Departement Mathematik

Analysis seminar

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For Zoom URL please contact Laura Keller

Herbstsemester 2016

Datum / Zeit Referent:in Titel Ort
27. September 2016
15:15-16:15 		Prof. Dr. Xavier Cabré
ICREA & UPC, Barcelona
Details

Analysis Seminar

Titel Curves and surfaces with constant nonlocal mean curvature
Referent:in, Affiliation Prof. Dr. Xavier Cabré, ICREA & UPC, Barcelona
Datum, Zeit 27. September 2016, 15:15-16:15
Ort HG G 43
Abstract The talk will be concerned with hypersurfaces of $\mathbb{R}^N$ with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. We first prove the nonlocal analogue of the Alexandrov result characterizing spheres as the only closed embedded hypersurfaces in $\mathbb{R}^N$ with constant mean curvature. Our second result establishes the existence of periodic cylinders in $\mathbb{R}^N$ with constant nonlocal mean curvature and bifurcating from a straight cylinder. These are Delaunay type cylinders in the nonlocal setting. Here we use a Lyapunov-Schmidt procedure for a quasilinear type fractional elliptic equation. Finally, we prove the existence of different types of periodic lattices made of near-spheres and having constant nonlocal mean curvature.
Curves and surfaces with constant nonlocal mean curvatureread_more
HG G 43
4. Oktober 2016
15:15-16:15 		Dr. Paolo Baroni
Università degli Studi di Napoli
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Analysis Seminar

Titel On the Cauchy-Dirichlet problem for a general class of parabolic equations
Referent:in, Affiliation Dr. Paolo Baroni, Università degli Studi di Napoli
Datum, Zeit 4. Oktober 2016, 15:15-16:15
Ort HG G 43
Abstract We consider a class of parabolic equations extending the evolutionary $p$-Laplacian in a natural way and we present some regularity results for solutions to the related Cauchy-Dirichlet problem. We shall also compare the local behaviour of solutions with the typical one of solutions to parabolic $p$-Laplace-type equations, both of singular and degenerate type, stressing differences and describing some open questions. The talk is based on a joint work with C. Lindfors (Aalto University, Helsinki).
On the Cauchy-Dirichlet problem for a general class of parabolic equationsread_more
HG G 43
25. Oktober 2016
15:15-16:15 		Prof. Dr. Alessio Porretta
Università di Roma "Tor Vergata"
Details

Analysis Seminar

Titel Long time behavior of mean field games
Referent:in, Affiliation Prof. Dr. Alessio Porretta, Università di Roma "Tor Vergata"
Datum, Zeit 25. Oktober 2016, 15:15-16:15
Ort HG G 43
Abstract Mean field games theory, introduced by J.-M. Lasry and P.-L.Lions in 2006, describes the limit of Nash equilibria in N-persons differential games when the number of agents N tends to infinity. The mean field limit leads to a forward-backward system of PDEs coupling Hamilton-Jacobi with Fokker-Planck equations, which macroscopically describes a stochastic optimization problem in finite horizon, in which the strategy depends on the distribution law of the controlled dynamics. In this talk I will discuss the limit of mean field games systems as the horizon T tends to infinity, explaining how the ergodic behavior of the system can be described and in which sense a convergence to a stationary problem is observed. Such a study points out the connections with so-called turnpike solutions in optimal control problems and to uncoupling methods in mean field games systems.
Long time behavior of mean field gamesread_more
HG G 43
* 8. November 2016
14:15-15:15 		Prof. Dr. Siddhartha Mishra
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel Statistical solutions of hyperbolic systems of conservation laws
Referent:in, Affiliation Prof. Dr. Siddhartha Mishra, ETH Zurich, Switzerland
Datum, Zeit 8. November 2016, 14:15-15:15
Ort HG G 43
Abstract Entropy solutions are widely accepted as the appropriate solution paradigm for hyperbolic systems of conservation laws. However, in view of recent non-uniqueness results and numerical experiments that suggest lack of convergence of standard numerical methods, their appropriateness has been questioned and alternative solution paradigms sought for. One such framework are the entropy measure valued solutions (space-time parametrized probability measures on phase space). We present a recent convergent Monte-Carlo ensemble based algorithm for constructing these solutions. The algorithm is shown to converge once the underlying numerical schemes satisfy some verifiable hypothesis. However, entropy measure valued solutions are not necessarily unique, particularly when the solution is non-atomic. We will present a very recent attempt to constrain entropy measure valued solutions by requiring information about multi-point spatial correlations. The resulting concept of statistical solutions are time-parametrized probability measures on function spaces. We will present well-posedness for the scalar case and a conditional global existence result for systems by showing convergence of a Monte-Carlo based algorithm. Connections of statistical solutions with the Kolmogorov theory of turbulence are also discussed.
Statistical solutions of hyperbolic systems of conservation lawsread_more
HG G 43
* 8. November 2016
15:45-16:45 		Prof. Dr. Laurent Hauswirth
Université de Marne La Vallée
Details

