Geometry & Topology

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Mark Behrens http://math.mit.edu/~mbehrens/ Algebraic topology, homotopy theory, homotopy groups of spheres, Goodwillie calculus	Martin Bridson http://www.maths.ox.ac.uk/~bridson/ Geometric group theory, low-dimensional topology, geometry in the presence of non-positive curvature
Jim Bryan http://www.math.ubc.ca/~jbryan/ Algebraic geometry, Gromov–Witten theory, moduli spaces, gauge theory	Dmitri Burago Metric geometry, Riemannian and Finsler geometry, differential geometry, dynamical systems
Danny Calegari http://www.its.caltech.edu/~dannyc/ Geometry, topology and dynamics in low dimensions; foliations/laminations; extremal problems in topology and geometric group theory	Ralph Cohen http://math.stanford.edu/~ralph/ Algebraic topological aspects of moduli spaces of Riemann surfaces, holomorphic mapping spaces holomorphic bundles, gauge theoretic moduli spaces; loop spaces, loop groups, and topological aspects of string theory; K–theory, homotopy theory
Tobias Colding Differential geometry, geometric analysis and PDEs.	Simon Donaldson http://www.ma.ic.ac.uk/~skdona/ 4-dimensional topology and geometry
Bill Dwyer http://www.nd.edu/~wgd/ Algebraic topology, stable and unstable homotopy theory, algebraic K–theory	Yasha Eliashberg Symplectic geometry and topology, several complex variables, singularities of smooth mappings
Benson Farb http://zaphod.uchicago.edu/~farb/ Discrete subgroups of Lie groups, geometric group theory, large-scale geometry, nonpositive curvature, mapping class groups, actions of infinite groups on manifolds	Steve Ferry http://www.math.rutgers.edu/~sferry/ High-dimensional geometric topology and related areas of differential geometry
Ron Fintushel http://www.mth.msu.edu/~ronfint/ Topology/geometry in dimension 4, gauge theory	Mike Freedman http://stationq.cnsi.ucsb.edu/~freedman/ Geometry
David Gabai http://www.math.princeton.edu/facultypapers/Gabai/index.html Low dimensional topology, knot theory, hyperbolic geometry, foliation and lamination theory	Paul Goerss http://www.math.northwestern.edu/~pgoerss/ Algebraic topology, homotopy theory, stable homotopy theory
Lothar Göttsche http://users.ictp.trieste.it/~gottsche/ Algebraic geometry, moduli spaces, Gromov–Witten invariants, enumerative geometry, gauge theory	Cameron Gordon http://www.ma.utexas.edu/text/webpages/gordon.html Knot theory, 3–dimensional topology
Jesper Grodal http://www.math.ku.dk/~jg/ Algebraic topology, homotopy theory, topology of Lie groups and homotopical group theory	Vaughan Jones http://math.berkeley.edu/~vfr/ Knots and braids, quantum invariants of 3–manifolds, loop groups and their representations
Robion Kirby http://math.berkeley.edu/~kirby/ Geometric and low dimensional topology, topology of 4–manifolds, topological quantum field theory	Frances Kirwan http://www.maths.ox.ac.uk/contact/details/kirwan Symplectic and algebraic geometry, group actions on symplectic manifolds and algebraic varieties, geometric invariant theory and moduli spaces
John Lott http://math.berkeley.edu/~lott Differential geometry, geometric analysis, index theory	Haynes Miller http://www-math.mit.edu/~hrm/ Homotopy theory, relations between elliptic curves and homotopy theory, the Steenrod algebra, the homotopy theory of Lie groups
Shigeyuki Morita Low dimensional topology, mapping class groups of surfaces, moduli space of curves, diffeomorphism groups	John Morgan http://www.math.columbia.edu/fac-bios/morgan/faculty.html Poincaré conjecture, geometric analysis, low dimensional topology
Tom Mrowka http://www-math.mit.edu/~mrowka/ Low dimensional topology, geometric PDEs	Walter Neumann http://www.math.columbia.edu/~neumann/ Topology/geometry in low dimensions, geometric structures, geometric group theory, topology of algebraic varieties
Jean-Pierre Otal Low-dimensional topology, hyperbolic manifolds, geodesic flows	Peter Ozsváth http://www.math.princeton.edu/~petero/ Gauge theory, low-dimensional topology, symplectic geometry
Leonid Polterovich http://www.math.tau.ac.il/~polterov/ Symplectic topology, geometric and topological aspects of dynamical systems	Colin Rourke http://www.maths.warwick.ac.uk/~cpr/ PL topology, low-dimensional topology, diagrams in group theory
Ron Stern http://www.math.uci.edu/~rstern/ Topology and (complex, symplectic and differential) geometry in four and fewer dimensions	Peter Teichner http://web.me.com/teichner/Math/Home.html Mathematical aspects of quantum field theory, elliptic cohomology, classical concordance
Richard Thomas http://www.ma.ic.ac.uk/~rpwt/ Algebraic geometry, mirror symmetry, gauge theory	Gang Tian Symplectic manifolds, differential and complex geometry, geometric analysis