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Autumn Semester 2012

Date / Time Speaker Title Location
25 September 2012
15:15-16:15 		Dr. Costante Bellettini
IAS Princeton, USA
Event Details

Analysis Seminar

Title Regularity issues for Calibrated Currents
Speaker, Affiliation Dr. Costante Bellettini, IAS Princeton, USA
Date, Time 25 September 2012, 15:15-16:15
Location HG G 43
Abstract Calibrated currents provide interesting explicit examples of solutions to Plateau's problem. Their role goes however much beyond that: they naturally appear when dealing with several geometric questions, some aspects of which require a deep understanding of regularity properties of calibrated currents. After this introduction I will present an "infinitesimal regularity" result, namely on the uniqueness of tangent cones for pseudo-holomorphic currents.
Regularity issues for Calibrated Currents read_more
HG G 43
2 October 2012
15:15-16:15 		Dr. Thomas Marquardt
ETH Zurich, Switzerland
Event Details

Analysis Seminar

Title The inverse mean curvature flow for hypersurfaces with boundary
Speaker, Affiliation Dr. Thomas Marquardt, ETH Zurich, Switzerland
Date, Time 2 October 2012, 15:15-16:15
Location HG G 43
Abstract We consider hypersurfaces with boundary which evolve in the direction of the unit normal with speed equal to the reciprocal of the mean curvature. During the evolution the hypersurfaces move along but stay perpendicular to a fixed supporting hypersurface. Restricting to the case where the supporting hypersurface is a convex cone we prove long-time existence for star-shaped initial hypersurfaces of positive mean curvature. In the general case, however, one can not expect the flow to exist for all time. Therefore, we use a level-set approach and a variational formulation to define weak solutions. After establishing a-priori estimates we prove existence and uniqueness of weak solutions for suitable supporting hypersurfaces.
The inverse mean curvature flow for hypersurfaces with boundary read_more
HG G 43
6 November 2012
15:15-16:15 		Antonio Ponno
University of Padova, Italy
Event Details

Analysis Seminar

Title The Fermi-Pasta-Ulam problem: recent results and new conjectures
Speaker, Affiliation Antonio Ponno, University of Padova, Italy
Date, Time 6 November 2012, 15:15-16:15
Location HG G 43
Abstract The talk concerns the so-called Fermi-Pasta-Ulam problem or paradox, consisting in the observed lack of relaxation to equilibrium of a one-dimensional chain of interacting particles (or beaded nonlinear string), when initial conditions far from equilibrium are chosen and the energy is small enough. Recent results (both numerical and analytical) on the subject are presented. In particular, the role played in the problem by important integrable models, such as the Korteweg-de Vries equation and the Toda model, is discussed. New conjectures are also presented.
The Fermi-Pasta-Ulam problem: recent results and new conjecturesread_more
HG G 43
13 November 2012
15:15-16:15 		Dorian Goldman
New York University
Event Details

Analysis Seminar

Title Energy driven pattern formation in a non-local Ginzburg-Landau/Cahn-Hilliard energy
Speaker, Affiliation Dorian Goldman, New York University
Date, Time 13 November 2012, 15:15-16:15
Location HG G 43
Abstract This describes joint work with Sylvia Serfaty and Cyrill Muratov. We study the asymptotic behavior of the screened sharp interface Ohta-Kawasaki energy in dimension 2 using the framework of Γ-convergence. In that model, two phases appear, and they interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating ``droplets" of that phase in a sea of the other phase. We consider perturbations to the critical volume fraction where droplets first appear, show the number of droplets increases monotonically with respect to the perturbation factor, and describe their arrangement in all regimes, whether their number is bounded or unbounded. When their number is unbounded, the most interesting case we compute the Γ limit of the `zeroth' order energy and yield averaged information for almost minimizers, namely that the density of droplets should be uniform. We then go to the next order, and derive a next order Γ-limit energy, which is exactly the ``Coulombian renormalized energy W" introduced in the work of Sandier/Serfaty, and obtained there as a limiting interaction energy for vortices in Ginzburg-Landau. The derivation is based on their abstract scheme, that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Without thus appealing at all to the Euler-Lagrange equation, we establish here for all configurations which have ``almost minimal energy," the asymptotic roundness and radius of the droplets as done by Muratov, and the fact that they asymptotically shrink to points whose arrangement should minimize the renormalized energy W, in some averaged sense. This leads to expecting to see hexagonal lattices of droplets.
Energy driven pattern formation in a non-local Ginzburg-Landau/Cahn-Hilliard energyread_more
HG G 43
20 November 2012
14:30-15:30 		Prof. Dr. Jonathan Dahl
Berkeley University
Event Details

