Cubulating a group means finding a proper cocompact action on a CAT(0) cube complex. I will describe how cubulating a group tells us some nice properties of the group, and explain a general strategy for finding cubulations.

In this talk I will introduce Hilbert's 10th Problem (H10) and the model-theoretic notions necessary to explore this problem from the perspective of mathematical logic. I will give a brief history of its proof, talk a little about its connection to decidability and definability, then close by speaking about generalisations of H10 - what has been proven and what has yet to be discovered.

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees d=1, 2, 3. For each d we prove the hyperbolicity of all but (perhaps) finitely many Jensen polynomials. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function. This result can be thought of as a proof of GUE for the Riemann zeta function in derivative aspect. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.
 

We will see some results and conjectures on the zeta and multizeta values in the function field context, and see how they relate to homological-homotopical objects, such as t-motives, iterated extensions, and to Hopf algebras, big Galois representations.

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about the numerical error. In this paper we propose a novel statistical model for this numerical error set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging.

This talk is associated with the NBFAS meeting.

We discuss the quantitative asymptotic behaviour of operator semigroups. Batty and Duyckaerts obtained upper and lower bounds on the rate of decay of a semigroup given bounds on the resolvent growth of the semigroup generator. They conjectured that in the Hilbert space setting and for the special case of polynomial resolvent growth it is possible to improve the upper bound so as to yield the exact rate of decay up to constants. This conjecture was proved to be correct by Borichev and Tomilov, and the conclusion was extended by Batty, Chill and Tomilov to certain cases in which the resolvent growth is not exactly polynomial but almost. In this talk we extend their result by showing that one can improve the upper bound under a significantly milder assumption on the resolvent growth. This result is optimal in a certain sense. We also discuss how this improved result can be used to obtain sharper estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary. The talk is based on joint work with J. Rozendaal and R. Stahn.

This is part of a meeting of the North British Functional Analysis Seminar

In this talk I will present some new $L_p$-$L_q$-Fourier multiplier theorems which hold for operator-valued symbols under geometric restrictions on the underlying Banach spaces such as (Fourier) (co)type. I will show how the multiplier theorems can be applied to obtain new stability results for semigroups arising in evolution equations. This is based on joint work with Jan Rozendaal (ANU, Canberra).

This is part of a meeting of the North British Functional Analysis Seminar.

In this talk I will present an overview on generalized square functions in Banach spaces and some of their recent uses in “Analysis in Banach Spaces”. I will introduce the notions of $R$-boundedness and $\gamma$-radonifying operators and discuss their origins and some of their applications to harmonic analysis, functional calculus, control theory, and stochastic analysis.