Some recent work was originally motivated by a connection between Apollonian circle packings and the structure of imaginary quadratic fields in turn coming out of a connection to abelian sandpiles! A Schmidt arrangement named for Asmus Schmidt is the orbit of the extended real line in the extended complex plane under the Mobius action of the Bianchi group PSL 2 O K here, O K is the ring of integers of the imaginary quadratic field. The resulting fractal of nested circles is an analogue to the Farey subdivision of the real line into nested intervals. It has interesting connections to the arithmetic of the field: for example, it is connected if and only if O K is Euclidean.
Melody is an accomplished violinist who has performance on national public television live from the Lincoln Center in New York with Itzhak Perlman. She plans to study mathematics at Cambridge University in then return to the United States to pursue a Ph. Both were cited for their course work and research. Click here for the article on the winner and runner-up of the Morgan Prize.
Adult stem cells reside in all tissues, where they replenish dying cells and repair wounds. Using mammalian skin as a model, Fuchs studies the remarkable properties of tissue stem cells, and how they know which tasks to perform and when. She explores how stem cells sense and communicate with other cells in their environment. Aiming at advancing therapeutics, she dissects how communication networks malfunction in inflammation, aging, and cancers.