Analysis Seminar

Titel Title: The classification of minimal annuli in S(2)xR and CMC tori in S(3) via integrable system
Referent:in, Affiliation Prof. Dr. Laurent Hauswirth, Université de Marne La Vallée
Datum, Zeit 8. November 2016, 15:45-16:45
Ort HG G 43
Abstract N. Hitchin introduced in 87 an algebraic correspondence between doubly-periodic harmonic map in S(2) or S(3) (the three dimensional sphere) with hyperelliptic Riemann surfaces S, called spectral curves. The period problem depends on the existence of an Abelian differential dh with prescribed poles on S. I will describe the construction of (S, dh) related to CMC annuli immersed in S(3) and minimal annuli in S(2)xR. We will study the differential structure on the space moduli of these surfaces induced by this representation. We describe how to navigate in the space of Alexandrov embedded surfaces by deformation of (S, dh). A global study of this algebraic representation give a complete classification of embedded CMC tori in S(3) via integrable system. Similar considerations will characterize a two-parameter family of annuli foliated by constant curvature curves in S(2)xR as the unique properly embedded minimal annuli.
Title: The classification of minimal annuli in S(2)xR and CMC tori in S(3) via integrable systemread_more
HG G 43
15. November 2016
15:15-16:15 		Prof. Dr. Francisco Martin
University of Granada
Details

Analysis Seminar

Titel Translating solitons of the mean curvature flow
Referent:in, Affiliation Prof. Dr. Francisco Martin, University of Granada
Datum, Zeit 15. November 2016, 15:15-16:15
Ort HG G 43
Abstract A translator is a surface in $\R^3$ that (up to a tangential diffeomorphism) moves  with velocity $v=(0,0,-1)$ by MCF. Equivalently, the mean curvature at each  point is $H= (0,0,-1)^{\perp}.$ Besides vertical planes, one of the simplest examples of complete translators is the grim reaper cylinder. In this talk we will describe several existence and uniqueness results for complete translators which are graphs over planar domains. This is a joint work with D. Hoffman and B. White.
Translating solitons of the mean curvature flowread_more
HG G 43
22. November 2016
15:15-16:15 		Prof. Dr. Manuel Del Pino
Universidad de Chile
Details

Analysis Seminar

Titel Finite time blow-up in the two-dimensional harmonic map flow
Referent:in, Affiliation Prof. Dr. Manuel Del Pino, Universidad de Chile
Datum, Zeit 22. November 2016, 15:15-16:15
Ort HG G 43
Finite time blow-up in the two-dimensional harmonic map flow
HG G 43
13. Dezember 2016
15:15-16:15 		Prof. Dr. Francesca Da Lio
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel Conservation laws in the blow-up analysis of free boundary surfaces
Referent:in, Affiliation Prof. Dr. Francesca Da Lio, ETH Zurich, Switzerland
Datum, Zeit 13. Dezember 2016, 15:15-16:15
Ort HG G 43
Conservation laws in the blow-up analysis of free boundary surfaces
HG G 43
20. Dezember 2016
15:15-16:15 		Prof. Dr. Simon Brendle
Columbia University
Details

Analysis Seminar

Titel Ricci flow with surgery in higher dimensions
Referent:in, Affiliation Prof. Dr. Simon Brendle, Columbia University
Datum, Zeit 20. Dezember 2016, 15:15-16:15
Ort HG G 43
Ricci flow with surgery in higher dimensions
HG G 43

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