Join us for our first event of term to discuss those topics which are slightly taboo. We’ll be talking about periods, pregnancy, chronic illness, gender identity... This event is open to all but we will be taking extra steps to make sure it is a safe space for everyone.
Please note unusual day and room.
Motivated by the SYZ conjecture, it is expected that $G_2$ and Spin(7)-manifolds also admit calibrated fibrations. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need that the fibration property is stable under deformation of the ambient Spin(7)-structure. Here the main difficulty lies in the analysis of the singular fibres. In this talk I will present a stability result for fibrations with conically singular Cayleys modeled on the complex cone $\{x^2 + y^2 + z^2 = 0\}$ in ${\mathbb C}^3$.
The microbiome is much in the news as the latest key to understanding our health. There is much research to be done and whether Kefir is the answer, who knows, but in the meantime why not pop down to the Café on Wednesday (24th) and try it?
Wednesday is also 'Stop Food Waste Day' in the Café. Look out for information downstairs.
The talk is based on joint work with Lasse Grimmelt. We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms to study Poincaré series over congruence subgroups while keeping track of interactions between multiple orbits. This approach offers increased flexibility over the widely used sums of Kloosterman sums techniques. We give applications to correlations of the divisor function twisted by periodic functions and the fourth moment of Dirichlet $L$-functions on the critical line.