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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)"
• 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"
• 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"
• 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 the Courant Institute of the Mathematical Sciences:

• 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 University:

• Bennett Chow (University of California at San Diego) Harnack estimates of Li-Yau-Hamilton type for the Ricci flow
• Anda Degeratu (Duke University) Geometrical McKay Correspondance
• Ron Donagi (University of Pennsylvania) Griffiths' intermediate Jacobians, integrable systems, and string theory
• John Etnyre (University of Pennsylvania) Legendrian knots in high dimensions
• Joe Harris (Harvard University) Are Cubics Rational?
• Claude LeBrun (SUNY at Stony Brook) Zoll Manifolds, Complex Surfaces, and Holomorphic Disks
• John Morgan (Columbia University) Variations of Hodge structure for 1-parameter families of Calabi-Yau three-folds
• Madhav Nori (University of Chicago) A modified Hodge conjecture
• Justin Sawon (SUNY at Stony Brook) Twisted Fourier-Mukai transforms for holomorphic symplectic manifolds
• Wilfried Schmid (Harvard University) Automorphic distributions, L-functions, and functional equations
• Jeff Viaclovsky (Massachusetts Institute of Technology) Fully nonlinear equations and conformal geometry
• Claire Voisin (Institut de Mathématiques de Jussieu) 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
• Juha Heinonen
  On the existence of quasiregular mappings

2005 at SUNY 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 Kahler 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 University of Pennsylvania:

• Jeff Cheeger (Courant)
  Differentiation, bi-Lipschitz nonembedding and embedding
• Charles Fefferman (Princeton University)
  Fitting a smooth function to data
• Helmut Hofer (Courant)
  On the analytic and geometric foundations of symplectic field theory
• Ko Honda (University of Southern California)
  Reeb vector fields and open book decompositions
• William Meeks (University of Massachusetts)
  The Dynamics Theorem for embedded minimal surfaces
• Yair Minsky (Yale University)
  Asymptotic geometry of the mapping class group
• Frank Morgan (Williams College)
  Manifolds with Density
• Zoltan Szabo (Princeton University)
  Link Floer homology and the Thurston norm

2007 at University of Maryland:

• Dan Freed (University of Texas at Austin)
  Secondary differential-geometric invariants, generalized cohomology, and QCD
• Xiaobo Lu (Notre-Dame)
  Mean curvature flow for isoparametric submanifolds
• Vitali Kapovith (Toronto and Maryland)
  Some open problems in comparison geometry
• Maryam Mirzakhani (Princeton University)
  Lattice point asymptotics and conformal densities on Teichmüller space
• Charles Epstein (University of Pennsylvania)
  Stein fillings and index theorems
• Guoliang Yu (Vanderbilt University)
  Group actions and K-theory
  
• Simon Brendle (Stanford University)
  Blow-up phenomena for the Yamabe PDE in high dimensions
  

2008 at Duke

• Michael Anderson
  Conformally compact Einstein metrics with prescribed conformal infinity
• Robert Bryant
  Riemannian Submersions as PDE
• Greg Galloway
  Stability of marginally trapped surfaces with applications to black holes
• Marcus Khuri
  The Yamabe Problem Revisited
• John Lott
  Optimal transport in Riemannian geometry and Ricci flow
• William Minicozzi
  The rate of change of width under flows
• Duong Phong
  Stability and constant scalar curvature
• Jeff Viaclovsky
  Orthogonal Complex Structures

2009 at Stony Brook

• Jeff Cheeger
  Quantitative Behavior of Maps from the Heisenberg Group to L1
• Marcos Dajczer
  Conformal Killing graphs with prescribed mean curvature
• Karsten Grove
  Positive curvature: the quest for examples
• Wolfgang Meyer
  The Contributions of Detlef Gromoll to Riemannian Geometry
• Gabriel Paternain
  Transparent Connections over Negatively Curved Surfaces
• Christina Sormani
  The Intrinsic Flat Distance between Riemannian Manifolds
• Guofang Wei
  Smooth Metric Measure Spaces

