Title: How to count constant maps? read more »
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The Fall 2019 Joseph Fels Ritt Lectures, by Professor Neshan Wickramasekera, will take place on Wednesday, October 23 and Thursday, October 24, 2019. Professor Neshan Wickramasekera (Cambridge University) , will deliver a two talk series titled: Lecture 1: Variational theory of minimal hypersurfaces of Riemannian manifolds Lecture 2: Regularity of CMC and prescribed-mean-curvature hypersurfaces A fundamental idea in the study of partial differential equations is to introduce generalized solutions and establish, possibly subject to further conditions, smoothness of the generalized solutions. Having in place such a “regularity theory” is useful in many ways: besides reducing the question of existence of classical (i.e. smooth) solutions to that of existence of generalized solutions, These lectures will describe progress made in the past several years for a large class of hypersurfaces where it is shown that this multiplicity issue has a satisfactory answer. The work culminates in a sharp regularity and compactness theory subject to certain structural conditions on the hypersurfaces and appropriate control on their mean curvature, mass and the Morse index (with respect to the relevant functional). The work includes minimal (i.e. zero mean curvature) and constant mean curvature (CMC) hypersurfaces as important special cases. We will also discuss applications of the theory including a streamlined PDE theoretic alternative to the classical Almgren–Pitts min-max existence theory for minimal hypersurfaces. The first lecture, intended for a general mathematical audience, will focus on the minimal hypersurface theory in fairly broad terms. The second lecture will discuss key differences for general mean curvature constraints (focusing on CMC) and some aspects of the proofs of the main theorems in all cases. The lectures will in part be based on a series of speaker’s works some of which are separate joint projects with C. Bellettini, O. Chodosh and Y. Tonegawa. Lecture 1 Wednesday, October 23, 2019 in room 520 from 4:30 – 5:30pm Lecture 2 Thursday, October 24, 2019 in room 417 from 5:30 – 6:30pm Tea will be served at 4 pm in 508 Mathematics.
Print this pageCome join us on Friday, September 27th, October 4th and 11th from 3:15 – 5pm in room 407. Starting Friday, September 27, 2019 Professor Makiko Sasada (University of Tokyo), will be giving a special lecture titled; The Box-ball System, Discrete Integrable Systems and Generalized Pitman’s Transform“The Korteweg-de Vries equation (KdV equation) and the Toda lattice are fundamental examples of classical integrable systems. These integrable systems with random initial measures have been intensively studied in recent years. In this series of lectures, I will present our recent results on discrete versions of the KdV equation and the Toda lattice starting from random initial conditions. As a fundamental example, in the first lecture, I will focus on the box-ball system (BBS). The model, introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour, and can be understood as a special case of the ultra-discrete KdV equation and the ultra-discrete Toda lattice. The BBS is also known to be obtained from a vertex model by crystallization. I will show a new description of the BBS dynamics using Pitman’s transform of a simple random walk path, and give several results related to the BBS with random initial measures. In the second and third lectures, I will introduce some generalizations of Pitman’s transform and show that the dynamics of several discrete integrable systems, such as the discrete KdV equation, the ultra-discrete KdV equation, the discrete Toda lattice and the ultra-discrete Toda lattice are given by them. This observation is applied to define the dynamics uniquely on the infinite configuration space and study the invariant measures. Some analogy between the discrete Toda lattice (resp. ultra-discrete Toda lattice) and the random polymers (resp. the last passage percolation) and the role of Burke’s theorem will be also discussed. The lectures are based on the joint work with David Croydon, Tsuyoshi Kato and Satoshi Tsujimoto.” Friday, September 27th, October 4th and October 11th from 3:15pm – 5pm Mathematics Hall, room 407 Tea will be served at 3:00 p.m. Print this pageTitle: Sphere packing, Fourier interpolation, and ground states in 8 and 24 dimensions read more » Print this pageA memorial conference for Patrick Ximenes Gallagher http://www.math.columbia.edu/~goldfeld/JointNTS.html will be held on Thursday, October 10. It will be followed by a banquet in the Auditorium of Earl Hall at 7pm. We welcome all to gather and commemorate his life and work. To register for the banquet please email Alenia Reynoso at reynoso@math.columbia.edu by Wednesday, September 25, 2019. Directions to Conference/Banquet Patrick Gallagher (1935 – 2019) taught at Columbia University until the end of 2017. He was beloved by his former students and many others. Print this pageDonations may now be made online to a fund in memory of Michael Zhao, a doctoral student in the Department who passed away on December 8, 2018. Michael Zhao was an outstanding undergraduate at the University of Utah, graduating in 2017. He completed Part III at the University of Cambridge and began here as a doctoral student in September 2018, only a few months before his tragic death. He had planned to specialize in number theory. Everyone here was devastated by the loss of such a promising young scholar. Donations to the memorial fund may be made here: http://www.math.columbia.edu/giving/michael-zhao-memorial/ Funds may be used for a physical memorial to Michael in the Department, for expenditures to benefit doctoral students in the Department, or both. Please give generously. Print this pageThis workshop will present recent developments on free Boundary Problems. For more information please visit the link below.
Organizers: Daniela De Silva, Nestor Guillen, Ovidiu Savin, and Hui Yu. May 23 and May 24, 2019 Mathematics Hall, Room 312 *Registration is required Print this pageThe spring 2019 Ritt Lectures, by Professor Laure Saint Raymond, will take place on Wednesday, May 8 and Thursday, May 9, 2019 from 4:30 – 5:30pm in Rm 417. Professor Laure Saint Raymond (École Normale Supérieure de Lyon), will deliver a two talk series titled: 1. Disorder Increases Almost Surely Consider a system of small hard spheres, which are initially (almost) independent and identically distributed. Then, in the low density limit, their empirical measure$\frac1N \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$converges almost surely to a non reversible dynamics. Where is the missing information to go backwards?
2. The Structure of Correlations Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales. How can combinatorial techniques help analyze this departure from chaos?
Tea will be served at 4 pm in 508 Mathematics.
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