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Autumn Semester 2021

Date / Time Speaker Title Location
23 September 2021
18:00-19:30 		Prof. Dr. Patrick Gérard
Université Paris-Sud
Event Details

PDE and Mathematical Physics

Title High frequency approximation of solutions of the Benjamin-Ono equation on the torus
Speaker, Affiliation Prof. Dr. Patrick Gérard, Université Paris-Sud
Date, Time 23 September 2021, 18:00-19:30
Location Y27 H 35/36
Abstract Abstract : The Benjamin-Ono equation is a well-known example of an integrable nonlinear dispersive equation in one space dimension. For solutions with periodic boundary conditions, I will discuss the link in the high frequency regime between the nonlinear Fourier transform inherited from the integrable structure, and a gauge transform introduced by T. Tao in 2004. As an application, we will get optimal high frequency approximations of solutions. This talk is based on a recent joint work with T. Kappeler and P. Topalov.
High frequency approximation of solutions of the Benjamin-Ono equation on the torusread_more
Y27 H 35/36
30 September 2021
18:00-19:30 		Dr. Pierre Emmanuel Jabin
Université de Nice
Event Details

PDE and Mathematical Physics

Title Mean-field limit for non-exchangeable multi-agent systems (zoom talk)
Speaker, Affiliation Dr. Pierre Emmanuel Jabin, Université de Nice
Date, Time 30 September 2021, 18:00-19:30
Location Y27 H 35/36
Abstract We are studying the asymptotic behavior of multi-agent or many-particle systems as the number of agents increases. In a major difference with classical mean-field limits however, agents are not identical and in particular, which pair of agents interact and how much is prescribed by a possibly time-dependent graph of interactions. This type of models are used in a wide range of applications from coupled oscillators to networks of biological neurons. Those applications require a large number of agents or particles, making the mean-field limit attractive. But the usual notion of propagation of chaos cannot hold anymore which forces major changes in the classical theory. This is a joint work with D. Poyato and J. Soler.
Mean-field limit for non-exchangeable multi-agent systems (zoom talk)read_more
Y27 H 35/36
28 October 2021
18:00-19:30 		Dr. Mihajlo Cekic
Universität Zürich
Event Details

PDE and Mathematical Physics

Title Holonomy Inverse Problem
Speaker, Affiliation Dr. Mihajlo Cekic, Universität Zürich
Date, Time 28 October 2021, 18:00-19:30
Location Y27 H 35/36
Abstract Given a compact Riemannian manifold (M, g) and a vector bundle over M equipped with a connection, we consider the following question: does the holonomy along closed geodesics determine the gauge (equivalence) class of the connection? If (M, g) has negative curvature or more generally its geodesic flow is Anosov, in this talk I will explain how in fact, only the traces of the holonomy along closed geodesics locally determine a generic connection; global uniqueness results are obtained in some cases. A direct consequence is an inverse spectral result for the connection (magnetic) Laplacian. The proof relies on two new ingredients: a Livsic type theorem in hyperbolic dynamics for unitary cocycles, and the interplay between the local geometry of the moduli space of connections with Pollicott-Ruelle resonances of a certain natural transport operator. Joint work with Thibault Lefeuvre.
Holonomy Inverse Problemread_more
Y27 H 35/36
4 November 2021
18:00-19:30 		Dr. Andreas Deuchert
Universität Zürich
Event Details

PDE and Mathematical Physics

Title Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
Speaker, Affiliation Dr. Andreas Deuchert, Universität Zürich
Date, Time 4 November 2021, 18:00-19:30
Location Y27 H 35/36
Abstract Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional for the case of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends two previous works of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell. The result was obtained in joint work with Christian Hainzl and Marcel Schaub.
Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Fieldread_more
Y27 H 35/36
11 November 2021
18:00-19:30 		Prof. Dr. Gigliola Staffilani
MIT
Event Details

PDE and Mathematical Physics

Title Energy transfer for solutions to the nonlinear Schrodinger equation on irrational tori.
Speaker, Affiliation Prof. Dr. Gigliola Staffilani, MIT
Date, Time 11 November 2021, 18:00-19:30
Location Y27 H 35/36
Abstract In this talk I will outline some results on the study of transfer of energy for solutions to the periodic 2D (torus domain) cubic defocusing nonlinear Schrodinger equation. In particular I will focus on the differences of the dynamics of solutions in the rational versus irrational torus. Some numerical experiments will also be presented.(The most recent work presented is in collaboration with A. Hrabski, Y. Pan and B. Wilson.)
Energy transfer for solutions to the nonlinear Schrodinger equation on irrational tori.read_more
Y27 H 35/36
18 November 2021
18:00-19:30 		Prof. Dr. Riccardo Adami
Politecnico di Torino
Event Details

PDE and Mathematical Physics

Title Ground states for the two-dimensional NLS in the presence of point interactions
Speaker, Affiliation Prof. Dr. Riccardo Adami, Politecnico di Torino
Date, Time 18 November 2021, 18:00-19:30
Location Y27 H 35/36
Abstract We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logarithmic singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.
Ground states for the two-dimensional NLS in the presence of point interactionsread_more
Y27 H 35/36

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