Michelle Manes, Ph.D. - US grants

ABSTRACT FOR THE NSF PROPOSAL GK-12: SUPER-M
PI: MONIQUE CHYBA
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF HAWAII

The School and University Partnership for Educational Renewal in Mathematics project (SUPER-M) will bring the knowledge and expertise of research mathematicians into K?12 classrooms, making an important contribution to improving school mathematics in Hawaii. The project will provide K?12 students with an enriching learning environment where mathematics is interesting and dynamic. The project will also contribute to the formation of a cadre of highly qualified teachers, bringing new mathematics expertise to schools throughout the State of Hawaii and helping to sustain the program. Over five years, 38 Fellows will be selected to partner with K?12 schools on Oahu, the Big Island and Maui. Fellows will take a semester long course on ?Issues in K?12 Mathematics Education,? learning about best practices in the design of professional development courses for teachers. Fellows will design and lead workshops for K?12 teachers arising from their areas of research. Upon completion of the course, Fellows will partner with a cooperating teacher, creating and leading mathematics activities for K?12 students. In this way, SUPER-M will provide K?12 students with a solid grounding in mathematics, increasing their opportunities to pursue careers in STEM disciplines. SUPER-M will serve under-represented populations by placing a special emphasis on recruiting Native Hawaiian and women Fellows. SUPER-M expects to profoundly impact the community at large through special events such as summer camps, public outreach events, and family math days.

In her thesis, the PI pioneered the study of the dynamics of rational maps having a nontrivial automorphism, that is maps for which conjugating by some nontrivial linear fractional transformation preserves not just the dynamics of the map but the map itself (its coefficients when written as a rational function, say). Since most rational maps have no automorphisms, this might be considered a dynamical version of complex multiplication. The intellectual merit of the proposed project lies in the PI's plan to create a theory of dynamical complex multiplication, with the goal of developing enough machinery that a proof of a Conjecture of Morton and Silverman for this family of maps is within reach.

Broader impacts of the work emerge from education and outreach activities, with a focus on gender equity issues and supporting women in research mathematics. Proposed activities include:
(1) mentoring women in mathematics at the University of Hawaii and thus broadening participation of underrepresented groups;
(2) establishing the Math Teachers' Circle of Hawaii; and
(3) continuing the University of Hawaii Mathematics Department's Distinguished Lecture Series.

The workshop Women in Numbers 4 will take place from August 14 to 18, 2017 at the Banff International Research Station. This workshop is the fourth in a series of research collaboration conferences for women in number theory. The format differs from a typical conference in that much of the time is reserved for collaboration in small groups. The specific goals of this conference are: produce significant and impactful research in number theory, broaden the research programs of women in number theory, especially of those who are pre-tenure, train female graduate students and postdocs by providing experience with collaborative research and the publication process, strengthen and extend a collaborative research network of women in number theory and related fields, enable women who are faculty at small colleges to participate actively in research activities, and highlight research activities of women in number theory.

This workshop will support the continued development of the community of women in number theory by bringing together researchers at various stages of their careers (from graduate students to senior mathematicians) for research collaboration and mentoring. The scientific focus of the workshop is on cutting-edge topics in number theory, including Apollonian circle packings, arithmetic dynamics, the Chabauty-Coleman method, computational aspects of supersingular elliptic curves, mock modular forms, Newton polygons on the Torelli locus, sieve techniques in analytic number theory, supersingular isogeny graphs in cryptography, and torsion subgroups on elliptic
curves. More information is available at http://www.math.washington.edu/~bviray/WIN4.html.