We are glad to welcome Hideki Tsuiki in Swansea again. This Thursday we really enjoyed his talk on “Imaginary Cubes — Mathematics, Puzzle, Art and Education”.
Abstract: Imaginary cubes are three-dimensional objects with square projections in three orthogonal ways just as a cube has. How many different kinds of imaginary cubes can you imagine? In this talk we show that there are 16 kinds of minimal convex imaginary cubes which includes regular tetrahedron, cuboctahedron, and two objects that we call H and T. As we will explain, H and T have a lot of beautiful mathematical properties related to tiling, fractal, and higher-dimensional geometry, and based on these properties, the speaker has designed a puzzle, constructed three-dimensional math-art objects, and used them for educations at various levels from elemental school to graduate schools. In this talk, I will explain mathematics of imaginary cubes and show the activities I have been engaged in. I will carry a couple of copies of the puzzle and some of the math-art objects so that the audience can enjoy them while I am staying in Swansea.
Following the Summer School, we are really proud to host the 2nd Proof Society Workshop. The workshop was an opportunity to listen to a lot of interesting invited and contributed talks on proof theory and various areas of its application:
Adam Wyner: Computational Law – The Case of Autonomous Vehicles Yong Cheng: Exploring the incompleteness phenomenon Matthias Baaz: Towards a Proof Theory for Henkin Quantifiers Sonia Marin: On cut-elimination for non-wellfounded proofs: the case of PDL Gilles Dowek: Logical frameworks, reverse mathematics, and formal proofs translation Benjamin Ralph: What is a combinatorial proof system? William Stirton: Ordinal assignments correlated with notions of reduction Oliver Kullmann: Practical proof theory: practical versions of Extended Resolution Anton Setzer and Ulrich Berger on behalf of Ralph Matthes: Martin Hofmann’s case for non-strictly positive data types – reloaded Laura Crosilla: Philosophy of mathematics and proof theory Takako Nemoto: Recursion Theory in Constructive Mathematics Arno Pauly: Combinatorial principles equivalent to weak induction Antonina Kolokolova: The proof complexity of reasoning over richer domains Joost Joosten: The reduction property revisited Helmut Schwichtenberg: Computational content of proofs
Thanks to all the speaker and participants and we hope to see you all again soon.
We were glad to welcome Takako Nemoto, who joined us on the second day of the Summer School and gave her course on Reverse Mathematics.
As a treat, the participants of the Summer School had a trip to Rhossili and enjoyed a walk along the Welsh coastal path with stunning views. Big thanks to Arved Friedemann and Melissa Antonnelli for the beautiful photos.
We were lucky with both the lovely weather and the fact that Bay Campus is located right at the seafront, so the evening brought a nice treat for everyone in a form of a BBQ at the beach. Big thanks to Arnold, Faron for their grilling and Ulrich, Rosalie, Monika, Arved, Aled, Anton, Olga and everyone else who helped with the organisation.
Federico Cerutti from Cardiff University is visiting us this Thursday. He will give a talk on Probabilistic Logic Programming with Beta-Distributed Random Variables.
Abstract: We enable aProbLog—a probabilistic logical programming approach—to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.
Federico Cerutti's research activity is focused mainly on nonmonotonic reasoning (in particular argumentation theory), and on decision support with uncertainty and trust.
Philipp Schlicht is visiting us today from Bristol. He’ll give us an introduction to automatic structures in the theory seminar today (2pm, CoFo 201).
Abstract: Automatic structures were first studied by Khoussainov and Nerode in 1995. I will first give an introduction with a focus on automatic ordinals and groups and then talk about tree-automatic structures. In particular, I will mention some recent partial results with Jain, Khoussainov and Stephan on the isomorphism problem for tree-automatic ordinals.
My research focus is set theory -- in particular, descriptive set theory, forcing, large cardinals -- and computability. I work as a Marie Curie Research Fellow on the project 'Inner models and infinite computations' together with Prof. Philip Welch.