# Magne Haveraaen visiting Swansea

Magne Haveraaen from the University of Bergen is visiting our Department in May-July 2018.

# Alison Jones passes PhD Viva

Congratulations, Alison!

# Amir Tabatabai and Rahele Jalali visiting

Amir Tabatabai and Rahele Jalali, both PhD students at the Institute of Mathematics of the Czech Academy of Sciences under the supervision of Pavel Pudlak, are visiting Swansea University 13 Nov – 6 Dec 2017. Amir will give a talk on Computational Flows in Arithmetic on 16 November. More information: A computational flow is a pair consisting of a sequence of computational  problems of a certain sort and a sequence of computational reductions among them. In this talk we will explain the basics of the theory of computational flows and how they make a sound and complete interpretation for bounded theories of arithmetic. This property helps us to decompose a first order arithmetical proof to a sequence of computational reductions by which we can extract the computational content of the low complexity statements in some bounded theories of arithmetic such as  .

# Arno Pauly joining our department

We would like to welcome Arno Pauly, who has recently joined the computer science department here in Swansea. Today he is going to give a talk on Noncomputability in analysis as a part of our Computational Foundry Seminar Series. More information: Many theorems in analysis state the existence of a certain object depending on some parameter. Each such theorem has an associated computational task: Compute the object from the parameter. From the viewpoint of a constructivist, these tasks are intricately linked to the meaningful truth of the theorems. From a pragmatic perspective, the applicability of a theorem to fields like physics or economics is tied to the solvability of the associated computational task.

# Break through result

Oliver Kullmann and his co-authors Marein Heule, and Victor Marek used SAT-solving techniques to solve a long standing open problem in Ramsey Theory known as the Boolean Pythagorean Triples Problem: It is impossible to divide the natural numbers into two parts such that none of the parts contains a Pythagorean triple, that is numbers a,b,c such that a^2+b^2=c^2. In fact, they found a smallest number N (namely N = 7825) such that the set {1,…,N} cannot be divided into two parts as described above. Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek. Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer. In Nadia Creignou and Daniel Le Berre (Ed.), Theory and Applications of Satisfiability Testing – SAT 2016. (pp. 228-245). Springer.

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