This workshop, sponsered by AIM and the NSF, will focus on the connection between random matrix theory and number theory, in the context of moments of the derivative of characteristic polynomials of matrices from the classical compact groups, and of the analogous L-functions.

These inquiries become particularly intricate when the exponent on the derivative is non-integer or when the evaluation point of the characteristic polynomial approaches the unit circle at varying rates. Exploring these statistics will improve our understanding of the distribution of zeros, and the value distribution of L-functions.

Possible topics, both for characteristic polynomials and L-functions:

• Moments of the derivative
• Distribution of zeros of the derivative
• Higher derivatives
• Related differential equations

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org