It's quiz time. Gather your team - or join one on the night - and come on down (or up) to the Common Room. There will be pizza and drinks for all, and prizes for the winning team.
Harry Stuart has once again written the quiz. For those of you who weren't at the department quiz in late 2023, you can expect a fun, general knowledge quiz with some extra puzzle-like elements to keep things interesting.
We discuss the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian N X N non-Hermitian random band matrices with a bandwidth W. Given W,N → ∞, we show that this behavior near the point in the bulk of the spectrum exhibits the crossover at W ∼√N: it coincides with those for Ginibre ensemble for W ≫√N, and factorized as 1 ≪ W ≪√N. The behavior of the correlation function near the threshold (W/√N →C) will be also discussed.
Compactifying topological actions using only de Rham forms fails to capture torsion sectors encoded in integral cohomology. Differential cohomology remedies this by combining integral characteristic classes, differential-form curvatures, and holonomy data into a single framework. In the context of deriving SymTFTs from M-theory, such a refinement is crucial for capturing background gauge fields for discrete 1-form global symmetries in the physical theory. In this talk, we will review the construction of differential cohomology and, time permitting, show how a refined Kaluza-Klein compactification leads to background gauge fields that encode these higher-form symmetries.