Analysis seminar

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For Zoom URL please contact Laura Keller

Spring Semester 2010

Date / Time Speaker Title Location
2 March 2010
15:15-16:15
Thomas Alazard
Paris Orsay, France
Event Details

Analysis Seminar

Title On the Cauchy problem for the water waves with surface tension
Speaker, Affiliation Thomas Alazard, Paris Orsay, France
Date, Time 2 March 2010, 15:15-16:15
Location HG G 43
Abstract This work is about the Cauchy theory for the water waves equations. Our main result is that, after suitable paralinearizations, the system can be arranged into an explicit symmetric system of Schroedinger type. We then show that the smoothing effect and Strichartz estimates for the (one dimensional) surface tension water waves as a consequence of this reduction. We are able to obtain sharp results in terms of regularity of the indexes of the initial data, and weights in the estimates (work in collaboration with Nicolas Burq and Claude Zuily)
On the Cauchy problem for the water waves with surface tensionread_more (CANCELLED)
HG G 43
9 March 2010
15:15-16:15
Dr. Yuxin Ge
University of Creteil-Paris 12, France
Event Details

Analysis Seminar

Title Regulatory of optimal transportation maps on compact locally nearly spherical manifolds
Speaker, Affiliation Dr. Yuxin Ge, University of Creteil-Paris 12, France
Date, Time 9 March 2010, 15:15-16:15
Location HG G 43
Abstract Given a couple of smooth positive measures of same total mass on a compact connected Riemannian manifold M, we look for a smooth optimal transportation map G, pushing one measure to the other at a least total squared distance cost, directly by using the continuity method to produce a classical solution of the elliptic equation of Monge-Ampere type satisfied by the potential function u, such that G=exp(grad u). This approach boils down to proving an a priori upper bound on the Hessian of u. In this talk, based on the recent local C^2 estimate of Ma-Trudinger-Wang, we treat the case of manifolds with curvature sufficiently close to 1 in C^2 norm.
Regulatory of optimal transportation maps on compact locally nearly spherical manifoldsread_more
HG G 43
16 March 2010
15:15-16:15
Prof. Dr. Bernhard Ruf
University of Milan, Italy
Event Details

Analysis Seminar

Title Blow-up solutions for critical Trudinger-Moser equations in R^2
Speaker, Affiliation Prof. Dr. Bernhard Ruf, University of Milan, Italy
Date, Time 16 March 2010, 15:15-16:15
Location HG G 43
Blow-up solutions for critical Trudinger-Moser equations in R^2
HG G 43
23 March 2010
15:15-16:15
Massimiliano Berti
University of Naple, Italy
Event Details

Analysis Seminar

Title Sobolev quasi-periodic solutions of NLS in any dimension d > 1
Speaker, Affiliation Massimiliano Berti, University of Naple, Italy
Date, Time 23 March 2010, 15:15-16:15
Location HG G 43
Abstract We prove the existence of quasi-periodic solutions for Schrodinger equations with merely differentiable nonlinearities under periodic boundary conditions in any spatial dimension d > 1. Our solutions have Sobolev regularity both in time and space. The proofs are based on an improved Nash-Moser iterati on schem ethods to prove the key tame estimates for the inverse linearized operators along Banach scales of Sobolev functions.
Sobolev quasi-periodic solutions of NLS in any dimension d > 1read_more
HG G 43
13 April 2010
15:15-15:15
Walter Craig
McMaster University, Canada
Event Details

Analysis Seminar

Title Lagrangian invariant tori for Hamiltonian systems with infinitely many degrees of freedom
Speaker, Affiliation Walter Craig, McMaster University, Canada
Date, Time 13 April 2010, 15:15-15:15
Location HG G 43
Lagrangian invariant tori for Hamiltonian systems with infinitely many degrees of freedom
HG G 43
27 April 2010
15:15-16:15
Benjamin Schlein

Event Details

Analysis Seminar

Title Derivation of effective evolution equations from many body quantum dynamics
Speaker, Affiliation Benjamin Schlein,
Date, Time 27 April 2010, 15:15-16:15
Location HG G 43
Abstract One of the main goals of non-equilibrium statistical mechanics is the derivation, from first principle quantum dynamics, of effective equations describing the evolution of many body systems. In this talk, I am going to discuss some recent results concerning the derivation of the nonlinear Hartree equations for mean field systems (in particular, for systems of gravitating particles), and the derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates.
Derivation of effective evolution equations from many body quantum dynamicsread_more
HG G 43
4 May 2010
15:15-16:15
Boyan Sirakov
Université Paris Ouest, France
Event Details

