123
reads

Tautness and Algebraicity
Prof. Quo-Shin Chi ( Washington University in St. Louis, USA )

2008 - 01 - 08 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

A compact submanifold in a sphere (or in an Euclidean space) is taut if all the spherical (Euclidean) distance functions are perfect Morse-Bott functions with respect to Z_2 coefficients. Tautness is preserved by stereographic projection, and so the theories in the two ambient spaces are essentially the same. Two important classes of taut submanifolds are isoparametric submanifolds and compact proper Dupin hypersurfaces in spheres, among many others. In a paper published in 1984, Kuiper raised the question as to whether a taut submanifold is real algebraic, i.e., whether a taut submanifold is an irreducible component of a real algebraic subvariety of the ambient space. In the 1980's the answer to this question was widely thought to be true, for a good reason, because intuitively a perfect Morse-Bott function should not be flabby anywhere. In this talk, I shall indicate a proof that the answer to this question of Kuiper's is affirmative if the dimension of the taut submanifold is less than or equal to four.

Time:14:00 - 15:00, Thursday, September 15, 2009 - June 30, 2010
Room:308, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizer:Shu-Cheng Chang ( Department of Mathematics, National Taiwan University )

Available Talk List

2007-10-02 (Tue.)		Isoperimetric Problem in Heisenberg group
2007-10-09 (Tue.)		Isoperimetric Problem in Heisenberg group
2007-10-16 (Tue.)		Proof of positive mass theorem II (after Schoen and Yau)
2007-10-23 (Tue.)		Proof of positive mass theorem II (after Schoen and Yau)
2007-10-30 (Tue.)		Proof of positive mass theorem II(after Schoen and Yau)
2007-10-30 (Tue.)		Rigidity Theorem of Higher Dimensional Black
2007-11-13 (Tue.)		Proof of positive mass theorem II (after Schoen and Yau)
2007-11-20 (Tue.)		The Mass and the Paneitz operator in CR geometry
2007-11-27 (Tue.)		A Remark on Degenerate Singularity in three Dimensional Ricci Flow
2007-12-04 (Tue.)		The balance between existence and nonexistence theorems via an index theory
2007-12-04 (Tue.)		Concentration phenomena for some singularly perturbed elliptic PDEs
2008-01-08 (Tue.)		Tautness and Algebraicity
2008-03-11 (Tue.)		The Strong Oka’s Lemma, bounded plurisubharmonic functions and the -Neumann problem
2008-03-25 (Tue.)		Vafa-Witten theory for non-simply laced gauge groups
2008-04-08 (Tue.)		The Cauchy problem of the Ward equation I
2008-04-15 (Tue.)		The Cauchy problem of the Ward equation II.
2008-04-22 (Tue.)		Contracting Convex Immersed Closed Plane Curves with Slow Speed of Curvature
2008-04-29 (Tue.)		Geometric aspects of random walks on a crystal lattice
2008-05-01 (Thu.)		Harmonic forms and Weight Poincar\'{e} inequality
2008-05-06 (Tue.)		Toward the QMMP via A + B model
2008-06-03 (Tue.)		Folded Holomorphic Maps
2008-06-10 (Tue.)		On Path Integrals
2008-06-17 (Tue.)		Constant Mean Curvature Foliation of Isolated Physical Systems
2008-06-17 (Tue.)		The positivity of quasi-local mass
2008-06-24 (Tue.)		A Torelli type theorem of birational equivalence
2008-07-18 (Fri.)		Classification of gradient shrinking solitons
2008-07-31 (Thu.)		The Bernstein problem on the Heisenbeg Groups
2008-09-23 (Tue.)		The Tian-Yau-Zelditch asymptotic expansion
2008-10-01 (Wed.)		Introducing a complexity to spatial graphs
2008-10-07 (Tue.)		On the singularities of the Szego projection for ''0,q'' forms
2008-10-14 (Tue.)		A resent result of Phong on Kähler-Ricci flow
2008-10-21 (Tue.)		On the moduli space of flat bundles over a 2-manifold
2008-10-28 (Tue.)		A note of weighted Poincaré inequality
2008-11-04 (Tue.)		CR Obata’s Theorem
2008-11-04 (Tue.)		Augmented Spinors
2008-11-11 (Tue.)		Energies of Knots and the Related Variational Problems
2008-11-18 (Tue.)		Immersed equations of the Hyperbolic Surfaces
2008-11-25 (Tue.)		Removable singularities and uniqueness of standard solution of Ricci flow
2008-11-25 (Tue.)		Lagrangian Submanifolds Foliated by (n-1)-spheres in R^2n
2008-12-02 (Tue.)		Interplays between Symmetries and Optimalities
2008-12-16 (Tue.)		A generalization of Lagrangian mean curvature flow
2008-12-16 (Tue.)		Toric Sasaki-Einstein manifolds
2009-02-17 (Tue.)		On Lagrangian submanifolds in complex hyperquadrics obtained from isoparametric hypersurfaces
2009-02-17 (Tue.)		Aronson–Benilan estimates for porous medium and fast diffusion equations.
2009-02-24 (Tue.)		Classification of isoparametric hypersurfaces
2009-03-03 (Tue.)		A Generalization of Hamilton’s Differential Harnack Inequality for the Ricci Flow.
2009-03-17 (Tue.)		Classification of Isoparametric Hypersurfaces II
2009-03-17 (Tue.)		The Dirac Operator on Contact Manifolds (I)
2009-03-24 (Tue.)		On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds
2009-03-31 (Tue.)		The Dirac Operator on Contact Manifolds (II)
2009-04-07 (Tue.)		Polynomial Growth Harmonic Functions on Complete Riemannian Manifolds
2009-04-14 (Tue.)		The CR Volume Comparison
2009-04-28 (Tue.)		Some recent developments in Hardy $H^p$ theory
2009-05-12 (Tue.)		Sub-elliptic Operator and Sub-Riemannian Geometry
2009-05-26 (Tue.)		Ends of locally symmetric spaces
2009-06-02 (Tue.)		The Poisson Kernel for Heisenberg Polynomials on the Disk
2009-06-09 (Tue.)		Differential forms, conservation laws, and monotonicity formulas in p-
2009-06-16 (Tue.)		p-Harmonic geometry, submanifolds of constant mean curvature, and Yang-Mills-Born-Infeld Theory
2009-07-30 (Thu.)		Graphic Bernstein type results and Mean Curvature flow in Higher Co-dimension
2009-09-10 (Thu.)		Introduction to the Toda lattice 1
2009-09-14 (Mon.)		Introduction to the Toda lattice 2
2009-09-17 (Thu.)		The Lee Conjecture on Pseudo-Einstein Metrics
2009-10-01 (Thu.)		The Refined Analytic Torsion
2009-10-08 (Thu.)		Geometry of surfaces on the Heisenberg group from the point of view of analysis
2009-10-15 (Thu.)		Quantum differential equation of weighted projective spaces
2009-10-22 (Thu.)		Massey Product and Chern-Simons Theory
2009-12-10 (Thu.)		On a generalization of Calabi-Yau equation
2010-03-11 (Thu.)		On a simple maximum principle technique on the circle
2010-03-18 (Thu.)		An Approach to Higher Order Linking Invariants Through Holonomy and Curvature
2010-03-25 (Thu.)		On heat kernels
2010-05-27 (Thu.)		Harmonic Polynomials of the Heisenberg sub-Laplacian and Dimension Analysis