AWM Piedmont-Triad Conference

Please join us at Wake Forest University on Saturday, March 2nd


Purpose

The AWM Piedmont-Triad conference is a student-led initiative that aims to bring local AWM chapters together to provide networking opportunities for graduate and undergraduates students. This one-day conference will allow students to promote their research, to network among professors and peers, and to enhance their professional and academic skills through informational panels. By participating in this conference, students will contribute to creating a strong sense of community among women in Mathematics. Moreover, by bringing different chapters and communities of students together, we will be able to empower and encourage women in Mathematics. We wish for our attendees to leave feeling supported within the Mathematics community and encouraged to continue to pursue their career in Math.

keynote speaker

Dr. Lillian Pierce

From Gauss to today: class numbers and class groups of number fields

Abstract:

Imagine an hourglass: within one bulb, we picture analytic number theory; within the other bulb, algebraic number theory. Pincered in between is the class number. As we imagine this hourglass, we visualize information trickling back and forth between the two fields, passing via the class number. And yet the constriction of the pinched neck suggests a certain inaccessibility...

Each number field has an associated class number, which measures the cardinality of the field's class group---a finite abelian group that encodes information about how arithmetic behaves within the field. It is natural to think of number fields in families---for example, all number fields of a fixed degree. Correspondingly, we can ask about the distribution of the class number, or of the class group, as the field varies over a family. Tantalizingly precise conjectures have been formulated, but remain out of reach.

We will describe a diverse array of work on these questions, starting 200 years ago with work of Gauss. True to the hourglass shape we first envisioned, it turns out that this question is closely connected to deep open questions on both sides, including counting number fields, and the Generalized Riemann Hypothesis.



tentative schedule

  • 9am - 10am - Registration/Coffee

  • 10am - 11am - Keynote Speaker

  • 11am - 12pm Student Presentations

  • 12pm - 1pm Lunch

  • 1pm - 2pm - Career Panel

  • 2pm - 2:30pm - Coffee Break

  • 2:30pm - 3:30pm - Graduate Panel