Previous Geometry Festival Speakers 

1985 at Penn:

• Marcel Berger 
• Pat Eberlein 
• Jost Eschenburg 
• Friedrich Hirzebruch 
• Blaine Lawson 
• Leon Simon 
• Scott Wolpert 
• Deane Yang 

1986 at Maryland: 

• Uwe Abresch, "Explicit constant mean curvature tori" 
• Zhi-yong Gao, "The existence of negatively Ricci curved metrics" 
• David Hoffman, "New results in the global theory of minimal surfaces" 
• Jack Lee, "Conformal geometry and the Yamabe problem" 
• Ngai-ming Mok, "Compact Kähler manifolds of non-negative curvature" 
• John Morgan, "Self dual connections and the topology of 4 manifolds" 
• Chuu-lian Terng, "Submanifolds with flat normal bundle" 

1987 at Penn: 

• Robert Bryant, "The construction of metrics with exceptional holonomy" 
• Francis Bonahon, "Hyperbolic 3-manifolds with arbitrarily short geodesics" 
• Keith Burns, "Geodesic flows on the 2-sphere" 
• Andreas Floer, "Instantons and Casson's invariant" 
• Hermann Karcher, "Embedded minimal surfaces in the 3-sphere" 
• Jürgen Moser, "Minimal foliations of tori" 
• Ed Witten. "Applications of quantum field theory to topology" 

1988 at North Carolina: 

• Detlef Gromoll, "On complete spaces of non-negative Ricci curvature" 
• Nicolas Kapouleas, "Constant mean curvature surfaces in E³" 
• Robert Osserman, "Gauss map of complete minimal surfaces" 
• Pierre Pansu, "L^p-cohomology of negatively curved manifolds" 
• Peter Petersen, "Bounding homotopy types by geometry" 
• Gang Tian, "Kähler-Einstein metrics on quasiprojective manifolds" 
• DaGang Yang, "Some new examples of manifolds of positive Ricci curvature" 
• Wolfgang Ziller, "Recent results on Einstein metrics" . 

1989 at Stony Brook: 

• Eugenio Calabi, "Extremal singular metrics on surfaces" 
• Harold Donnelly, "Nodal sets of eigenfunctions on Riemannian manifolds" 
• Yasha Eliashberg, "Symplectic geometric methods in several complex variables" 
• Thomas Farrell, "A topological analogue of Mostow's rigidity theorem" 
• Lesley Sibner, "Solutions to Yang-Mills equations which are not self-dual" 
• Carlos Simpson, "Moduli spaces of representations of fundamental groups" 

1990 at Maryland: 

• Michael T. Anderson, "Behavior of metrics under Ricci curvature bounds" 
• Kevin Corlette, "Harmonic maps and geometric superrigidity" 
• Kenji Fukaya, "Fundamental groups of almost non-negatively curved manifolds" 
• Misha Gromov, "Recent progress in symplectic geometry" 
• Werner Müller, "On spectral theory for locally symmetric manifolds with finite volume" 
• Rick Schoen, "Least area problems for Lagrangian submanifolds" 
• Gudlaugur Thorbergsson, "Isoparametric submanifolds and their Tits buildings" 
• Shing-Tung Yau, "Some theorems in Kähler geometry" 

1991 at Duke: 

• Jeff Cheeger, "Transgressed Euler classes of SL(2n,Z)-bundles and adiabatic limits of eta-invariants" 
• Chris Croke, "Volumes of balls in manifolds without conjugate points and rigidity of geodesic flows" 
• Carolyn Gordon, "When you can't hear the shape of a manifold" 
• Wu-Yi Hsiang, "Sphere packing and spherical geometry: The Kepler conjecture and beyond" 
• Alan Nadel, "On the geometry of Fano varieties" 
• Grigori Perelman, "Alexandrov's spaces with curvature bounded from below" 
• Stefan Stolz, "On the space of positive curvature metrics modulo diffeomorphisms" 

1992 at NYU/Courant: 

• Jonathan Block, "Aperiodic tilings, positive scalar curvature and other homological phenomena" 
• John Franks, "Infinitely many closed geodesics on the 2-sphere" 
• Karsten Grove, "The inevitable presence of singular spaces in Riemannian geometry" 
• Lisa Jeffrey, "Volumes of moduli spaces of flat connections on Riemannian surfaces" 
• Jun Li, "Anti-self-dual connections on SU(2) bundles over algebraic surfaces" 
• Dusa McDuff, "Symplectic 4-manifolds" 
• Clifford Taubes, "Anti-self dual conformal structures in 4 dimensions" 

1993 at Penn: 

• Shing-Shen Chern, "Finsler geometry" 
• Richard Hamilton, "An isoperimetric estimate for the curve-shrinking flow" 
• Vaughan Jones, "Loop groups and operator algebras" 
• Claude LeBrun, "Compact Kähler manifolds of constant scalar curvature" 
• Louis Nirenberg, "The maximum principle and related things" 
• Xiaochun Rong, "Collapsing in low dimensions and rationality of geometric invariants" 
• I. M. Singer, "Geometry and quantum field theory" 

1995 at Stony Brook: 

