Analysis seminar

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Frühjahrssemester 2011

Datum / Zeit Referent:in Titel Ort
1. März 2011
15:15-16:15
Paul Laurain
ENS Lion
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Analysis Seminar

Titel Place of concentration of constant mean curvature surfaces
Referent:in, Affiliation Paul Laurain , ENS Lion
Datum, Zeit 1. März 2011, 15:15-16:15
Ort HG G 43
Abstract Understanding the moduli space of surfaces with constant mean curvature (CMC) in a variety has been the subject of numerous investigations over the past two decades. Successively, Ye, and Pacard Malchiodi, have constructed examples of CMC concentrating in a neighborhood of a critical point of the scalar curvature. We look at the question of the uniqueness of such constructions, by studying the sequences of solutions of the equation of constant mean curvature using the technique of "blowing up", particularly in trying to obtain precise estimate on the decomposition into a sum of "bubble" of our suite of solutions.
Place of concentration of constant mean curvature surfacesread_more
HG G 43
8. März 2011
15:15-16:15
Dr. Armin Schikorra
ETH Zürich, Switzerland
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Analysis Seminar

Titel H'elein's Moving Frame Technique for Fractional Harmonic Maps
Referent:in, Affiliation Dr. Armin Schikorra, ETH Zürich, Switzerland
Datum, Zeit 8. März 2011, 15:15-16:15
Ort HG G 43
Abstract An adaption of H'elein's "Moving Frame"-technique to regularity theory in the setting of nonlocal (fractional) polyharmonic maps into manifolds in the critical dimension is presented.
H'elein's Moving Frame Technique for Fractional Harmonic Mapsread_more
HG G 43
15. März 2011
15:15-16:15
Carlo Mercuri
SISSA (Trieste)
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Analysis Seminar

Titel "On some quasilinear problems involving critical nonlinearities"
Referent:in, Affiliation Carlo Mercuri, SISSA (Trieste)
Datum, Zeit 15. März 2011, 15:15-16:15
Ort HG G 43
"On some quasilinear problems involving critical nonlinearities"
HG G 43
22. März 2011
15:15-16:15
Prof. Dr. Robert Hardt
Rice University (Texas)
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Analysis Seminar

Titel "Rectifiable and Flat G Chains in a Metric Space"
Referent:in, Affiliation Prof. Dr. Robert Hardt, Rice University (Texas)
Datum, Zeit 22. März 2011, 15:15-16:15
Ort HG G 43
"Rectifiable and Flat G Chains in a Metric Space"
HG G 43
29. März 2011
15:15-16:15
Prof. Dr. Patrick Gerard
Paris Orsay
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Analysis Seminar

Titel An integrable system on the Hardy space
Referent:in, Affiliation Prof. Dr. Patrick Gerard, Paris Orsay
Datum, Zeit 29. März 2011, 15:15-16:15
Ort HG G 43
Abstract I shall introduce a Hamiltonian system on the Hardy space of holomorphic functions on the unit disc with square integrable traces on the circle, which can be seen as a toy model for nonlinear Schroedinger equations with degenerate dispersive properties. I shall discuss the introduction of action angle variables for this sytem with applications to new inverse spectral problems for Hankel operators.
An integrable system on the Hardy space read_more
HG G 43
5. April 2011
15:15-16:15
Dr. Thomas Mettler
University of California, Berkeley
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Analysis Seminar

Titel Weyl metrisability for projective surfaces
Referent:in, Affiliation Dr. Thomas Mettler, University of California, Berkeley
Datum, Zeit 5. April 2011, 15:15-16:15
Ort HG G 43
Abstract The existence problem for Riemannian metrics on a surface with prescribed unparametrised geodesics was first studied by R. Liouville. He observed that the problem can be formulated as a linear first order PDE system which in general will not admit solutions. The necessary and sufficient conditions for local existence of solutions were found only recently by Bryant, Dunajski and Eastwood. Surprisingly the conditions are rather complicated. However if one looks for Weyl structures on surfaces with prescribed unparametrised geodesics the situation is different. In this talk I will use techniques from complex geometry to show that the corresponding PDE system always admits local solutions. I will also show that the Weyl structures on the 2-sphere whose geodesics are the great circles, are in ono-to-one correspondence with the smooth conics without real points in the complex projective plane.
Weyl metrisability for projective surfacesread_more
HG G 43
12. April 2011
15:15-16:15
Prof. Dr. Pierre Albin

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Analysis Seminar

Titel Ricci flow and the determinant of the Laplacian on non-compact surfaces
Referent:in, Affiliation Prof. Dr. Pierre Albin,
Datum, Zeit 12. April 2011, 15:15-16:15
Ort HG G 43
Abstract The determinant of the Laplacian is an important invariant of closed surfaces and has connections to the dynamics of geodesics, Ricci flow, and physics. Its definition is somewhat intricate as the Laplacian has infinitely many eigenvalues. I'll explain how to extend the determinant of the Laplacian to non-compact surfaces where one has to deal with additional difficulties like continuous spectrum and divergence of the trace of the heat kernel. On surfaces (even non-compact) this determinant has a simple variation when the metric varies conformally. I'll explain how to use Ricci flow to see that the largest value of the determinant occurs at constant curvature metrics. This is joint work with Clara Aldana and Frederic Rochon.
Ricci flow and the determinant of the Laplacian on non-compact surfaces read_more
HG G 43
19. April 2011
15:15-16:15
PD Dr. Yvan Martel

