VPW: Generalized P-Adic Local Zeta Functions

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This research pursues some questions which are related to and inspired in part by discussions the P.I., Dr. Diane Meuser, has had and and continue to have with Professor Kazhdan and Professor Mazur of Harvard University. Professor Meuser is studying properties of a generalized p-adic local Igusa zeta function. A special case is the "p-adic volume" of a variety which is the integral of the analytic differential w on a compact analytic variety X and it is this case that she has been discussing with Kazhdan and Mazur. A special case she is working on in detail is the generalized zeta function in the case where X is an elliptic curve and w is the unique invariant differential on the elliptic curve. Interactive activities include: involvement with graduate and undergraduate women through a Women in Mathematics organization, and serving as a faculty advisor to a residence hall at Harvard University.