Winter Semester 2025/26
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Speaker: Yannick Sire (Johns Hopkins University)
Date & Time: October 14, 2025, 14:00 - 15:00
Location: Übungsraum 2, Gyrhofstraße
Title:
Regularity vs singularity formation for harmonic map heat flows with free boundaries.
Abstract:
I will report on recent results on geometric flows associated to harmonic mappings with free boundary.
Those maps are instrumental in several geometric problems, such as extremal metrics for the Steklov spectrum for instance and one can formulate several possible parabolic equations whose stationnary solutions are such maps.
I will describe these formulations, each of which offering interesting applications and analytic problems. In various cases, one can derive partial regularity results for weak solutions and describe the structure of the singular set. I will try to give an overview of such results. However, a formulation, related to the Plateau flow, poses more challenging issues and I will formulate some conjectures about its singularity formation. The construction of solutions blowing up in finite or infinite time uses a new gluing technique, which has been successfully used recently to investigate singularity formations in other flows, such as Fast Diffusion equations or Yang-Mills heat flow.
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Speaker: Martin Spitz (Universität Bielefeld)
Date & Time: November 4, 2025, 14:00 - 15:00
Location: Übungsraum 2, Gyrhofstraße
Title: Modified scattering for the three dimensional Maxwell-Dirac system
Abstract:
In this talk, we discuss global well-posedness and modified scattering for the massive Maxwell-Dirac system in the Lorenz gauge in (1+3)-dimensional spacetime for small, sufficiently smooth and decaying initial data. Our approach both exploits the close connection of the massive Maxwell-Dirac system with the wave-Klein-Gordon equations and specific structural properties of the Dirac equation. The modified scattering result follows from a precise description of the asymptotic behavior of the solution inside the light cone, which we derive via the method of testing with wave packets of Ifrim-Tataru.
The talk is based on joint work with Sebastian Herr and Mihaela Ifrim.
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Bonn-Cologne Analysis & PDE Day 2025
Date & Time: November 28, 2025, 14:00 - 19:00
Location: Hörsaal 203, Mathematisches Institut
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Speaker: Dejan Gajic (Universität Leipzig)
Date & Time: December 2, 2025, 14:00 - 15:00
Location: Übungsraum 2, Gyrhofstraße
Title: TBA
Abstract: TBA
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Speaker: Yongming Li (Texas A&M University)
Date & Time: December 9, 2025, 14:00 - 15:00
Location: Übungsraum 2, Gyrhofstraße
Title: Asymptotic stability of solitary waves for the 1D focusing cubic Schrödinger equation
Abstract:
In this talk we present a perturbative proof of the asymptotic stability of the solitary wave solutions for the 1D focusing cubic Schrödinger equation under small perturbations in weighted Sobolev spaces. The strategy of our proof is based on the space-time resonances approach based on the distorted Fourier transform and modulation techniques to capture the asymptotic behavior of the solution. A major difficulty throughout the nonlinear analysis is the slow local decay of the radiation term caused by the threshold resonances in the spectrum of the linearized operator around the solitary wave. The presence of favorable null structures in the quadratic terms mitigates this problem through the use of normal form transformations.
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