The 2018 Mathematics Research Communities will have five conferences in the summer of 2018. Below is one of the conferences. The other four conferences are separately listed on this site.
Week 2b: June 10 – 16, 2018 - Number Theoretic Methods in Hyperbolic Geometry
Organizers:
Benjamin Linowitz (Oberlin College)
David Ben McReynolds (Purdue University)
Matthew Stover (Temple University)
The canonical example of an arithmetic lattice is the modular group PSL(2, Z), whose deep connections with geometry and number theory (among many other areas) have been of profound interest for well over a century. Geometric invariants of the modular surface—the quotient of the complex upper half-plane by PSL(2, Z)—are typically paired with objects of equally deep interest in number theory. For example, its volume in its metric of constant curvature -1 is naturally related to a special value of the Riemann zeta function, and the lengths of its closed geodesics are intimately related to class numbers and regulators of real quadratic fields. More generally, rigidity phenomena (Weil, Mostow, etc.) imply that similar connections exist between number theory and the geometry of higher-dimensional hyperbolic manifolds.
The primary focus during the workshop will be to introduce the participants to problems at the interface of geometry and number theory that are currently attracting significant interest, and provide them with the tools necessary to make progress on some open questions. General areas to be discussed include the Laplace eigenvalue spectra and geodesic length spectra of hyperbolic 2- and 3-manifolds, growth of the systole of a hyperbolic manifold, and the ‘realization problem’ for trace fields of hyperbolic 3-manifolds. The number theoretic techniques that we will use to address these problems make use of quaternion algebras over number fields, Mahler measures of algebraic integers, and classical results from multiplicative number theory. The ultimate goal of this workshop is to start a dialogue between young mathematicians from different backgrounds that will lead to new and long-lasting collaborations between fields that have a great deal to say to one another. No background in either subject is expected.
About the Mathematics Research Communities:
Mathematics Research Communities (MRC), a program of the American Mathematical Society (AMS), nurtures early-career mathematicians--those who are close to finishing their doctorates or have recently finished--and provides them with opportunities to build social and collaborative networks through which they can inspire and sustain each other in their work.
The structured program is designed to engage and guide all participants as they start their careers. For each topic,the program includes a one-week summer conference; a Special Session at the next Joint Mathematics Meetings; and a longitudinal study of early career mathematicians.
The summer conferences of the MRC are held in the serene setting of the Whispering Pines Conference Center, West Greenwich, Rhode Island, where participants can enjoy the natural beauty and a collegial atmosphere. Those accepted into this program will receive support (full room and board at the Whispering Pines Conference Center and full or partial airfare) for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2019.
ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs or within one to five years after receipt of their PhDs are welcome to apply. The MRC program is open to individuals who are U.S. citizens as well as to those who are affiliated with U.S. institutions. A few international participants may be accepted. Women and underrepresented minorities are especially encouraged to apply. All participants are expected to be active in the full MRC program.
Please contact Steven Ferrucci at ams-mrc@ams.org if you have additional questions.
American Mathematical Society
Date Posted: Jul 18, 2017
Deadline: Feb 15, 2018