Analysis Seminar

Title Fundamental solutions and Liouville results for fully nonlinear elliptic equations
Speaker, Affiliation Boyan Sirakov, Université Paris Ouest, France
Date, Time 4 May 2010, 15:15-16:15
Location HG G 43
Abstract We construct fundamental solutions of fully nonlinear, positively homogeneous, uniformly elliptic equations, examples of which include second-order Hamilton-Jacobi-Bellman and Bellman-Isaacs equations from stochastic control and game theory. We show that up to multiplication and addition of constants, these solutions are the unique solutions in $\R^n \setminus \{ 0 \}$ which are bounded on one side both in a neighborhood of the origin and a neighborhood of infinity. Isolated singularities of solutions which are bounded on one side are completely characterized, extending the classical result of Maxime Bocher for the Laplacian. Further, we show how the homogeneity of the fundamental solution provides information about the long-time behavior of the corresponding controlled diffusion processes and about the existence or non-existence of positive solutions of nonlinear inequalities.
Fundamental solutions and Liouville results for fully nonlinear elliptic equationsread_more
HG G 43
* 11 May 2010
14:15-15:15
Dr. Reto Mueller
SNS, Pisa, Italy
Event Details

Analysis Seminar

Title A compactness theorem for complete Ricci shrinkers
Speaker, Affiliation Dr. Reto Mueller, SNS, Pisa, Italy
Date, Time 11 May 2010, 14:15-15:15
Location HG G 43
Abstract We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. In contrary to previous results, we do not need any pointwise assumptions, volume or diameter bounds. In dimension four, the local integral Riemann bound can be replaced by an upper bound for the Euler characteristic and a mild extra assumption. This is joint work with Robert Haslhofer.
A compactness theorem for complete Ricci shrinkersread_more
HG G 43
* 11 May 2010
16:00-17:00
Prof. Dr. Gang Zhou
ETH
Event Details

Analysis Seminar

Title Equipartition of Energy in Nonlinear Schrodinger / Gross-Pitaevskii Equations
Speaker, Affiliation Prof. Dr. Gang Zhou, ETH
Date, Time 11 May 2010, 16:00-17:00
Location HG G 43
Abstract In this talk I will present a result, jointly with M. I. Weinstein, on the mass transfer between the neutral modes and ground states of weakly nonlinear NLS. Our result confirmed rigorously what was observed in physical experiments, in which the ground states grow by half of the mass of the neutral modes as the solution reaches the equilibrium.
Equipartition of Energy in Nonlinear Schrodinger / Gross-Pitaevskii Equationsread_more
HG G 43
18 May 2010
15:15-16:15
Robert Haslhofer
ETH Zurich, Switzerland
Event Details

Analysis Seminar

Title Perelman's lambda-functional and the stability of Ricci-flat metrics
Speaker, Affiliation Robert Haslhofer, ETH Zurich, Switzerland
Date, Time 18 May 2010, 15:15-16:15
Location HG G 43
Abstract We use Perelman's lambda-functional to study the stability of compact Ricci-flat metrics. Under the assumption that the premoduli space of Ricci-flat metrics is a manifold of prescribed dimension, we prove: (A) a Ricci-flat metric is a local maximizer of lambda in a C^2,alpha-sense iff its Lichnerowicz Laplacian is nonpositive on TT, (B) lambda satisfies a Lojasiewicz-Simon type gradient inequality, (C) the Ricci flow does not move mostly in gauge directions in an L^2-sense. As consequences, we obtain a rigidity result, a new proof of Sesum's dynamical stability theorem and a dynamical instability theorem.
Perelman's lambda-functional and the stability of Ricci-flat metricsread_more
HG G 43
25 May 2010
15:15-16:15
Victor Nistor
Penn State University
Event Details

Analysis Seminar

Title Dyson series and short time asymptotics for the Green function of stochastic volatility models in Finance
Speaker, Affiliation Victor Nistor, Penn State University
Date, Time 25 May 2010, 15:15-16:15
Location HG G 43
Abstract After some preliminaries, I will present a new type of local asymptotic formula for the Green's function G_t(x,y) of a parabolic linear operator with non-constant coefficients. This formula is polynomial in t (neglecting the t^{-n/2} factor) and is obtained using dilations and a Taylor expansions at a point z(x,y). Our method is based on a Dyson series expansion of the Taylor approximation of a dilated operator. The resulting time ordered products can be computed using the Baker-Campbell-Hausdorff commutator formula. Our procedure leads to an elementary, algorithmic construction of approximate solutions to parabolic equations which are accurate to arbitrary prescribed order in the short-time limit. We establish mapping properties and precise error estimates in exponentially weighted, L^p-type Sobolev spaces that appear in practice. Numerical test show the usefulness of such approximations for the pricing of contingent claims (options). This is part of joint works with R. Constantinescu (JPMorgan), N. Costanzino (PSU), J. Liechty (PSU statistics), A. Mazzucato (PSU), and W. Cheng (PSU).
Dyson series and short time asymptotics for the Green function of stochastic volatility models in Financeread_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.

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

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