A recent trend in geometry and topology is to develop models for geometric spaces. Such models sacrifice a certain degree of precision in the interest of capturing more large-scale structure. In a recent result of Brock with his collaborators, such models were used to classify all 'hyperbolic' three-dimensional spaces of infinite volume. This result solved the long-standing conjecture of W. Thurston that a certain piece of 'mathematical DNA' for a space determines its structure.
Jeffrey Brock's research focuses on low-dimensional geometry and topology, particularly on spaces with hyperbolic geometry (the most prevalent kind of non-Euclidean geometry). His recent joint work with R. Canary and Y. Minsky resulted in a solution to the `ending lamination conjecture' of W. Thurston, giving a kind of classification theorem for hyperbolic 3-dimensional manifolds that are topologically finite in terms of certain pieces of `mathematical DNA' called laminations. He received his undergraduate degree in mathematics at Yale University and his Ph.D. in mathematics from U.C. Berkeley, where he studied under Curtis McMullen. After holding postdoctoral positions at Stanford University and the University of Chicago, he came to Brown as an associate professor. He was awarded the Donald D. Harrington Faculty Fellowship to visit the University of Texas, and has had continuous National Science Foundation support since receiving his Ph.D. He was recently awarded a John S. Guggenheim Foundation Fellowship. He and his wife Sarah live in Barrington, RI, with their two boys Elliot and Sam and their daughter Nora.
On The Web:
Brock's Papers and Preprints
Mathematical Reviews of Brock's Papers
Taming the Hyperbolic Jungle - (D. Mackenzie)
Collaborators at other institutions:
Are you Jeffrey Brock? Click here to edit your research profile.