Termine

Abstract: In this semi-expository talk, I will explain the conjectural extension, due to Weissman, of the local Langlands correspondence to covers of reductive groups. Contrary to the usual local Langlands correspondence, certain fibers of this correspondence (called ?L-packets") are empty. I will explain my on-going joint work with Luozi Shi, which tells us where to look for the missing L-packets.

A hypersurface of a Lorentzian manifold is called null, if its induced metric is degenerate. In such geometries, classical some geometric concepts are unavailable and for this reason there is little knowledge about curvature flows in such spaces. Building upon a definition of mean curvature flow I developed with Henri Roesch few years ago, we extend and improve the analysis to constrained mean curvature flows, which will then enable us to foliate large classes of null hypersurfaces by surfaces of constant spacetime mean curvature. This is joint work with Wilhelm Klingenberg (Durham) and Ben Lambert (Leeds).

A hypersurface of a Lorentzian manifold is called null, if its induced metric is degenerate. In such geometries, classical some geometric concepts are unavailable and for this reason there is little knowledge about curvature flows in such spaces. Building upon a definition of mean curvature flow I developed with Henri Roesch few years ago, we extend and improve the analysis to constrained mean curvature flows, which will then enable us to foliate large classes of null hypersurfaces by surfaces of constant spacetime mean curvature. This is joint work with Wilhelm Klingenberg (Durham) and Ben Lambert (Leeds).

Eigenvarieties are parameter spaces of certain p-adic automorphic forms of varying weights. Part of the p-adic Langlands program aims to relate eigenvarieties to spaces of trianguline Galois representations, which contain all crystalline Galois representations. For definite unitary groups, this connection has been developed extensively. Our goal is to consider p-adic automorphic forms without self-duality conditions. Namely, we prove that many eigenvarieties for the group GL_n over a CM field have associated Galois representations which are trianguline. Our proof strategy is to realize such eigenvarieties inside a single eigenvariety for a unitary group, which might be of independent interest.

A Cartan subalgebra exists in every classifiable C*-algebra, and in particular, every classifiable C*-algebra which is stably finite, contains a C*-diagonal. However, not much is known about the existence of C*-diagonals in Kirchberg algebras. I will give an overview and explain how to construct Cantor spectrum C*-diagonals in the Cuntz algebra O_k when k finite.

The geometry of perceived color space is widely recognized as non-Euclidean, with the Riemannian framework commonly adopted for its analysis. However, existing evidence, such as the principle of diminishing returns, suggests that the color space may be globally non-Riemannian. In this work, I investigate the local inhomogeneities of the perceived color space under the Riemannian setting. Specifically, the local agreement between the Riemannian model and the color-difference function are evaluated. In numerical experiments, the accuracy of the parallelogram law is assessed -- a necessary condition for the local validity of the metric tensor. Furthermore, I introduce several measures of local anisotropy to quantify directional variations in perceived color distances and compute these measures within the chromatic planes of the CIELAB color space. My findings describe the spatial variation of Riemannian inhomogeneities and distance anisotropy, which can be used to construct adaptive spatial meshes and improve the accuracy of computations in color space. While the proposed techniques are demonstrated on the CIELAB color model with the $\Delta E_{2000}$ metric, they are generalizable to the discretization of arbitrary non-Euclidean metric spaces.

Science communication is a very large umbrella term for a variety of jobs and activities that could be very interesting for academics and people who want to leave academia. I will give an overview of what these jobs are and where to find them.