Geometry Festival

The Geometry Festival is an annual mathematics conference held in the United States.

The festival has been held since 1985 at the University of Pennsylvania, the University of Maryland, the University of North Carolina, the State University of New York at Stony Brook, Duke University and New York University's Courant Institute of Mathematical Sciences. It is a three day conference that focuses on the major recent results in geometry and related fields.

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 Ngaiming 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 Edward 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, Lp-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 Yakov Eliashberg, Symplectic geometric methods in several complex variables F. 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 Mikhail 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 Stephan Stolz, On the space of positive curvature metrics modulo diffeomorphisms

1992 at 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 Shiing-Shen Chern, Finsler geometry Richard S. 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 Isadore Singer, Geometry and quantum field theory

1995 at Stony Brook Dimitri Burago, Asymptotic geometry of Z^n-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 Tomasz 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 John C. 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 Grigory Margulis, Quantitative Oppenheim Conjecture Sergei P. Novikov, Laplace and Darboux transformations Richard Schwartz, The Devil's Pentagram Guofang 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 II, 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) Mikhail 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 Shing-Tung 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 Mikhail 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

2002 at Courant Denis Auroux, Singular plane curves and topological invariants of symplectic manifolds Hugh Bray, On the mass of higher dimensional black holes Alice Chang, Conformally invariant operators and the Gauss-Bonnet integrand Xiuxiong Chen, The space of Kähler metrics George Daskalopoulos, On the Yang-Mills flow in higher dimensions Alex Eskin, Billiards and lattices Juha Heinonen, On the existence of quasiregular mappings

2003 at Duke Bennett Chow, Harnack estimates of Li–Yau–Hamilton type for the Ricci flow Anda Degeratu, Geometrical McKay Correspondence Ron Donagi, Griffiths' intermediate Jacobians, integrable systems, and string theory John Etnyre, Legendrian knots in high dimensions Joe Harris, Are Cubics Rational? Claude LeBrun, Zoll Manifolds, Complex Surfaces, and Holomorphic Disks John Morgan, Variations of Hodge structure for 1-parameter families of Calabi–Yau three-folds Madhav Nori, A modified Hodge conjecture Justin Sawon, Twisted Fourier–Mukai transforms for holomorphic symplectic manifolds Wilfried Schmid, Automorphic distributions, L-functions, and functional equations Jeff Viaclovsky, Fully nonlinear equations and conformal geometry Claire Voisin, K-correspondences and intrinsic pseudovolume forms

2004 at Courant Jean-Michel Bismut, The Hypoelliptic Laplacian on the Cotangent Bundle Yasha Eliashberg, Positive Loops of Contact Transformations Blaine Lawson, Projective Hulls and the Projective Gelfand Transformation Dusa McDuff, Applications of J-holomorphic Curves Xiaochun Rong, Local splitting structures on nonpositively curved manifolds Dennis Sullivan, Algebraic topology in string backgrounds Gang Tian, Extremal Metrics and Holomorphic Discs Edward Witten, Gauge Theory Scattering From Curves In CP3

2005 at Stony Brook Nancy Hingston, Periodic solutions of Hamilton's equations on tori Sergiu Klainerman, Null hypersurfaces and curvature estimates in general relativity Bruce Kleiner, Singular structure of mean curvature flow Frank Pacard, Blowing up Kähler manifolds with constant scalar curvature Rahul Pandharipande, A topological view of Gromov-Witten theory Igor Rodniansky, Non-linear waves and Einstein geometry Yum-Tong Siu, Methods of singular metrics in algebraic geometry Katrin Wehrheim, Floer theories in symplectic topology and gauge theory

2006 at Penn Jeff Cheeger, Differentiation, bi-Lipschitz nonembedding and embedding Charles Fefferman, Fitting a smooth function to data Helmut Hofer, On the analytic and geometric foundations of symplectic field theory Ko Honda, Reeb vector fields and open book decompositions William H. Meeks, The Dynamics Theorem for embedded minimal surfaces Yair Minsky, Asymptotic geometry of the mapping class group Frank Morgan, Manifolds with Density Zoltan Szabo, Link Floer homology and the Thurston norm

2007 at Maryland Dan Freed, Secondary differential-geometric invariants, generalized cohomology, and QCD Xiaobo Lu, Mean curvature flow for isoparametric submanifolds Vitali Kapovitch, Some open problems in comparison geometry Maryam Mirzakhani, Lattice point asymptotics and conformal densities on Teichmüller space Charles Epstein, Stein fillings and index theorems