"Convergence polygons for p-adic differential equations"
Event details
| Date | 23.03.2015 |
| Hour | 15:15 › 16:15 |
| Speaker | Prof. Kiran Sridhara Kedlaya (University of California) |
| Location | |
| Category | Conferences - Seminars |
The catalog of special functions in real and complex analysis is largely constructed by solving ordinary differential equations. In number theory, solutions of p-adic
differential equations also play an important role; for instance, as discovered by Dwork in the 1960s, zeta functions of algebraic varieties over finite fields can often be described in terms of solutions of p-adic differential equations.
However, convergence of these solutions is in many respects a subtler question than in the archimedean case. We describe an emerging theory of "Newton polygons" for padic differential equations, which combines over 50 years of prior work with some recent innovations introduced in work of Baldassarri, Poineau, Pulita, and the speaker.
differential equations also play an important role; for instance, as discovered by Dwork in the 1960s, zeta functions of algebraic varieties over finite fields can often be described in terms of solutions of p-adic differential equations.
However, convergence of these solutions is in many respects a subtler question than in the archimedean case. We describe an emerging theory of "Newton polygons" for padic differential equations, which combines over 50 years of prior work with some recent innovations introduced in work of Baldassarri, Poineau, Pulita, and the speaker.
Practical information
- Informed public
- Free
Organizer
- Prof. Ph. Michel
Contact
- Prof. Ph. Michel