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 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.
More recently, he has worked un understanding applications of geometry and topology to the structure of massive and complex data sets, and the implications of the increasing use of algorithms in science and society.
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. In 2008 he was 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.
|Brock, Jeffrey, Bromberg, Kenneth, Canary, Richard, Lecuire, Cyril Convergence and divergence of Kleinian surface groups. Journal of Topology. 2015; 8 (3) : 811-841.|
|Brock, Jeffrey F, Dunfield, Nathan M Injectivity radii of hyperbolic integer homology 3–spheres. Geom. Topol.. 2015; 19 (1) : 497-523.|
|Brock, Jeffrey F, Bromberg, Kenneth W, Canary, Richard D, Minsky, Yair N Convergence properties of end invariants. Geom. Topol.. 2013; 17 (5) : 2877-2922.|
|Brock, Jeffrey, Canary, Richard, Minsky, Yair The classification of Kleinian surface groups, II: The Ending Lamination Conjecture. Ann. Math.. 2012; 176 (3) : 1-149.|
|Brock, Jeffrey, Masur, Howard, Minsky, Yair Asymptotics of Weil–Petersson Geodesics II: Bounded Geometry and Unbounded Entropy. Geom. Funct. Anal.. 2011; 21 (4) : 820-850.|
|Brock, J., Bromberg, K. Geometric inflexibility and 3-manifolds that fiber over the circle. Journal of Topology. 2011; 4 (1) : 1-38.|
|Brock, Jeffrey F, Bromberg, Kenneth W, Canary, Richard D, Minsky, Yair N Local topology in deformation spaces of hyperbolic 3–manifolds. Geom. Topol.. 2011; 15 (2) : 1169-1224.|
|Brock, Jeffrey, Masur, Howard, Minsky, Yair Asymptotics of Weil–Petersson Geodesics I: Ending Laminations, Recurrence, and Flows. Geom. Funct. Anal.. 2009; 19 (5) : 1229-1257.|
|Brock, Jeffrey, Masur, Howard Coarse and synthetic Weil–Petersson geometry: quasi-flats, geodesics and relative hyperbolicity. Geom. Topol.. 2008; 12 (4) : 2453-2495.|
|Brock, J., Souto, J. Algebraic limits of geometrically finite manifolds are tame. Geom. Funct. Anal.. 2006; 16 (1) : 1-39.|
|Brock, Jeffrey, Farb, Benson Curvature and rank of Teichmuller space. American Journal of Mathematics. 2006; 128 (1) : 1-22.|
|Brock, Jeffrey F. The Weil–Petersson Visual Sphere. Geometriae Dedicata. 2005; 115 (1) : 1-18.|
|Brock, Jeffrey F., Bromberg, Kenneth W. On the density of geometrically finite Kleinian groups. Acta Mathematica. 2004; 192 (1) : 33-93.|
Asymptotics of Weil-Petersson geodesics I: ending laminations, recurrence and flows. (With Howard Masur and Yair Minsky). Geom. & Funct. Anal., 19 (2010), pp. 1229-1257.
Coarse and synthetic Weil-Petersson geometry: quasi-flats, geodesics, and relative hyperbolicity. (With Howard Masur). Geometry and Topology, 12 (2008), pp. 2453-2495.
Curvature and rank of Teichmüller space (with B. Farb). Amer. J. Math. 128 (2006), pp. 1-22.
Algebraic limits of geometrically finite manifolds are tame (with J. Souto). Geom. and Funct. Anal. 16 (2006)
On the density of geometrically finite Kleinian groups (with K. Bromberg). Acta Mathematica 192 (2004), pp. 33-93.
The classification of Kleinian surface groups II: the Ending Lamination Conjecture (with R. Canary and Y. Minsky, 2004). Submitted for publication.
The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores. J. Amer. Math. Soc. 16 (2003), pp. 495-535
Weil-Petersson translation distance and volumes of mapping tori. Comm. Anal. Geom. 11 (2003), pp. 987-999.
Tameness on the boundary and Ahlfors' measure conjecture (with K. Bromberg, R. Evans, and J. Souto). Publ. Math. I.H.É.S. 98 (2003), pp. 145-166
Pants decompositions and the Weil-Petersson metric. In Complex Manifolds and Hyperbolic Geometry, American Mathematical Society, Providence, RI, 2002, pp. 27-40.
Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds. Duke Math. J., 106 (2001), pp. 527-552.
Iteration of mapping classes and limits of hyperbolic 3-manifolds. Invent. Math. 143 (2001), pp. 523-570.
Continuity of Thurston's length function. Geom. & Funct. Anal. 10 (2000), pp. 741-797.
The standard double soap bubble in R2 uniquely minimizes perimeter (with F. Morgan et. al.). Pacific Journal of Mathematics, 159 (1993), no. 1, pp. 47-59.
|Szegö Assistant Professor||Stanford University, Mathematics||1997-2000||Palo Alto, CA, USA|
|Merck, Derek||Assistant Professor of Diagnostic Imaging (Research), Assistant Professor of Engineering (Research), Assistant Professor of Radiation Oncology (Research)|
|Merck, Lisa||Assistant Professor of Emergency Medicine, Assistant Professor of Diagnostic Imaging, Assistant Professor of Neurosurgery|
|Sandstede, Bjorn||Royce Family Professor of Teaching Excellence, Professor of Applied Mathematics|
|MATH 0060 - Analytic Geometry and Calculus|
|MATH 2420 - Topology|
|MATH 2710Q - Punctured Torus Groups|