The 2018 Jacqueline B. Lewis Memorial Lecturer is Camillo De Lellis

*Institute for Advanced Study, Princeton, NJ*

26th Jacqueline B. Lewis Memorial Lectures

Wed Oct 24 @12:00PM - 01:00PMThe Oriented Plateau ProblemCamillo De Lellis, IAS, Princeton Abstract: The Plateau problem, named by Henry Lebesgue after the Belgian physicist, consists in finding the surface of least area which spans a given contour. In order to tackle such question, generations of mathematicians have investigated the very fundamental notions of ``surface", ``boundary" and ``area", proposing a variety of different theories. In this talk I will give a brief exposition of the so-called theory of currents, introduced by Federer and Fleming in the 60's after the pioneering work of De Giorgi in the case of hypersurfaces. I will then discuss an open question relating the shapes of the contour and that of the minimizer, posed by Almgren in the early eighties and recently solved in a joint work with Guido de Philippis, Jonas Hirsch and Annalisa Massaccesi. Hill 705 |

Thu Oct 25 @ 3:30PM - 04:40PMRegularity of Area Minimizing Currents: InteriorCamillo De Lellis, IAS, Princeton Abstract: The theory of integral currents, developed by Federer and Fleming in the 60's, gives a powerful framework to solve the Plateau's problem in every dimension and codimension and general ambient manifolds. The interior and boundary regularity theory for the codimension one case is rather well understood, thanks to the work of several mathematicians in the 60's, 70's and 80's. In codimension higher than one the phenomenon of branching causes instead very serious problems. A celebrated monograph of Almgren provided a far-reaching interior regularity theorem. However, his original (typewritten) manuscript was more than 1700 pages long. Four years ago, in a series of works with Emanuele Spadaro we have given a substantially shorter and simpler version of Almgren's theory, building upon large portions of his program. This has allowed us to go beyond Almgren's result in several directions. Hill 705 Hospitality 2:30-3:30pm in Room 703 |

Fri Oct 26 @ 2:00PM - 03:00PMRegularity of Area Minimizing Currents: boundaryCamillo De Lellis, IAS, Princeton Abstract: At the end of his monograph Almgren addresses the question of regularity of solutions at the boundary. Full regularity was proved by Allard in his Ph.D. thesis when the ambient manifold is the Euclidean space and the boundary surface lies in the boundary of uniformly convex open set. The general case in codimension 1 ws then settled by Hardt and Simon in the early 80's. But in codimension higher than 1 and in general ambient manifolds the current state of the art does not even give guarantee the existence of a single boundary regular point. This prevents the understanding of seemingly innocent questions like the following: does the connectedness of the boundary imply the connectedness of the minimizer? In a joint work with Guido de Philippis, Jonas Hirsch and Annalisa Massaccesi we give a first general boundary regularity theory which allows us to answer positively to the question above. Hill 705 Hospitality 1:00-2:00pm in Room 703 |

**Jacqueline B. Lewis**was a mathematician and former Dean of Rutgers' University College in New Brunswick who died in 1982 after a career spanning nearly 20 years at Rutgers. She served as an Associate Dean of University College from 1974 to 1978 and as Vice Dean of the school from 1978 to 1981, when she was appointed Dean. She also served as Acting Dean of the Faculty of Professional Studies from June 1981 to September 1982. The lectures were endowed in 1983 by a gift from Dean Lewis' aunt, Lillian Nassau.

Lecturer | Date | Title | |
---|---|---|---|

Nolan Wallach | October | 2015 | Basic Geometric Invariant Theory I, II Some Applications of Geometric Invariant Theory |

Yum-Tong Siu | December | 2013 | The Complex Neumann Problem and Multiplier Ideal Sheaves Methods of Partial Differential Equations in Complex Algebraic Geometry Analytic Methods of Constructing Bundle Sections and their Geometric Applications |

Jennifer Tour Chayes | November | 2010 | The Mathematics of Dynamic Random Networks |

Andrei Zelevinsky | April | 2010* |
Introduction to Cluster Algebras Cluster Algebras of Finite Type and their Geometric Realizations Quivers with Potentials and Generalized Reflection Functors * – Postponed from 2009 |

Terence Tao | March | 2008 | Szemerédi's Regularity Lemma Revisited Three Lectures on Discrete Random Matrices: Singularity and Determinant of Discrete Random Matrices The Least Singular Value of Discrete Random Matrices Eigenvalue Distributions of Discrete Random Matrices |

Andrei Okounkov | April | 2007 | Moduli of Curves and Combinatorics |

Shmuel Weinberger | October | 2004 | Themes in Quantitative Topology: Problems and naive examples Computation, entropy, and variational problems Embeddings, symmetry, and rigidity |

Jean-Michel Coron | October | 2003 | Controllability and nonlinearity for some flow control systems |

Richard P. Stanley | October | 2002 | Six Recent Developments in Algebraic Combinatorics: The Laurent phenomenon; longest increasing subsequences The Saturation Conjecture; the n! Conjecture Gromov-Witten invariants; graphical degree sequences |

Graeme Segal | April | 2001 | The Mathematical Structure of Quantum Field Theory; Quantum Field Theory and K-Theory; Quantum Field Theory and Representation Theory |

Yves Meyer | March | 2000 | Wavelets and Image Processing: Theory and Application to Denoising Hubble Space Telescope Images; Oscillations, Vibrations, Time-Frequency Analysis and the Virgo Program (Detection of Gravitati onal Waves); The Role of Oscillations in Some Non-Linear Evolution Equations: Application to Navier-Stokes Equations |

Don Zagier | March | 1997 | Modular Forms and Differential Operators |

Alain Connes | April | 1996 | Gravity Coupled with Matter and the Foundation of Noncommutative Geometry |

Karen Uhlenbeck | September | 1994 | Moduli Spaces of Solutions to PDE |

V. I. Arnold | November | 1993 | On Some Problems in Singularity Theory |

Ian Macdonald | March | 1993 | Symmetric Functions and Orthogonal Polynomial |

L. Craig Evans | March | 1992 | Compactness for Solutions of Nonlinear Partial Differential Equations |

Jurgen Moser | March | 1991 | Stability in Dynamics and Minimal Solutions in the Calculus of Variations |

Yasha G. Sinai | April | 1990 | Random Behavior of Eigenvalues of Laplacians |

Paul Rabinowitz | April | 1989 | Periodic Solutions of Hamiltonian Systems |

H. Blaine Lawson | April | 1988 | Algebraic Cycles |

David Kazhdan | March | 1987 | Representations of Reductive P-Adic Groups |

Lipman Bers | October | 1985 | Teichmüller Theory for Beginners |

G. D. Mostow | March | 1985 | Braids, Hypergeometric Functions, and Lattices |

Stephen Smale | March | 1984 | The Topology of Classical Algorithms |