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Patterns in thick compact sets
We introduce a connection between Newhouse thickness and patterns through a variant of Schmidt’s game introduced by Broderick, Fishman and Simmons....
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A Game with Two Players Choosing the Coefficients of a Polynomial
We consider some versions of a game when two players Nora and Wanda in some order are choosing the coefficients of a degree d polynomial. The aim of...
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A note on badly approximable systems of linear forms over a field of formal series
We prove that the set of badly approximable systems of M linear forms in N variables over the field of formal power series is hyperplane absolute...
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Percentage
Up to now I have always taken the percentage as given and then calculated what it means in concrete terms, for example in euros and cents. That does...
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Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet
Bartel L. van der Waerden credits “Baudet” [sic] with conjecturing the result about monochromatic arithmetic progressions. Decades later, Van der...
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Leeds
We moved to Leeds at the start of August 2016, though we spent the first week of my appointment on a pre-arranged holiday. This was a rather active...
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Topics in Homogeneous Dynamics and Number Theory
This is a survey of some topics at the interface of dynamical systems and number theory, based on lectures delivered at CIRM Luminy, the University...
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François Le Lionnais and the Oulipo
“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in...
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On Certain Unusual Large Subsets Arising as Winning Sets of Some Games
Consider the space \(\mathbb {R}\) of real numbers. When...
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Gravitating to Google
Billions of people turn to Google to find information, but there is no guarantee that what you find there is accurate. As awareness of fake news has...
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“Sehr geehrter Herr Professor!” Proof Theory in 1949 in a Letter from Schütte to Bernays
We present a letter which Kurt Schütte sent in 1949 to his former de-facto PhD supervisor Paul Bernays. This letter contains an outline of the...
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On Non-dense Orbits of Certain Non-algebraic Dynamical Systems
In this paper, we manage to apply Schmidt games to certain non-algebraic dynamical systems. More precisely, we show that the set of points with...
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Badly approximable points on manifolds
This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport’s problem regarding badly approximable points...
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Metric Diophantine Approximation—From Continued Fractions to Fractals
Diophantine approximation is concerned with the quantitative study of the density of the rational numbers inside the real numbers. The Diophantine...