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.^[1]

Previous Geometry Festival speakers edit

1985 at Penn edit

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

1986 at Maryland edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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 edit

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
Guoliang Yu, Group actions and K-theory
Simon Brendle, Blow-up phenomena for the Yamabe PDE in high dimensions

2008 at Duke edit

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 edit

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 edit

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 Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
Marianna Csörnyei (University College London and Yale): Tangents of null sets
Larry Guth (U Toronto): Contraction of surface areas vs. topology of mappings
Jeremy Kahn (Stony Brook): Essential immersed surfaces in closed hyperbolic three-manifolds
Gang Tian (Princeton): Kähler–Ricci flow through finite-time singularities

2011 at Penn edit

Hubert Bray (Duke): On dark matter, spiral galaxies, and the axioms of general relativity
Tobias Colding (MIT): Generic mean curvature flow
Claude LeBrun (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 edit

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 edit

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 edit

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 (Stony Brook): 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 (Stony Brook): Kähler-Einstein metrics: Gromov-Hausdorff limits and algebraic geometry

2015 at Courant edit

Gábor Székelyhidi (Notre Dame): Kahler-Einstein metrics along the smooth continuity method
Blaine Lawson (Stony Brook): Potential theory for nonlinear PDE's
John Pardon (Stanford): Existence of Lefschetz vibrations on Stein/Weinstein domains
Raanan Schul (Stony Brook): Qualitative and quantitative rectifiability
Ursula Hamenstädt (Bonn): A Gromov/Thurston rigidity theorem for hyperbolic groups
Tatiana Toro (Washington): Almost minimizers with free boundary
Richard Bamler (Berkeley): There are finitely many surgeries in Perelman's Ricci flow

2016 at Princeton edit

Claude LeBrun (Stony Brook): Mass in Kähler Geometry
Ian Agol (UC Berkeley and IAS): Pseudo-Anosov stretch factors and homology of mapping tori
Davi Maximo (Stanford): Minimal surfaces with bounded index
Fernando Marques (Princeton): Morse index and multiplicity of min-max minimal hypersurfaces
Nancy Hingston (The College of New Jersey): Loop Products, Index Growth, and Dynamics
Jennifer Hom (Georgia Tech and IAS): Symplectic four-manifolds and Heegaard Floer homology
Fengbo Hang (NYU, Courant): Fourth order Paneitz operator and Q curvature equation
Jake Solomon (Hebrew University): The space of positive Lagrangians

2017 at Duke edit

Lucas Ambrozio (Imperial College) - Some new results for free boundary minimal surfaces
Otis Chodosh (Princeton) - Some new results on the global geometry of scalar curvature
Mark Haskins (Imperial College)
Chi Li (Purdue) - On metric tangent cones at Klt singularities
Marco Radeschi (Notre Dame) - "When all geodesics are closed"
Christina Sormani (CUNY) - "The Limits of Sequences of manifolds with Nonnegative Scalar Curvature"
Jeff Streets (UC Irvine) - Generalized Kahler Ricci flow and a generalized Calabi conjecture

2018 at Penn edit

Jean-Pierre Bourguignon (IHES)
Eugenio Calabi (Penn)
Yakov Eliashberg (Stanford)
Carolyn S. Gordon (Dartmouth)
Daniel Ketover (Princeton)
Yevgeny Liokumovich (MIT)
Rick Schoen (UC Irvine)
Jenny Wilson (Stanford)

2019 at Maryland edit

Yann Brenier (ETH, Zurich) - Fluid Mechanics and Geometry
Dietmar Salamon (CNRS, DMA-École Normale Supérieure ) - Moment maps in symplectic and Kähler geometry
Aleksandr Logunov (IAS, Princeton) - Zero sets of Laplace eigenfunctions
Jim Bryan (University of British Columbia) AG - The enumerative geometry and arithmetic of some of the world’s Tiniest Calabi–Yau threefolds
Yi Wang (Johns Hopkins University) - Boundary operator associated to σ_k curvature
Steven Zelditch (Northwestern University) - Spectral asymptotics on stationary spacetimes
Xuwen Zhu (University of California, Berkeley) Spherical Metrics with Conical Singularities
Alex Wright (University of Michigan) - Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

2021 at Stony Brook (via Zoom) edit

Joel Spruck (Johns Hopkins University) - A Personal Tribute to Louis Nirenberg
Akito Futaki (Yau Center, Tsinghua) - Deformation Quantization, and Obstructions to the Existence of Closed Star Products
Jean-Pierre Demailly (Institut Fourier, Grenoble) - Holomorphic Morse Inequalities, Old and New
Tristan Collins (MIT) - SYZ Mirror Symmetry for del Pezzo Surfaces
Jim Isenberg (University of Oregon) - Some Recent Results on Ricci Flow
Chiu-Chu Melissa Liu (Columbia University) - Topological Recursion and Crepant Transformation Conjecture
Bing Wang (USTC) - Local entropy along the Ricci flow
Simon Donaldson (SCGP, Stony Brook/ Imperial College, London) - Some boundary value and mapping problems for differential forms

2022 at Courant (online) edit

Panagiota Daskalopoulos (Columbia University) - Ancient solutions to geometric flows
Jingyin Huang (The Ohio State University) - The Helly geometry of some fundamental groups of complex hyperplane arrangement complements
Wenshuai Jiang (Zhejiang University) - Gromov–Hausdorff limit of manifolds and some applications
Chao Li (Courant Institute of Mathematical Sciences) - The geometry and topology of scalar curvature in low dimensions
Ciprian Manolescu (Stanford University) - A knot Floer stable homotopy type
Assaf Naor (Princeton University) - Extension, separation and isomorphic reverse isoperimetry
André Neves (University of Chicago) - Geodesics and minimal surfaces
Lu Wang (Yale University) - Hypersurfaces of low entropy are isotopically trivial
Ruobing Zhang (Princeton University) - Metric geometry of Calabi–Yau manifolds in complex dimension two

References edit

^ "NSF Award Search: Award # 0072580 - Geometry Festival". NSF. Retrieved 2022-04-24.

[1] "NSF Award Search: Award # 0072580 - Geometry Festival". NSF. Retrieved 2022-04-24.

[1]