Department of Mathematics

Search

Analysis seminar

×

Modal title

Modal content

For Zoom URL please contact Laura Keller

Autumn Semester 2019

Date / Time Speaker Title Location
24 September 2019
15:15-16:15 		Prof. Dr. Yann Brenier
ENS Paris
Event Details

Analysis Seminar

Title Sharp measure-valued solutions for Euler and porous media incompressible flows
Speaker, Affiliation Prof. Dr. Yann Brenier, ENS Paris
Date, Time 24 September 2019, 15:15-16:15
Location HG G 43
Abstract The concept of measure-valued solutions for the Euler equations of incompressible flows has been introduced more than 30 years ago by DiPerna-Majda. It is closely related to the concept of "subsolutions" that plays a crucial role in the convex integration approach of De Lellis and Szekelyhidi to the Euler equations. A more precise concept of "sharp" measure-valued solutions has been introduced 20 years ago and shown to be well-suited to the two-point time boundary value problem, or, more precisely, to the minimizing geodesic problem, according to Arnold's geometric interpretation of the Euler equations. In dramatic contrast with the classical framework, these solutions may have, in a suitable sense, a finite Boltzmann entropy, which has been recently shown, by Lavenant and Baradat-Monsaingeon, to be convex along minimizing geodesics. This could be an indication that the corresponding group of volume-preserving diffeomorphisms has, in some sense a nonnegative Ricci curvature. Unfortunately, concerning the initial value problem, the resulting equations are frequently ill-posed (but not always, depending on the initial conditions, in strong connection with the "Penrose stability criterium" in Plasma Physics, as recently shown by Han-Kwan and Rousset). In this talk, we explain why the situation is dramatically changed in the case of friction dominated ("porous medium") incompressible flows subject to gravity forces. Then, sharp measure-valued solutions obey a locally well-posed set of conservation laws which preserve the Boltzmann entropy.
Sharp measure-valued solutions for Euler and porous media incompressible flowsread_more
HG G 43
15 October 2019
15:15-16:15 		Prof. Dr. Juan Luis Vazquez
Universidad autonoma de Madrid
Event Details

Analysis Seminar

Title Nonlinear Diffusion Equations driven by Fractional Operators
Speaker, Affiliation Prof. Dr. Juan Luis Vazquez, Universidad autonoma de Madrid
Date, Time 15 October 2019, 15:15-16:15
Location HG G 43
Abstract Nonlocality plays now an important role in the mathematical modelling of diffusion phenomena. The talk presents work on the existence, regularity and typical behaviour ofthe solutions of nonlinear fractional elliptic and parabolic equations, posed in the whole space or in bounded domains. Attention is given to functional aspects, to the boundary behaviour, and to the long time asymptotics. Work with different collaborators will be mentioned.
Nonlinear Diffusion Equations driven by Fractional Operatorsread_more
HG G 43
22 October 2019
15:15-16:15 		Prof. Dr. Alessandro Carlotto
ETH Zurich, Switzerland
Event Details

Analysis Seminar

Title Constrained deformations of positive scalar curvature metrics
Speaker, Affiliation Prof. Dr. Alessandro Carlotto, ETH Zurich, Switzerland
Date, Time 22 October 2019, 15:15-16:15
Location HG G 43
Abstract What manifolds support metrics of positive scalar curvature? If so, what can one say about the associated moduli space? These are two fundamental problems in Riemannian Geometry, for which great progress has been made over the last fifty years, but that are still highly elusive and far from being fully resolved. Partly motivated by the study of initial data sets for the Einstein equations in General Relativity, I will present some results that aim at moving one step further, studying the interplay between two different curvature conditions, given by pointwise inequalities on the scalar curvature of a manifold, and the mean curvature of its boundary. In particular, after a broad contextualization, I will focus on recent joint work with Chao Li (Princeton University), where we give a complete topological characterization of those compact 3-manifolds that support Riemannian metrics of positive scalar curvature and mean-convex boundary and, in any such case, we prove that the associated moduli space of metrics is path-connected. We can also refine our methods so to construct continuous paths of non-negative scalar curvature metrics with minimal boundary, and to obtain analogous conclusions in that context as well. In particular, note that we can derive the path-connectedness of asymptotically flat scalar flat Riemannian 3-manifolds with minimal boundary, which goes in the direction of understanding the space of vacuum black-hole solutions to the Einstein field equations. Our work relies on a combination of earlier fundamental contributions by Gromov-Lawson and Schoen-Yau, on the smoothing procedure designed by Miao to handle singular interfaces, and on the interplay of Perelman's Ricci flow with surgery and conformal deformation techniques introduced by Codá Marques in dealing with the closed case.
Constrained deformations of positive scalar curvature metricsread_more
HG G 43
5 November 2019
15:15-16:15 		Dr. Yash Jhaveri
Institute for Advanced Study, Princeton University
Event Details

Analysis Seminar

Title Regularity of the Singular Set in the Thin Obstacle Problem
Speaker, Affiliation Dr. Yash Jhaveri, Institute for Advanced Study, Princeton University
Date, Time 5 November 2019, 15:15-16:15
Location HG G 43
Abstract In this talk, I will give an overview of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary, the topological boundary of the contact set of the solution and the obstacle. This is joint work with Xavier Fernández-Real.
Regularity of the Singular Set in the Thin Obstacle Problemread_more
HG G 43
12 November 2019
15:15-16:15 		Prof. Dr. Xavier Cabré
ICREA and UPC (Barcelona)
Event Details

