The negative Pell equation and class groups.
Seminar in Mathematics
Abstract:
Pell's equation has a rich and long history going back to the ancient Greeks. Refining an earlier conjecture of Nagell from the 1930s, Stevenhagen made a fundamental conjecture about the negative Pell equation 30 years ago. I will discuss my recent proof, in joint work with Carlo Pagano, of this conjecture. A central object in the proof is the so-called class group, which plays a prominent role in modern number theory. We give an introduction to class groups, explain its central role in modern number theory and explain its connection to the negative Pell equation.
Abstract:
Pell's equation has a rich and long history going back to the ancient Greeks. Refining an earlier conjecture of Nagell from the 1930s, Stevenhagen made a fundamental conjecture about the negative Pell equation 30 years ago. I will discuss my recent proof, in joint work with Carlo Pagano, of this conjecture. A central object in the proof is the so-called class group, which plays a prominent role in modern number theory. We give an introduction to class groups, explain its central role in modern number theory and explain its connection to the negative Pell equation.
Practical information
- Informed public
- Free
- This event is internal
Organizer
- Institute of Mathematics
Contact
- Prof. Maryna Viazovska, Director