The Gelfand--Kirillov dimension is a classical invariant that measures the size of smooth representations of p-adic groups. It acquired particular relevance in the mod p Langlands program because of the work of  Breuil--Herzig--Hu--Morra--Schraen, who computed it for the mod p cohomology of GL_2 over totally real fields, and used it to prove several structural properties of the cohomology. In this talk, we will present a simplified proof of this result, which has the added benefit of working unchanged for nonsplit inner forms of GL_2. This is joint work with Bao V. Le Hung.

In this seminar, we explore the quantitative convergence of wide deep neural networks with Gaussian weights to Gaussian processes, establishing novel rates for their Gaussian approximation. We show that the Wasserstein distance between the network output and its Gaussian counterpart scales inversely with network width, with bounds apply for any finite input set under specific non-degeneracy conditions of the covariances. Additionally, we extend our analysis to the Bayesian framework, by studying exact posteriors for neural networks, when endowed with Gaussian priors and regular Likelihood functions, but we also provide recent advancements in quantitative approximation of trained networks via gradient descent in the NTK regime. Based on joint works with A. Basteri, and A. Agazzi and E. Mosig.

Are you thinking of launching your own start-up or considering joining an early-stage company? Navigating the entrepreneurial landscape can be both exciting and challenging. Join Pete for an interactive exploration of the unwritten rules and hidden insights that can make or break a start-up journey.

Drawing from personal experience, Pete's talk will offer practical wisdom for aspiring founders and team members, revealing the challenges and opportunities of building a new business from the ground up.

Whether you're an aspiring entrepreneur, a potential start-up team member, or simply curious about innovative businesses, you'll gain valuable perspectives on the realities of creating something from scratch.

This isn't a traditional lecture – it will be a lively conversation that invites participants to learn, share, and reflect on the world of start-ups. Come prepared to challenge your assumptions and discover practical insights that aren't found in standard business guides.
 

Speaker: Professor Pete Grindrod