The talks of the Analysis workshop will be held in room K-1.56 of the King's Building.
Tea & Coffee will be offered in the Small Committee Room.
Invited speakers
Tuesday 7th 14.15 - 15.05: Andrea Mondino
15.05 - 15.30: Tea & Coffee [KB 0 Small Committee Room] 15.30 - 16.20: Olga Maleva 16.20 - 16.45: Tea & Coffee [KB 0 Small Committee Room] 16.45 - 17.30: Adam Harper |
Wednesday 8th 14.15 - 15.05: Maria Bruna
15.05 - 15.30: Tea & Coffee [KB 0 Small Committee Room] 15.30 - 16.20: Claudia Garetto 16.20 - 16.45: Tea & Coffee [KB 0 Small Committee Room] 16.45 - 17.30: Jonathan Hickman |
Andrea Mondino
Smooth and non-smooth aspects of Ricci curvature lower bounds Abstract. After recalling the basic notions coming from differential geometry, the colloquium will be focused on spaces satisfying Ricci curvature lower bounds.
The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the ‘80s and was pushed by Cheeger and Colding in the ‘90s who investigated the fine structure of possibly non-smooth limit spaces. |
Maria Bruna
Well-posedness of an integro-differential model for active matter Abstract. In this talk, we discuss a general strategy for solving space-periodic nonlinear evolution problems with an underlying integro-differential structure, where no natural maximum/minimum principle is available. This is motivated by the study of several macroscopic models of active matter (or self-propelled particles). We focus on a specific semilinear parabolic equation, which is the macroscopic model for a system of active Brownian particles with strong repulsive interactions. This is joint work with Martin Burger (FAU Erlangen-Nürnberg), Antonio Esposito (Oxford) and Simon Schulz (Wisconsin-Madison). |
Olga Maleva
Differentiability of typical Lipschitz functions Abstract. The classical Rademacher Theorem guarantees that every Lipschitz function between finite-dimensional spaces is differentiable almost everywhere. There are, however, null subsets S of R^{n} (with n>1) with the property that every Lipschitz function on R^{n} has points of differentiability in S; one says that S is a universal differentiability set (UDS).... |
Claudia Garetto
Hyperbolic Cauchy problems with multiplicities Abstract. In this talk I will discuss well-posedness of hyperbolic Cauchy problems with multiplicities and the role played by the lower order terms (Levi conditions). I will present results obtained in collaboration with Christian Jäh (Göttingen) and Michael Ruzhansky (QMUL/Ghent) on higher order equations and non-diagonalisable systems. |
Adam Harper
The distribution of short moving character sums Abstract. Sums of Dirichlet characters are one of the most studied objects in analytic number theory. In this talk I will describe some work on the distribution of \(\sum_{x < n \leq x+H} \chi(n)\), where \(\chi\) is a non-principal character mod \(q\) and \(x\) varies between 0 and \(q-1\). This problem was investigated by Davenport and Erd, and more recently by Lamzouri and others. Lamzouri conjectured that provided \(H \rightarrow \infty\) but \(H = o(q/\log q)\), the sum should have a Gaussian limiting distribution. I will present some results that shed more light on this conjecture. There are connections with classical work of Salem and Zygmund on random Fourier series. |
Jonathan Hickman
On convergence of Fourier integrals Abstract. In the first half of the 20th century great advances were made in understanding convergence of Fourier series and integrals in one dimension. Many natural convergence problems in higher dimensions are still poorly understood, however, despite great attention by many prominent mathematicians over the last five decades. In this gentle talk I will introduce the basic questions, describe their rich underlying geometry, and explain some recent developments in various joint works which have applied tools from incidence and algebraic geometry to these problems. |