Fourier expansions of vector-valued automorphic functions
Monday, 10.1.22, 16:15-17:15, BBB (link will be distributed via the Diffgeo mailing list)
In this talk, I provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility or unitarity are made. Examples of such eigenfunctions include vector-valued twisted automorphic forms of Fuchsian groups. We will discuss a detailed description of the Fourier coefficients and explicitly identify each of their constituents, which intimately depend on the eigenvalues of the twisting endomorphism and the size of its Jordan blocks. In addition, we determine the growth properties of the Fourier coefficients.
Die Weierstraßdarstellung von Minimalflächen
Monday, 17.1.22, 16:15-17:15, BBB-Raum (s. Diffgeo-Liste)
In diesem Vortrag wird die Weierstraß-Darstellung für konform parametrisierte Minimalflächen hergeleitet, in welcher eine holomorphe und eine meromorphe Funktion auftreten, die eine solche Fläche unter geringen Zusatzbedingungen beschreiben. Anfangs wird dafür an einige Begriffe der Elementaren Differentialgeometrie und der Funktionentheorie erinnert. Besonderes Augenmerk liegt im weiteren Verlauf auf der Korrespondenz zwischen der Menge der konform parametrisierten Minimalflächen und der Menge der holomorphen, isotropen Funktionen auf demselben Definitionsbereich, da diese Beziehung den Ausgangspunkt der Weierstraß'schen Konstruktion darstellt.
Yamabe Flow on Singular Spaces
Monday, 24.1.22, 16:15-17:15, BBB (link will be distributed via the Diffgeo mailing list)
I will talk about the Yamabe flow on compact spaces with conical singularities (and more generally: smoothly stratified spaces with iterated cone-edge metrics). I will present the classical Yamabe problem, and talk about why the Yamabe flow exists for all time in our setting. I will end by discussing convergence (and failure thereof). \n\nThis is joint work with Gilles Carron and Boris Vertman, arXiv:2106.01799 .\n\n\n
Giant Gravitons in twisted holography
Monday, 31.1.22, 16:15-17:15, BBB (link will be distributed via the Diffgeo mailing list)
I will talk about a correspondence between solutions of certain matrix equations and holomorphic curves in SL(2,C). The correspondence is motivated by twisted holography, which is a physical duality between a chiral algebra and topological B-model on SL(2,C). Determinant operators in the chiral algebra are dual to the Giant Graviton branes in the B-model. For each saddle of the correlation functions of determinants, we will define a spectral curve in SL(2,C), which we will identify with the worldsheet of the dual Giant Graviton brane.