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 scenic mountain setting of the Snowbird Resort, Utah, 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 Snowbird Resort and up to $650 in airfare) for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2018.

ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs, or up 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.

For any program, fellowship, prize or award that has a maximum period of eligibility after receipt of the doctoral degree, the selection committee may use discretion in making exceptions to the limit on eligibility for candidates whose careers have been interrupted for reasons such as family or health. Therefore, an applicant who has had to slow down or temporarily stop his or her career for personal reasons may request to be considered for an extension in the amount of time after the PhD degree. Please send exception requests to ams-mrc@ams.org.

REQUIREMENTS: Completed on-line application form One (1) reference letter submitted by a professor or supervisor who knows the applicant and can address how the applicant will benefit from, and contribute to, the MRC program.

Individuals who can cover their MRC participation costs from other sources of funding should contact AMS Senior Program Coordinator Steven Ferrucci at sxf@ams.org for instructions on how to apply.

Note that all applicants will be notified of their status by May 1, 2017.

Week 3: June 19 – 24, 2017-- Dynamical Systems: Smooth, Symbolic, and Measurable

Organizers:
Jon Chaika, University of Utah
Vaughn Climenhaga, University of Houston
Boris Hasselblatt, Tufts University
Bryna Kra, Northwestern University
Daniel Thompson, The Ohio State University

Smooth dynamics, symbolic dynamics, and measurable dynamics are different branches of a single subject and each branch has its own questions and techniques. Many fundamental advances in the field have been made by understanding the relations among these branches, leading to developments such as symbolic models for smooth systems, topological models for measurable systems, and thermodynamic formalism. This rich interplay among the smooth, symbolic, and measurable theory is the focus of this workshop.

The workshop will explore questions of contemporary interest, including characterization of the space of invariant measures, statistical properties of distinguished invariant measures, and symbolic models for smooth systems. Classical theory tells us that in the best-understood settings, one obtains different answers in the high-complexity (hyperbolic) case from those one does in the low-complexity (zero entropy) case. We will describe this general dichotomy and focus on specific problems where the classical phenomena may or may not continue to hold, including (1) non-uniformly hyperbolic systems, (2) geodesic flow on manifolds beyond the compact negative curvature case, (3) commuting maps, and (4) flat surfaces and interval exchange transformations.