Details

Analysis Seminar

Titel Inelastic interaction of solitons for the quartic gKdV equation
Referent:in, Affiliation PD Dr. Yvan Martel,
Datum, Zeit 19. April 2011, 15:15-16:15
Ort HG G 43
Abstract We present two recent works in collaboration with Frank Merle concerning the interaction of two solitons for the (nonintegrable) quartic (gKdV) equation. In two specific asymptotic cases (almost equal speeds / very different speeds), we can describe the collision in details. In particular, we prove that at the main order, the two solitons are preserved by the interaction as in the integrable case. However, unlike in the integrable case, we prove that the collision is inelastic. References: Y. Martel et F. Merle, Description of two soliton collision for the quartic gKdV equation, to appear in Annals of Math. http ://arxiv.org/abs/0709.2672 Y. Martel et F. Merle, Inelastic interaction of nearly equal solitons for the quartic gKdV equation, to appear in Inventiones Mathematicae. http ://arxiv.org/abs/0910.3204.
Inelastic interaction of solitons for the quartic gKdV equationread_more
HG G 43
3. Mai 2011
15:15-16:15
Dr. Marjolaine Puel
Université de Toulouse
Details

Analysis Seminar

Titel Diffusion approximation and homogenization for the linear Boltzmann equation.
Referent:in, Affiliation Dr. Marjolaine Puel, Université de Toulouse
Datum, Zeit 3. Mai 2011, 15:15-16:15
Ort HG G 43
Abstract This is a joint work with Naoufel Ben Abdallah, M. Vogelius and G. Bal. The aim of this work is to separate the two phenomena of diffusion approximation and homogenization for the Boltzmann equation. We justify that both limits can be taken simultaneously and we compute the homogenized diffusion coefficient. We have both a strong convergence result for regular initial data obtained via a Hilbert method and a weak result for more general initial data obtained via a moment method.
Diffusion approximation and homogenization for the linear Boltzmann equation.read_more
HG G 43
10. Mai 2011
15:15-16:15
Scott Armstrong
University of Chicago
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Analysis Seminar

Titel Homogenization of viscous and non-viscous Hamilton-Jacobi equations in stationary ergodic, unbounded environments
Referent:in, Affiliation Scott Armstrong, University of Chicago
Datum, Zeit 10. Mai 2011, 15:15-16:15
Ort HG G 43
Abstract I will present recent work in collaboration with P. E. Souganidis on the stochastic homogenization of Hamilton-Jacobi equations. We prove that, as the microscopic scale tends to zero, the equation averages to a deterministic Hamilton-Jacobi equation and study some properties of the effective Hamiltonian. Our work is strongly related to results of A.-S. Sznitman on the quenched large deviations of Brownian motion interacting with a Poissonian potential, and can be thought of as giving a PDE point-of-view to this circle of ideas, as well as extending his results to a general class of problems.
Homogenization of viscous and non-viscous Hamilton-Jacobi equations in stationary ergodic, unbounded environments read_more
HG G 43
17. Mai 2011
15:15-16:15
Prof. Dr. Martino Bardi
University of Padova, Italy
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Analysis Seminar

Titel Multiscale financial models and Hamilton-Jacobi-Bellman equations
Referent:in, Affiliation Prof. Dr. Martino Bardi, University of Padova, Italy
Datum, Zeit 17. Mai 2011, 15:15-16:15
Ort HG G 43
Abstract We consider optimal stochastic control problems with state variables evolving on different time-scales. They arise in many engineering applications as well as in models of financial markets with fast stochastic volatility. We study the asymptotics of the associated Hamilton-Jacobi-Bellman partial differential equations by viscosity methods inspired by the theory of homogenization. In some cases we can derive explicitly the limit control problem by suitable averaging of the data. As an example we discuss the classical Merton portfolio optimization problem with volatility depending on a fast ergodic diffusion process.
Multiscale financial models and Hamilton-Jacobi-Bellman equationsread_more
HG G 43
24. Mai 2011
15:15-16:15
Dr. María González
Universitat Politècnica de Catalunya
Details

Analysis Seminar

Titel The Yamabe problem for the conformal fractional Laplacian
Referent:in, Affiliation Dr. María González , Universitat Politècnica de Catalunya
Datum, Zeit 24. Mai 2011, 15:15-16:15
Ort HG G 43
Abstract Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf type maximum principle together with interplays between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extend the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem. This is joint work with J. Qing.
The Yamabe problem for the conformal fractional Laplacian read_more
HG G 43
31. Mai 2011
15:15-16:15
Mahir Hadzic
Universität Zürich, Switzerland
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Analysis Seminar

Titel Orthogonality conditions and stability in the Stefan problem with surface tension
Referent:in, Affiliation Mahir Hadzic, Universität Zürich, Switzerland
Datum, Zeit 31. Mai 2011, 15:15-16:15
Ort HG G 43
Abstract Stefan problem is a well known free boundary problem modelling a liquid-solid phase transition within a fixed domain $\Omega$. We establish a sharp nonlinear stability/instability criterion for the steady state spheres in the Stefan problem with surface tension. The nonlinear stability proof relies on a high-order energy method and the introduction of suitable orthogonality conditions.
Orthogonality conditions and stability in the Stefan problem with surface tensionread_more
HG G 43

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

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