We hosted an afternoon meeting at the University of St Andrews on Monday 2nd September 2019.
This was funded by the
Edinburgh Mathematical Society and speakers were
► Pablo Shmerkin (Universidad Torcuato Di Tella, Buenos Aires)
► Mike Whittaker (University of Glasgow)
► Alexia Yavicoli (Universidad de Buenos Aires)
The schedule was:
1.30pm - 2.30pm: Pablo Shmerkin. Some new results on the dimensions of distance sets.
Abstract: I will present recent some recent progress on the problem of estimating the (Hausdorff, packing) dimensions of distance sets of planar Borel sets. Partly based on joint work with T. Keleti.
2.30pm - 3.30pm: Alexia Yavicoli. On the dimension of sets of Furstenberg type.
Abstract: I will talk about joint work with K. Hera and P. Shmerkin, where we generalize a result of Katz and Tao/Bourgain on the dimension of 1/2-Furstenberg sets to a more general class of Furstenberg-type sets.
3.30pm - 4.00pm: Coffee break.
4.00pm - 5.00pm: Mike Whittaker. Aperiodic tilings: from the Domino problem to aperiodic monotiles.
Abstract: Almost 60 years ago, Hao Wang posed the Domino Problem: is there an algorithm that determines whether a given set of square prototiles, with specified matching rules, can tile the plane? Robert Berger proved the undecidability of the Domino Problem by producing a set of 20,426 prototiles that tile the plane, but any such tiling is nonperiodic (lacks any translational symmetry). This remarkable discovery began the search for other (not necessarily square) aperiodic prototile sets, a finite collection of prototiles that tile the plane but only nonperiodically. In the 1970s, Roger Penrose reduced this number to two. Penrose's discovery led to the planar einstein (one-stone) problem: is there a single aperiodic prototile? In a crowning achievement of tiling theory, the existence of an aperiodic monotile was resolved almost a decade ago by Joshua Socolar and Joan Taylor. My talk will be somewhat expository, and culminate in both a new direction in aperiodic tiling theory and a new aperiodic monotile.
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