Departement Mathematik

PDE and mathematical physics

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Frühjahrssemester 2024

Datum / Zeit Referent:in Titel Ort
29. Februar 2024
16:15-18:00 		Dr. Rishabh Gvalani
ETH Zürich
Details

PDE and Mathematical Physics

Titel Mean-field Gibbs measures: Sharp and optimal rates of convergence
Referent:in, Affiliation Dr. Rishabh Gvalani, ETH Zürich
Datum, Zeit 29. Februar 2024, 16:15-18:00
Ort Y27 H 46
Abstract We study the invariant Gibbs measure of mean-field interacting diffusions and prove optimal global and local rates of convergence to its thermodynamic limit in the full sub-critical regime of temperatures \(T>T_c\) for a large class of potentials. Our proof relies on a non-asymptotic Sanov-type upper bound for the global rate (which is of independent interest itself) combined with an application of Stein's method for the local rate. We also apply these techniques to prove sharp exponential concentration inequalities for i.i.d empirical measures in negative Sobolev norms. This is joint work with Matías G. Delgadino (U. T. Austin).
Mean-field Gibbs measures: Sharp and optimal rates of convergenceread_more
Y27 H 46
7. März 2024
16:15-18:00 		Dr. Luca Fresta
Universität Zürich
Details

PDE and Mathematical Physics

Titel Fermionic stochastic analysis
Referent:in, Affiliation Dr. Luca Fresta, Universität Zürich
Datum, Zeit 7. März 2024, 16:15-18:00
Ort Y27 H 46
Abstract Ever since Osterwalder and Schrader's pioneering work, it has been established that Fermionic systems can be described using Grassmann variables and Grassmann measures. In my talk, I will delve into this perspective, elucidating fundamental stochastic analytical tools, such as Grassmann Brownian motion and non-commutative $L^{p}$ spaces, which allow for a more thorough stochastic analytical characterisation of Grassmann measures. To exemplify the utility of this approach, I will discuss the advancements achieved in describing some prototypical subcritical interacting Grassmann measures. Based on joint work with F. De Vecchi, M. Gordina and M. Gubinelli.
Fermionic stochastic analysisread_more
Y27 H 46
14. März 2024
16:15-18:00 		Dr. Simon Becker
ETH Zürich
Details

PDE and Mathematical Physics

Titel Magic moire materials with a twist
Referent:in, Affiliation Dr. Simon Becker, ETH Zürich
Datum, Zeit 14. März 2024, 16:15-18:00
Ort Y27 H 46
Abstract I will review the mathematical analysis behind two classes of new exciting materials: Twisted bilayer graphene (TBG) and twisted semiconductors (TMDs) with an emphasis on their mathematical properties and differences. If time permits I will discuss results on these models under disorder. Joint work with Maciej Zworski Izak Oltman Martin Vogel and Mengxuan Yang
Magic moire materials with a twistread_more
Y27 H 46
28. März 2024
16:15-18:00 		Prof. Dr. Marcin Napiórkowski
University of Warsaw
Details

PDE and Mathematical Physics

Titel Beliaev damping in Bose gas
Referent:in, Affiliation Prof. Dr. Marcin Napiórkowski, University of Warsaw
Datum, Zeit 28. März 2024, 16:15-18:00
Ort Y27 H 46
Abstract According to the Bogoliubov theory, the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In my talk I will explain how the damping rate of phonons at low momenta, the so-called Beliaev damping, can be computed with simple arguments involving an effective Friedrichs model for phonons.
Beliaev damping in Bose gasread_more
Y27 H 46
11. April 2024
16:15-18:00 		Cristina Caraci
Universität Zürich
Details

PDE and Mathematical Physics

Titel Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime.
Referent:in, Affiliation Cristina Caraci, Universität Zürich
Datum, Zeit 11. April 2024, 16:15-18:00
Ort Y27 H 46
Abstract We consider a system of N bosons confined in a unit box with periodic boundary conditions. We assume that the particles interact through a repulsive two-boxy potential with scattering length of order 1/N, i.e. the Gross-Pitaevskii regime. We establish a precise bound for the ground state energy E(N) of the system. While the leading contribution, of order N, to the energy has been known since the pioneering works of Lieb-Seiringer-Yngvason in the early 2000s, and the second order (of order one) corrections were more recently first determined by Boccato-Brennecke-Cenatiempo-Schlein, our estimate also resolves the next term in the asymptotic expansion of E(N), which is of the order (log N)/N, confirming Wu's predictions in 1959. Based on a joint work with Alessandro Olgiati, Diane Saint Aubin and Benjamin Schlein.
Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime.read_more
Y27 H 46
25. April 2024
16:15-18:00 		Dr. Louise Gassot
CNRS IRMAR
Details

PDE and Mathematical Physics

Titel Zero-dispersion limit for the Benjamin-Ono Equation
Referent:in, Affiliation Dr. Louise Gassot, CNRS IRMAR
Datum, Zeit 25. April 2024, 16:15-18:00
Ort Y27 H 46
Abstract We focus on the Benjamin-Ono equation on the line with a small dispersion parameter. The goal of this talk is to precisely describe the solution at all times when the dispersion parameter is small enough. This solution may exhibit locally rapid oscillations, which are a manifestation of a dispersive shock. The description involves the multivalued solution of the underlying Burgers equation, obtained by using the method of characteristics. This work is in collaboration with Elliot Blackstone, Patrick Gérard, and Peter Miller.
Zero-dispersion limit for the Benjamin-Ono Equationread_more
Y27 H 46
23. Mai 2024
16:15-18:00 		Prof. Dr. Charles Collot
CY Cergy Paris Université
Details

PDE and Mathematical Physics

Titel Asymptotic stability of traveling waves for one-dimensional nonlinear Schrodinger equations
Referent:in, Affiliation Prof. Dr. Charles Collot, CY Cergy Paris Université
Datum, Zeit 23. Mai 2024, 16:15-18:00
Ort Y27 H 46
Abstract We consider one dimensional nonlinear Schrodinger equations around a traveling wave. We prove its asymptotic stability for general nonlinearities, under the hypotheses that the orbital stability condition of Grillakis-Shatah-Strauss is satisfied and that the linearized operator does not have a resonance and only has 0 as an eigenvalue. As a by-product of our approach, we show long-range scattering for the radiation remainder. Our proof combines for the first time modulation techniques and the study of space-time resonances. We rely on the use of the distorted Fourier transform, akin to the work of Buslaev and Perelman and, and of Krieger and Schlag, and on precise renormalizations, computations and estimates of space-time resonances to handle its interaction with the soliton. This is joint work with Pierre Germain.
Asymptotic stability of traveling waves for one-dimensional nonlinear Schrodinger equationsread_more
Y27 H 46
30. Mai 2024
16:15-18:00 		Dr. Min Jun Jo
Duke University
Details

PDE and Mathematical Physics

Titel Cusp formation in singular vortex patches
Referent:in, Affiliation Dr. Min Jun Jo, Duke University
Datum, Zeit 30. Mai 2024, 16:15-18:00
Ort Y27 H 46
Abstract 'We prove the instantaneous cusp formation from a single corner of the vortex patch solutions. This positively settles the conjecture given by Cohen-Danchin in Multiscale approximation of vortex patches, SIAM J. Appl. Math. 60 (2000), no. 2, 477-502. This is a joint work with Tarek Elgindi (Duke University).'
Cusp formation in singular vortex patchesread_more
Y27 H 46

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