2010 at Courant

• Tim Austin (UCLA)
  Rational group ring elements with kernels having irrational von Neumann dimension
• Xiuxiong Chen (UW Madison)
  The space of Kaehler metrics
• Tobias Colding (MIT)
  Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• Marianna Csornyei (University College London and Yale)
  Tangents of null sets
• Larry Guth (UToronto)
  Contraction of surface areas vs. topology of mappings
• Jeremy Kahn (SUNY Stony Brook)
  Essential Immersed Surfaces in Closed Hyperbolic Three-Manifolds
• Gang Tian (Princeton)
  Kähler-Ricci flow through finite-time singularities

2011 at Penn

• Hubert Bray (Duke)
  On dark matter, spiral galaxies, and the axioms of general relativity
• Tobias Colding (MIT)
  Generic mean curvature flow
• Claude LeBrun (SUNY Stony Brook)
  On Hermitian Einstein 4-manifolds
• Natasa Sesum (Rutgers)
  Yamabe Solitons
• Pete Storm (Jane Street Capital)
  Infinitesimal rigidity of hyperbolic manifolds with totally geodesic boundary
• Brian Weber (Courant)
  Regularity and convergence of extremal Kaehler metrics
• Shing-Tung Yau (Harvard)
  An appreciation of Eugenio Calabi and his work
• Shing-Tung Yau (Harvard)
  Quasi-local mass in general relativity

2012 at Duke

• John Etnyre (Georgia Institute of Technology)
  Surgery and tight contact structures
• Valentino Tosatti (Columbia University)
  The evolution of a Hermitian metric by its Chern-Ricci curvature
• Carla Cederbaum (Duke University)
  From Newton to Einstein: A guided tour through space and time
• Jan Metzger (Institute for Mathematics, University of Potsdam)
  On isoperimetric surfaces in asymptotically flat manifolds
• Fernando Codá Marques (IMPA, Brazil)
  Min-max theory and the Willmore conjecture
• Yanir Rubinstein (Stanford University)
  Einstein metrics on Kähler manifolds
• Simon Brendle (Stanford University)
  Rotational symmetry of self-similar solutions to the Ricci flow
• Mu-Tao Wang (Columbia University)
  A variational problem for isometric embeddings and its applications in general relativity
• Gordana Matic (University of Georgia)
  Contact invariant in Sutured Floer Homology and fillability

2013 at Maryland

• Bo Berndtsson (Chalmers University)
  Variations of Bergman kernels and symmetrization of plurisubharmonic functions
• Simon Donaldson (Imperial College, London)
  Kähler-Einstein metrics, extremal metrics and stability
• Hans-Joachim Hein (Imperial College, London)
  Singularities of Kähler-Einstein metrics and complete Calabi-Yau manifolds
• Peter Kronheimer (Harvard University)
  Instanton homology for knots and webs
• Andrea Malchiodi (SISSA)
  Uniformization of surfaces with conical singularities
• Aaron Naber (MIT)
  Characterizations of bounded Ricci curvature and applications
• Yuval Peres (Microsoft Research)
  The geometry of fair allocation to random points
• Brian White (Stanford University)
  Gap theorems for minimal submanifolds of spheres

2014 at Stony Brook

• Robert Bryant (Duke University)
  Rolling surfaces and exceptional geometry
• Alice Chang (Princeton University)
  On positivity of a class of conformal covariant operators
• Mihalis Dafermos (Princeton University)
  On null singularities for the Einstein vacuum equations and the strong cosmic censorship conjecture in general relativity
• Kenji Fukaya (Simons Center)
  Mirror symmetry between Toric A model and LG B model: some recent progress
• Matthew Gursky (Notre Dame University)
  Critical metrics on connected sums of Einstein four-manifolds
• Robert Haslhofer (New York University)
  Mean curvature flow with surgery
• Andre Neves (Imperial College)
  Existence of minimal hypersurfaces
• Song Sun (Simons Center)
  Kähler-Einstein metrics: Gromov-Hausdorff limits and algebraic geometry