Hideki Tsuiki visiting Swansea

Professor Hideki Tsuiki from Kyoto University is visiting Swansea University from 22nd to 24th of January. Yesterday, he gave a talk on Coinductive View of Shadows of 3D Fractals. 

The talk did not only give insight into a fascinating area of research, but was also entertaining. You may want to check out some of Prof. Tsuiki's videos, e.g. https://www.youtube.com/watch?v=VsFD37f-2ck  

Elvira Mayordomo visiting Swansea

Elvira Mayordomo is visiting us this week. Today she gave a talk as a part of our seminar series.

Title: On information theory in geometric measure theory

Abstract

Effective and resource-bounded dimensions were defined by Lutz in 2003 and have proven to be useful and meaningful for quantitative analysis in the contexts of algorithmic randomness, computational complexity and fractal geometry.

The point-to-set principle (PSP) of J. Lutz and N. Lutz (2018) fully characterizes Hausdorff and packing dimensions in terms of effective dimensions in the Euclidean space, enabling effective dimensions to be used to answer open questions about fractal geometry, with already an interesting list of geometric measure theory results.

In this talk I will review the point-to-set principles focusing on recent applications and extensions and presenting open questions as well as further application opportunities.

Research visit

Thomas Powell and Davide Barbarossa (Bath University) are visiting Swansea this week. This afternoon Thomas will give a talk on the "Rates of convergence for stochastic processes" as a part of our seminar series.  

Abstract: I will present two ongoing projects in the new area of proof mining  in stochastic optimization, each representing a distinct inroad into the area.  First, I will give an account of recent work with Morenikeji Neri that focuses on convergence proofs based on martingales: This quantitative study of  martingale convergence has resulted in several variants of the famous  Robbins-Siegmund theorem that come equipped with numerical information, with applications including stochastic quasi-Fejer monotone sequences and gradient-descent type algorithms. Second, I will report on some work in progress with Nicholas Pischkeon a new stochastic alternating Halpern-Mann scheme with noise terms: In addition to new convergence results (both qualitative and quantitative), this project has led to an interesting application in reinforcement learning, demonstrating that the techniques of proof mining are relevant for current research in the mathematics of artificial intelligence.

GoSCAI 2024

Arnold, Monika, Bertie and Jay went to Grenoble 1-4 July to attend the GoSCAI workshop and discussion of research opportunities with Grenoble.