Analysis Seminar

Title The multi-marginal optimal transportation problem and minimal networks
Speaker, Affiliation Prof. Dr. Jonathan Dahl, Berkeley University
Date, Time 20 November 2012, 14:30-15:30
Location HG G 43
Abstract I will discuss the multi-marginal generalization of the optimal transportation problem, as well as the related minimal network problem in $L^2$ Wasserstein space. For the minimal network problem, I will also show methods for obtaining pointwise entropy and $L^\infty$ estimates.
The multi-marginal optimal transportation problem and minimal networks read_more
HG G 43
20 November 2012
15:30-16:30 		Prof. Dr. Laure Saint-Raymond
ENS Paris
Event Details

Analysis Seminar

Title "The irreversibility in gas dynamics, a matter of probability"
Speaker, Affiliation Prof. Dr. Laure Saint-Raymond, ENS Paris
Date, Time 20 November 2012, 15:30-16:30
Location HG G 43
Abstract The goal of this lecture is to present a derivation of the Boltzmann equation starting from the hamiltonian dynamics of particles in the Boltzmann-Grad limit, i.e. when the number of particles $N\to \infty$ and their size $\eps \to 0$ with $N\eps^2 = 1$. We will especially discuss the origin of irreversibility and the phenomenon of relaxation towards equilibrium, which are apparently paradoxical properties of the limiting dynamics.
"The irreversibility in gas dynamics, a matter of probability"read_more
HG G 43
27 November 2012
15:15-16:15 		Verena Bögelein
Universität Erlangen
Event Details

Analysis Seminar

Title A quantitative isoperimetric inequality in higher codimension
Speaker, Affiliation Verena Bögelein, Universität Erlangen
Date, Time 27 November 2012, 15:15-16:15
Location HG G 43
Assets https://math.ethz.ch/ndb/00006/02712/AbstractVerena.pdffile_download
A quantitative isoperimetric inequality in higher codimensionread_more
HG G 43
11 December 2012
15:15-16:15 		Jacob Bernstein
University of Cambridge
Event Details

Analysis Seminar

Title A curious variational property of classical minimal surfaces
Speaker, Affiliation Jacob Bernstein, University of Cambridge
Date, Time 11 December 2012, 15:15-16:15
Location HG G 43
Abstract Let $\Sigma$ be a nowhere umbilic classical minimal surface in $R3$. We observe that the induced metric, $g$, on $\Sigma$ may be conformally deformed—in an explicit manner—to a smooth metric $\hat{g}$ which is a critical point of a natural geometric functional $\mathcal{E}$. The diffeomorphism invariance of $\mathcal{E}$ gives rise to a conservation law $T$. We characterize several important model surfaces in terms of $T$. This is joint work with T. Mettler.
A curious variational property of classical minimal surfaces read_more
HG G 43
18 December 2012
15:15-16:15 		Dr. Lu Wang
John Hopkins University, USA
Event Details

Analysis Seminar

Title Rigidity of Self-similar Solutions of Geometric Flows
Speaker, Affiliation Dr. Lu Wang, John Hopkins University, USA
Date, Time 18 December 2012, 15:15-16:15
Location HG G 43
Abstract In this talk, we will discuss some rigidity (at infinity) results of self-similar solutions of various geometric flows, including the mean curvature flow. As applications, we can show some non-existence of self-similar solutions with certain asymptotic behaviors. One of the main ingredients in the proofs is the (anisotropic) Carleman estimate for parabolic equations in non-compact and incomplete domains.
Rigidity of Self-similar Solutions of Geometric Flowsread_more
HG G 43

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Organizers: Francesca Da Lio, Tom Ilmanen, Thomas Kappeler, Tristan Rivière, Michael Struwe

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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