Mathematics Department - Joseph D'Atri Memorial Lectures

Joseph D'Atri Memorial Lectures

The 2015-16 D'Atri Memorial Lecturer is Fernando Coda Marques
Professor of Mathematics at Princeton University
22nd D'Atri Memorial Lectures
Open to the Public – Use Lots 60A or 64 behind Hill Center
D'Atri Memorial Lecture Series
Min-max Theory for the Area Functional - A Panorama
Friday, February 19  |  Tuesday, February 23
In these lectures we will give a current panorama of the min-max theory for the area functional, initially devised by Almgren in the 1960s and improved by Pitts (1981). This is a deep high-dimensional version of the variational theory of closed geodesics. The setting is very general, being that of Geometric Measure Theory, and the main application until very recently was the construction of minimal varieties of any dimension in a compact Riemannian manifold. In the past few years we have discovered new applications of this old theory, including a proof of the Willmore conjecture, of the Freedman-He-Wang conjecture, and of Yau's conjecture (about the existence of infinitely many minimal hypersurfaces) in the positive Ricci curvature setting. We will give an overview of these results, describe our current efforts to develop the theory further (the first general Morse index estimates) and discuss future directions. Most of the material covered in these lectures is based on joint work with Andre Neves.
Lecture 1 :
"Min-max Theory for the Area Functional - A Panorama – Part I"
Friday, February 19, 2016
Time/Location :    2:00pm    Hill Center 705
Lecture 2 :
"Min-max Theory for the Area Functional - A Panorama – Part II"
Tuesday, February 23, 2016
Time/Location :    1:40pm    Hill Center 705
Joseph D'Atri was born in 1938, received an A.B. from Columbia College in 1959, and received a Ph.D. from Princeton University in 1964. He was a member of the Rutgers University Mathematics Department from 1963 until his death in 1993 and served as Chair of the Department from 1985 until 1990. Further information about Professor D'Atri and his work in geometry may be found in the book Topics in Geometry: in Memory of Joseph D'Atri edited by Simon Gindikin and published in 1996 by Birkhauser as volume 20 in the series Progress in Nonlinear Differential Equations and Their Applications.
Previous D'Atri Memorial Lectures
Frank Merle Jan 2015 A Road Map for the Soliton Resolution Conjecture
Universality Questions for Blow-up Behavior for the Mass Critical Korteweg-de-Vries Equations
Nicola Fusco Jan 2014 Stability and Minimality of a Non-local Variational Problem
The Quantitative Isoperimetric Inequality
Vladimir Sverak Dec 2012 Mathematical Aspects of the Navier-Stokes and Euler's Equations
Sun-Yung Alice Chang Feb 2012 Conformal Invariants: Perspectives From Geometric PDE
Higher Order Isoperimetric Inequalities – An Approach via Method of Optimal Transport
Gang Tian Dec 2010 Geometric Equations in Dimension 4
B-field Renormalization Flow on Complex Surfaces
Carlos Kenig Feb 2010 Some Recent Applications of Unique Continuation to Mathematical Physics, PDE, and Fourier Analysis
The Global Behavior of Solutions to Critical Non-Linear Dispersive and Wave Equations
Yakov Eliashberg Oct 2008 Symplectic Topology of Stein Manifolds
On the Border between Flexible and Rigid Mathematics
Henri Berestycki Nov 2006 Reaction-Diffusion Equations in Nonhomogeneous Media
Neil Trudinger Mar 2006 Nonlinear Elliptic PDE and Optimal Transportation
Nonlinear Elliptic PDE and Geometric Invariance
Helmut Hofer Nov 2004 Somewhere Between Hamiltonian Dynamics and Symplectic Geometry
Paul Rabinowitz 2004 An Aubry-Mather Theory for Partial Differential Equations
Richard Hamilton 2003 On the Ricci Flow
Luis A. Caffarelli 2002 Constraint Methods for Nonlinear Homogenization in Periodic and Random Media, I, II
Brian White 2001 Total Curvature, Soap Films and the Unreasonable Effectiveness of Mathematics
Stefan Hildebrandt 2000 On Two-dimensional Parametric Variational Problems
Uniqueness Results for Minimal Surfaces with Free Boundaries
Richard Schoen 1999 The Plateau Problem in Complex Geometry
Nigel Hitchin 1998 Hyperkahler Geometry
Misha Gromov 1997 Metric Geometry of Algebraic Manifolds
Eugenio Calabi 1995 On Singular Sympletic Structures
John Milnor 1994 Geometry and Dynamics
Jacques Faraut 1993 Ordered Symmetric Spaces
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