Termine

|
Claudia Rüdiger

Josefien Kuijper (Utrecht University): The Dehn invariant for spherical scissors congruence as spectral Hopf algebra

Monday, 16.12.2024 14:15 im Raum M3

Mathematik und Informatik

Abstract: The Dehn invariant is known to many as the satisfying solution to Hilbert?s 3rd problem: a three-dimensional polyhedron P can be cut into pieces and reassembled into a polyhedron Q if and only if Q and P have not only the same volume, but also the same Dehn invariant. Generalised versions of Hilbert?s 3rd problem concern the so-called scissors congruence groups of euclidean, hyperbolic and spherical geometry in varying dimensions, and in these contexts one can define a generalised Dehn invariant. In the spherical case, Sah showed that the Dehn invariant makes the scissors congruence groups into a graded Hopf algebra. Zakharevich has shown that one can lift the scissors congruence group to a K-theory spectrum. In this talk I will discuss a lift of the Dehn invariant to the spectrum level, and we will see how it gives rise to a spectral version of Sah?s Hopf algebra. This talk is based on joint work in progress with Inbar Klang, Cary Malkiewich, David Mehrle and Thor Wittich.



Angelegt am 28.11.2024 von Claudia Rüdiger
Geändert am 28.11.2024 von Claudia Rüdiger
[Edit | Vorlage]

Oberseminare und sonstige Vorträge
Sonstige Vorträge
Vorträge des SFB 1442
Veranstaltungen am Mathematischen Institut
|
Sandra Huppert

Oberseminar Differentialgeometrie: Lucas Lavoyer de Miranda (Universitä Münster), Vortrag: Smoothing out polyhedral manifolds via Ricci flow

Monday, 16.12.2024 16:15 im Raum SRZ 216

Mathematik und Informatik

Abstract: We consider closed polyhedral manifolds which are non-negatively curved in the sense of Alexandrov. We show that there exists a smooth Ricci flow, starting from such a polyhedral manifold, which has positive curvature operator for positive times. Even more, for positive times the flow has positive co-sectional curvature, which confirms a conjecture of Petrunin. This is joint work with Man-Chun Lee and Felix Schulze.



Angelegt am 28.11.2024 von Sandra Huppert
Geändert am 28.11.2024 von Sandra Huppert
[Edit | Vorlage]

Oberseminare und sonstige Vorträge
|
Sandra Huppert

Oberseminar Differentialgeometrie: Tomás Otero Casal (Universitä Münster), Vortrag: tba

Monday, 16.12.2024 17:00 im Raum SRZ 216

Mathematik und Informatik



Angelegt am 28.11.2024 von Sandra Huppert
Geändert am 28.11.2024 von Sandra Huppert
[Edit | Vorlage]

Oberseminare und sonstige Vorträge
|
Anke Pietsch

Prof. Dr. Jonas Lührmann (Texas A&M University): Asymptotic stability of kinks outside symmetry

Tuesday, 17.12.2024 14:15 im Raum SRZ 203

Mathematik und Informatik

We consider scalar field theories on the line with Ginzburg-Landau (double-well) self-interaction potentials. Prime examples include the \phi^4 model and the sine-Gordon model. These models feature simple examples of topological solitons called kinks. The study of their asymptotic stability leads to a rich class of problems owing to the combination of weak dispersion in one space dimension, low power nonlinearities, and intriguing spectral features of the linearized operators such as threshold resonances or internal modes. We present a perturbative proof of the full asymptotic stability of the sine-Gordon kink outside symmetry under small perturbations in weighted Sobolev norms. The strategy of our proof combines a space-time resonances approach based on the distorted Fourier transform to capture modified scattering effects with modulation techniques to take into account the invariance under Lorentz transformations and under spatial translations. A major difficulty is the slow local decay of the radiation term caused by the threshold resonances of the non-selfadjoint linearized matrix operator around the modulated kink. Our analysis hinges on two remarkable null structures that we uncover in the quadratic nonlinearities of the evolution equation for the radiation term as well as of the modulation equations. The entire framework of our proof, including the systematic development of the distorted Fourier theory, is not specific to the sine-Gordon model and extends to many other asymptotic stability problems for moving kinks and other Klein-Gordon solitons. We conclude with a discussion of potential applications in the generic setting (no threshold resonances) and with a discussion of the outstanding challenges posed by internal modes such as in the well-known \phi^4 model. This is joint work with Gong Chen (GeorgiaTech).



Angelegt am 28.11.2024 von Anke Pietsch
Geändert am 28.11.2024 von Anke Pietsch
[Edit | Vorlage]

Kolloquium Holzegel/Seis/Weber
|
Julia Moudden

Hendrik Kleikamp (Disputation): Parametrized optimal control and transport-dominated problems: Reduced basis methods, nonlinear reduction strategies and data-driven surrogates

Thursday, 19.12.2024 09:00 im Raum 120.030

Mathematik und Informatik



Anlagen
Aushang_Disputation_Kleikamp.pdf

Angelegt am 04.12.2024 von Julia Moudden
Geändert am 04.12.2024 von Julia Moudden
[Edit | Vorlage]

Sonstige Vorträge
|
Zahra Mohammadi Khangheshlaghi

Christmas Session

Veröffentlicht Tuesday, 10.12.2024 17:08 im Raum SRZ 216/17

Mathematik und Informatik

Abstract



Angelegt am 10.12.2024 von Zahra Mohammadi Khangheshlaghi
Geändert am 10.12.2024 von Zahra Mohammadi Khangheshlaghi
[Edit | Vorlage]

MM Connect