series) and their applications in the asymptotic solutions of nonlinear differential equations. In 2018, he was invited to give a 45-minute invited talk at the International Congress of Mathematicians. In 2019, he and David Harvey discovered the fastest integer multiplication algorithm, and this achievement was published in the Annals of Mathematics in 2021. He has received the Karp Award and the N.G. de Bruijn Award. In terms of software development, he is a major developer of GNU TeXmacs (a free scientific editing platform) and Mathe Magix (a free computer algebra and analysis system). | |