Analysis Seminar

Title Nonlocal minimal surfaces: gradient estimate and fractional Michael-Simon inequality
Speaker, Affiliation Prof. Dr. Xavier Cabré, ICREA and UPC (Barcelona)
Date, Time 12 November 2019, 15:15-16:15
Location HG G 43
Abstract The talk will be concerned with nonlocal minimal surfaces, that is, hypersurfaces of R^n with zero nonlocal mean curvature. This is the equation associated to critical points of the fractional perimeter. We will present a joint result with M. Cozzi in which we establish a gradient estimate for nonlocal minimal graphs. This work motivated to study the possibility of having a fractional analogue of the Michael-Simon and Allard Sobolev inequality. We will present recent progress on this question, joint with M. Cozzi and G. Csató, in which we prove such a fractional version on C^2 hypersurfaces which are boundaries of convex sets. We will conclude with an application to a new upper bound for the extinction time of the fractional mean curvature flow of a convex set.
Nonlocal minimal surfaces: gradient estimate and fractional Michael-Simon inequalityread_more
HG G 43
* 26 November 2019
15:15-16:15 		Prof. Dr. David Bourne
Heriot-Watt University
Event Details

Analysis Seminar

Title Optimal Lattice Quantizers and Best Approximation in the Wasserstein Metric
Speaker, Affiliation Prof. Dr. David Bourne, Heriot-Watt University
Date, Time 26 November 2019, 15:15-16:15
Location HG G 43
Abstract In this talk I will discuss the problem of the best approximation of the three-dimensional Lebesgue measure by a discrete measure supported on a Bravais lattice. Here 'best approximation' means best approximation with respect to the Wasserstein metric W_p, p \in [1,\infty). This problem is known as the quantization problem and it arises in numerical integration, electrical engineering, discrete geometry, and statistics.
Optimal Lattice Quantizers and Best Approximation in the Wasserstein Metricread_more
HG G 43
* 26 November 2019
16:30-17:30 		Prof. Dr. Lucia Scardia
Heriot-Watt University
Event Details

Analysis Seminar

Title Korn and Poincaré-Korn inequalities for functions with small jump set
Speaker, Affiliation Prof. Dr. Lucia Scardia, Heriot-Watt University
Date, Time 26 November 2019, 16:30-17:30
Location HG G 43
Abstract In this talk I will present a regularity result and a Korn inequality in the space $GSBD^p$ of generalised functions with bounded deformation, for any $p> 1$ and any dimension $n \geq 2$. This is work in collaboration with Filippo Cagnetti (University of Sussex) and Antonin Chambolle (\'Ecole Polytechnique, Palaiseau).
Korn and Poincaré-Korn inequalities for functions with small jump setread_more
HG G 43
3 December 2019
15:15-16:15 		Dr. Ludovic Cesbron
Université Paris-Dauphine
Event Details

Analysis Seminar

Title Derivation of fractional diffusion equations confined to bounded domains
Speaker, Affiliation Dr. Ludovic Cesbron, Université Paris-Dauphine
Date, Time 3 December 2019, 15:15-16:15
Location HG G 43
Abstract This talk will be concerned with the question of confining non-local diffusion phenomena to bounded domains. There are several possible approaches to this question, for instance stochastic and spectral theory approaches which have received a lot of interest in recent year. In this talk, I will present another approach based on kinetic theory. The idea is to see fractional diffusion as the anomalous diffusion limit of particular kinetic models. One can then derive confined fractional diffusion equations from kinetic models confined in spatially bounded domain. We will see, in particular, that the choice of boundary condition at the kinetic scale has a great impact on the fractional diffusion limit, even more than it does in the non-fractional setting.
Derivation of fractional diffusion equations confined to bounded domainsread_more
HG G 43
17 December 2019
15:15-16:15 		Prof. Dr. Annamaria Montanari
Università di Bologna
Event Details

Analysis Seminar

Title On the Harnack inequality in doubling quasi-metric spaces and applications
Speaker, Affiliation Prof. Dr. Annamaria Montanari , Università di Bologna
Date, Time 17 December 2019, 15:15-16:15
Location HG G 43
Abstract It is well known that key tools in the study of regularity properties of solutions to PDEs are scale invariant Harnack-type inequalities.
The literature regarding this subject for subelliptic operators in divergence form is wide. On the contrary, when one considers subelliptic linear operators in non-divergence form with purely measurable coefficients and with the ratio between the maximum and the minimum eigenvalues of the coefficient matrix uniformly bounded, only a few and recent results are known.
In this talk I will discuss an axiomatic approach to prove Harnack inequality in the setting of doubling Hölder quasi-metric spaces. Then, I will show a scale invariant Harnack inequality on metric balls for non negative solutions of a class of subelliptic operators in non-divergence form and with measurable coefficients, involving Grushin vector fields. This is a joint work with C. Guidi.
On the Harnack inequality in doubling quasi-metric spaces and applicationsread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location and if you want you can subscribe to the iCal/ics Calender.

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

JavaScript has been disabled in your browser