Scientific Organisers
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Jonathan Fraser, University of St Andrews
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Xiong Jin, University of Manchester
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Tom Kempton, University of Manchester
About:
Fractal geometry is a vibrant and important area of mathematics. Roughly speaking, fractals are objects which display complex features on a large range of scales, such as stock market fluctuations, the surface of a lung, or the distribution of stars in the galaxy.
This workshop brought together researchers with common interests in fractals and related areas such as ergodic theory, geometric measure theory, and analysis. The aim of the workshop was to stimulate collaboration and research activity between the various groups in the UK, encourage and support the work of early career researchers in this area, and provide a platform for dissemination of work in fractal geometry.
It was also an opportunity to celebrate the 70th birthday of Kenneth Falconer and acknowledge his many deep contributions to Fractal Geometry.
Funding
We are grateful for the financial support from the Glasgow Mathematical Journal Learning and Research Support Fund, Edinburgh Mathematical Society Fund and the Royal Society of Edinburgh Fund.
Programme:
| MONDAY 3 July 2023 | ||
| Registration and Refreshments | ||
| Welcome and Housekeeping | ||
| Pertti Mattila, University of Helsinki | Hausdorff dimension and principal values of singular integrals | |
| Refreshments | ||
| Julien Barral, Sorbonne Paris Nord University | Sparse sampling and dilation operations on a Gibbs weighted tree, and multifractal formalism | |
| Lunch | ||
| Peter Varju, University of Cambridge | Quantitative aspects of Bourgain's discretized sum-product theorem | |
| Refreshments | ||
| Tuomas Orponen, University of Jyväskylä | Projections, Ahlfors-regularity, and the ABC sum-product problem | |
| Welcome Reception, hosted at ICMS | ||
| TUESDAY 4 July 2023 | ||
| Mark Pollicott, University of Warwick | The dimension of the Feigenbaum attractor. | |
| Alexia Yavicoli, The University of British Columbia | Thickness and a Gap Lemma in $\mathbb{R}^d$ | |
| Refreshments | ||
| Sascha Troscheit, University of Oulu | Metric spaces in random geometry: dimension theory and applications | |
| Lunch | ||
| Henna Koivusalo, University of Bristol | Dimension of \tau-badly approximable points as a subset of \tau-well approximable points | |
| Refreshments | ||
| Lightning talks (5 mins) | ||
| WEDNESDAY 5 July 2023 | ||
| Pablo Shmerkin, University of British Columbia | Some recent developments on the Falconer distance set problem | |
| Han Yu, University of Warwick | Arithmetic properties of missing-digit numbers | |
| Refreshments |
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| Tamas Keleti, Eötvös Loránd University, Budapest | Lipschitz images of the Cantor set | |
| Kenneth Falconer, University of St Andrews | Some problems in fractal geometry | |
| Lunch | ||
| THURSDAY 6 July 2023 |
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| De-Jun Feng, The Chinese University of Hong Kong | Dimensions of arithmetic sums of typical self-affine sets | |
| Ariel Rapaport, Technion – Israel Institute of Technology | A new result on the dimension of diagonal self-affine sets and measures. | |
| Refreshments |
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| Thomas Jordan, University of Bristol | The shrinking target problem for certain self-affine sets. | |
| Lunch |
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| Rhiannon Dougall, Durham University | Proving a ratio limit theorem for random walks on groups using the variational principle. | |
| Refreshments |
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| Natalia Jurga, University of St Andrews | Hausdorff dimension of the Rauzy gasket | |
| Drink reception | ||
| Conference dinner | ||
| FRIDAY 7 July 2023 |
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| Martina Zahle, Institute of Mathematics, University of Jena | Geometric Parameters For Different Classes Of Fractals | |
| Steffen Winter, Karlsruhe Institute of Technology | Regularity properties of parallel volume and parallel surface area | |
| Refreshments |
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| Jiaxin Hu, Tsinghua University | A dichotomy on the self-similarity of graph-directed attractors |
