Geometry & Topology

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Joan Birman http://www.math.columbia.edu/~jb/ Classical knot theory, theory of braids, knots in dynamical systems, mapping class groups of surfaces.	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	Ben Chow http://math.ucsd.edu/~benchow/ Geometric evolution equations, Ricci flow, geometric analysis.
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.
Tom Goodwillie http://www.math.brown.edu/faculty/goodwillie.html Manifolds, algebraic K–theory, homotopy 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.
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.columbia.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://math.berkeley.edu/~teichner/ 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.