• Dimitri Burago, "Asymptotic geometry of Zⁿ-periodic metrics" 
• Tobias Colding, "Ricci curvature and convergence" 
• Dominic Joyce, "Compact Riemannian manifolds with exceptional holonomy groups" 
• Yael Karshon, "Hamiltonian torus actions" 
• David Morrison, "Analogues of Seiberg-Witten invariants for counting curves on Calabi-Yau manifolds" 
• Tom Mrowka, "The Seiberg-Witten equations and 4-manifold topology" 
• Yongbin Ruan, "Higher genus pseudo-holomorphic curves" 
• Edward Witten, "Monopoles and four-manifolds" 

1996 at Maryland: 

• J. Baez, "Quantum gravity and BF theory in 4 dimensions" 
• Jean-Luc Brylinski, "Gauge groups and reciprocity laws on algebraic varieties" 
• Bruce Kleiner, "Spaces of nonpositive curvature" 
• G. Margulis, "Quantitative Oppenheim Conjecture" 
• S. P. Novikov, "Laplace and Darboux transformations" 
• Richard Schwartz, "The Devil's Pentagram" 
• Guofong Wei, "Volume comparison with integral curvature bounds" 
• Shmuel Weinberger, "Equivariant rigidity: For and against" 

1997 at Duke:

• Jeanne Nielsen Clelland , "Geometry of Conservation Laws for Parabolic PDE's" 
• Anatole Katok , "Rigidity and invariant geometric structures for differentiable group actions" 
• François Labourie , "Monge-Ampere problems, holomorphic curves and laminations" 
• Gang Liu, "Floer Homology and the Arnold Conjecture" 
• William Minicozzi, "Harmonic functions on manifolds" 
• Lorenz Schwachhöfer, "The classification of irreducible holonomies of torsion free connections" 
• Matthias Schwarz, "Symplectic fixed points and quantum cohomology" 
• Stephen Semmes , "Geometry with little smoothness" 

1998 at Stony Brook: 

• Scott Axelrod, "Generalized Chern-Simons invariants as a generalized Lagrangian field theory" 
• Jean-Michel Bismut, "Chern-Simons classes, Bott Chern classes and analytic torsion" 
• Spencer Bloch, "Algebro-geometric Chern-Simons classes" 
• Robert Bryant, "Recent progress on the holonomy classification problem" . 
• Robert Bryant for S.-S. Chern, "Recent results and open problems in Finsler geometry" 
• Jeff Cheeger and Blaine Lawson, "The mathematical work of James Simons" 
• Jeff Cheeger, "Ricci Curvature" 
• Jürg Fröhlich, "Physics and the Chern-Simons form 

(from anomalies to the quantum Hall effect to magnetic stars)" 
• Mikhael Gromov, "Dynamics on function spaces" 
• Maxim Kontsevich, "On regulators, critical values and q-factorials" 
• Blaine Lawson, "Connections and singularities of maps" 
• Robert MacPherson, "Spaces with torus actions" 
• John Milnor, "Remarks on geometry and dynamics" 
• I.M. Singer, TBA . 
• Dennis Sullivan "A combinatorial model for non-linearity" 
• Clifford Taubes, "Seiberg-Witten invariants, harmonic forms, and their pseudo-holomorphic curves" 
• Gang Tian, "Yang-Mills connections and calibration" . 
• C.-N. Yang, "Vector potentials and connections" . 
• S.-T. Yau, "Mirror symmetry and rational curves" 

1999 at Penn: 

• Peter Sarnak, "Some spectral problems on negatively curved manifolds" 
• Zheng-xu He, "The gradient flow for the Möbius energy of knots" 
• Curtis McMullen, "The moduli space of Riemann surfaces is Kähler-hyperbolic" 
• Paul Biran, "Lagrange skeletons and symplectic rigidity" 
• Helmut Hofer, Holomorphic curves and contact geometry" 
• Werner Ballmann, "On negative curvature and the essential spectrum of geometric operators" 
• Shlomo Sternberg, "Multiplets of representations and Kostant's Dirac operator" 

2000 at Maryland:

• Samuel Ferguson, "The Kepler Conjecture" 
• Robert Meyerhoff, "Rigorous computer-aided proofs in the theory of hyperbolic 3-manifolds" 
• Herman Gluck, "Geometry, topology and plasma physics" 
• Burkhard Wilking, "New examples of manifolds with positive sectional curvature almost everywhere" 
• John Roe, "Amenability and assembly maps" 
• Eleny Ionel, "Gromov invariants of symplectic sums" 
• Mikhael Gromov, "Spaces of holomorphic maps" 

 2001 at Northeastern:

• Robert Bryant, "Rigidity and quasirigidity of extremal cycles in Hermitian symmetric spaces" 
• Tobias Colding, "Embedded minimal surfaces in 3-manifolds"
• Boris Dubrovin, "Normal forms of integrable PDE's" 
• John Lott, "Heat equation methods in noncommutative geometry" 
• Dusa McDuff, "Seminorms on the Hamiltonian group and the nonsqueezing theorem" 
• Rick Schoen, "Variational approaches to the construction minimal lagrangian submanifolds" 
• Shing-Tung Yau, "Mirror symmetry"