| 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. Those accepted into this program will receive a flat rate transportation allowance for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2021. ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs, and up to five years after receipt of their PhDs, are welcome to apply. Most of those supported by NSF funds to participate in the MRC program will be US-based, that is, employed by or a full-time student at a US institution at the time of the MRC summer conference. However, the terms of the grant allow for a limited number of individuals who are not US-based. A few international participants may be accepted. Depending on space and other factors, a small number of participant slots may be available for self-funders. Applicants wishing to be considered as possible self-funded participants should email ams-mrc@ams.org at the time they apply and state that intention. Self-funders must satisfy the same criteria for admission as those who receive grant support. Individuals who have once previously been an MRC participant will be considered for admission, and their applications must include a rationale for repeating. Please note that individuals cannot participate in the MRC program more than twice. Applications from individuals who have twice been MRC participants will not be considered. 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:
Applications will close at 11:59 p.m. Eastern Time on Saturday, February 15, 2020. Note that all applicants will be notified of their status by May 1, 2020. Week 3: June 14 – 20, 2020-- Finding Needles in Haystacks: Approaches to Inverse Problems using Combinatorics and Linear Algebra
Organizers: Inverse eigenvalue problems encompass many important problems in science and engineering and often can be reduced to the mathematical question of whether or not there is a matrix with a prescribed structure whose invariants (eigenvalues) have a desired property. Progress has been slow because particular inverse eigenvalue problems can be difficult—much like finding a needle in a haystack. The inverse eigenvalue problem of a graph asks us to determine the possible eigenvalues of a real symmetric matrix with the nonzero off-diagonal pattern described by the edges of a graph. Recently developed tools have accelerated progress and opened up new lines of inquiry by giving linear algebraic and combinatorial criteria for the existence of a “nice” needle in a given haystack that guarantees the existence of a needle in each nearby haystack. The inverse eigenvalue problem of a graph has also stimulated work on zero forcing, a graph coloring process that has applications to graph searching, monitoring electric power networks, and control of quantum systems, in addition to serving as an upper bound for maximum eigenvalue multiplicity. Recent work on zero forcing has also included investigations of propagation time (the minimum time needed to color the entire graph starting with a set of minimum possible size, and throttling (minimizing the sum of the resources needed to and the time needed to accomplish a task). This MRC conference will provide participants with the expertise in needed to launch productive research projects in these new lines of inquiry. We expect that a participant will have expertise linear algebra or graph theory, but need not have worked in both. We look forward to bringing together advanced graduate students, postdocs, and junior faculty from a mix of backgrounds.
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