Aktuelles

Dienstag, 30.05.2023: Bulk-edge correspondence for unbounded Dirac-Landau operators

Prof. Horia Cornean (University of Aalborg)

We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while their topological consequences are presented as corollaries of some more general identities involving magnetic derivatives of local traces of fast decaying functions of the bulk and edge operators. One of these corollaries leads to the so-called Streda formula: if the bulk operator has an isolated compact spectral island, then the integrated density of states of the corresponding bulk spectral projection varies linearly with the magnetic field as long as the gaps between the spectral island and the rest of the spectrum are not closed, and the slope of this variation is given by the Chern character of the projection. The same bulk Chern character is related to the number of edge states which appear in the gaps of the bulk operator. This is joint work with M. Moscolari and K. Sørensen.

Uhrzeit:	14:30
Ort:	C3N16
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Dienstag, 30.05.2023: Vacuum solutions in the theory of electroweak interactions

Israel Michael Sigal (Toronto)

In this talk I will describe the vacuum sector of the Weinberg-Salam (WS) model of electroweak forces. In the vacuum sector the WS model yields the U(2)-Yang-Mills-Higgs equations. We show that at large constant magnetic fields the translational symmetry of the equations is broken spontaneously. Namely, there are solutions, which in the plane orthogonal to the magnetic field have the symmetry of a lattice and which have lower energy locally than the homogeneous (gauge-translationally invariant) solutions. The stability of these solutions is an open problem.

Uhrzeit:	16:00
Ort:	C3N16
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Donnerstag, 01.06.2023: A Green’s function proof of the positive mass theorem and related topics

Virginia Agostiniani (University of Trento, Italy)

In this talk, we will explore the role of harmonic and p-harmonic functions in establishing fundamental geometric inequalities in mathematical relativity, such as the positive mass theorem and the Penrose inequality. We will introduce new monotonicity formulas along the level flow of these functions, which provide simple proofs for these inequalities. Additionally, we will discuss how these formulas can be used to characterize the nonnegativity of the scalar curvature, suggesting a synthetic notion of this concept applicable in non-smooth contexts.

Uhrzeit:	15:30
Ort:	online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Martina Jung
Gruppe:	Oberseminar
Einladender:	Carla Cederbaum