Jeffrey Farlowe Brock (born June 14, 1970 in Bronxville, New York) is an American mathematician, working in low-dimensional

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

and

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. He is known for his contributions to the understanding of

hyperbolic 3-manifold In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1. It ...

s and the geometry of

Teichmüller space In mathematics, the Teichmüller space T(S) of a (real) topological (or differential) surface S, is a space that parametrizes complex structures on S up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmüll ...

s. Since July 2018, Brock has been a Professor of Mathematics at

Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

, and in January 2019 he became the first FAS (Faculty of Arts and Sciences) dean of science at Yale. In July 2019, he was additionally appointed Dean of the

Yale School of Engineering & Applied Science The Yale School of Engineering & Applied Science is the engineering school of Yale University. When the first professor of civil engineering was hired in 1852, a Yale School of Engineering was established within the Yale Scientific School, and ...

. Before joining

Yale Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wor ...

, he was a professor at Brown University, and also founding director of the Data Science Initiative at Brown University.

Biography

Brock obtained a BA (with distinction in Mathematics) from

in 1992. He completed a Ph.D. in mathematics from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

in 1997, under the supervision of

Curtis T. McMullen Curtis Tracy McMullen (born May 21, 1958) is an American mathematician who is the Cabot Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüll ...

. Brock then held positions as (NSF-funded) Szego Assistant Professor at Stanford University (1997–2000), assistant professor at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

(2000–2003), and Donald D. Harrington Faculty Fellow at the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,07 ...

(2003–2004). He became associate professor with tenure at Brown University in 2004, and a full professor in 2007. He was chair of the Mathematics Department from 2013 to 2017. Brock has been associate director of ICERM since 2013. Previously, he had been deputy director between 2010 and 2013. Since July 2018, Brock has been a Professor of Mathematics at

, and in January 2019 he became the first FAS (Faculty of Arts and Sciences) dean of science at Yale. In July 2019, he was additionally appointed Dean of the

. Brock is also an accomplished

jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a m ...

musician. He was the founding bassist of the Vijay Iyer Trio, led by the acclaimed jazz pianist

Vijay Iyer Vijay Iyer (born October 26, 1971) is an American composer, pianist, bandleader, producer and writer based in New York City. ''The New York Times'' has called him a "social conscience, multimedia collaborator, system builder, rhapsodist, histori ...

. He is married and has three children.

Research

Jeffrey Brock's research focuses on

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

and geometry, particularly on spaces with

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P ...

or negative curvature. His joint work with

Richard Canary Richard Douglas Canary (born in 1962) is an American mathematician working mainly on low-dimensional topology. He is a professor at the University of Michigan. Canary obtained his Ph.D. from Princeton University in 1989 under the supervision of W ...

and

Yair Minsky Yair Nathan Minsky (born in 1962) is an Israeli-American mathematician whose research concerns three-dimensional topology, differential geometry, group theory and holomorphic dynamics. He is a professor at Yale University. He is known for having ...

resulted in a solution to the "Ending Lamination Conjecture" of

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thursto ...

, culminating in the geometric classification theorem for (topologically finite) hyperbolic 3-manifolds in terms of their fundamental group and the structure of their ends. More recently, he has worked to understand applications of

and

to the structure of massive and complex data sets and the risks and implications of the increasing use of 'black box' algorithms in science and society.

Honors and awards

* Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 2017. * Simons Fellowship (declined), 2016. *

John Simon Guggenheim John Simon Guggenheim (December 30, 1867 – November 2, 1941) was an American businessman, politician and philanthropist. Life Born in Philadelphia, Pennsylvania of Jewish descent, Simon Guggenheim was the son of Meyer Guggenheim and Barbara G ...

Fellow, 2008. * Donald D. Harrington Faculty Fellow,

, 2003–2004. *

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National ...

Postdoctoral Fellow, Stanford University, 1997–2000. * Alfred P. Sloan Doctoral Dissertation Fellow, U.C. Berkeley, 1996–1997. * Outstanding Graduate Student Instructor Award, U.C. Berkeley, 1996. *

Graduate Fellow, U.C. Berkeley, 1993–1996. * Stanley and DeForest Mathematics Prizes,

, 1991 and 1992.

Selected invited talks

* Geometric Topology in Low Dimensions (

University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020� ...

), 2017. * Geometry, Topology and Dynamics of Moduli Spaces ( National University of Singapore), 2016. * Classical and quantum hyperbolic geometry and topology (

Orsay Orsay () is a commune in the Essonne department in Île-de-France in northern France. It is located in the southwestern suburbs of Paris, France, from the centre of Paris. A fortified location of the Chevreuse valley since the 8th centur ...

), 2015. * Hyperbolic Geometry and Minimal Surfaces (IMPA), 2015. * Hyperbolic Geometry and Geometric Group Theory (

Tokyo Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and List of cities in Japan, largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, ...

), 2014.

Selected publications

* (with Nathan Dunfield) "Norms on the cohomology of hyperbolic 3-manifolds", ''Invent. Math.'' 210 (2017), no. 2, 531–558. * (with

, Hossein Namazi and Juan Souto), "Bounded combinatorics and uniform models for hyperbolic 3-manifolds." ''J. Topol.'' 9 (2016), no. 2, 451–501. * (with

and

) "The classification of Kleinian surface groups, II: The ending lamination conjecture." ''Ann. of Math. (2)'' 176 (2012), no. 1, 1–149. * (with

Benson Farb Benson Stanley Farb (born October 25, 1967) is an American mathematician at the University of Chicago. His research fields include geometric group theory and low-dimensional topology. Early life A native of Norristown, Pennsylvania, Farb earned ...

) "Curvature and rank of Teichmüller space." ''Amer. J. Math.'' 128 (2006), no. 1, 1–22. * (with Kenneth Bromberg) "On the density of geometrically finite Kleinian groups." ''Acta Math.'' 192 (2004), no. 1, 33–93. * "The Weil–Petersson metric and volumes of 3-dimensional hyperbolic convex cores." ''J. Amer. Math. Soc.'' 16 (2003), no. 3, 495–535. * "Iteration of mapping classes and limits of hyperbolic 3-manifolds." ''Invent. Math.'' 143 (2001), no. 3, 523–570. * "Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds." ''Duke Math. J.'' 106 (2001), no. 3, 527–552.

References

{{DEFAULTSORT:Brock, Jeffrey 1970 births Living people 20th-century American mathematicians Brown University faculty Yale College alumni UC Berkeley College of Letters and Science alumni Fellows of the American Mathematical Society 21st-century American mathematicians