The seminars are held on Friday at 2pm-3pm
Term 1 2017/18 - Room MS.04
|6 Oct||Short talks by several members of the department||
Dan Král' - Uniqueness of extremal configurations
Andrzej Grzesik - Forcing cycles in oriented graphs
Alex Wendland - A generalisation of Cayley graphs
Péter Pach - Forbidden arithmetic progressions
Hong Liu - TBA
Agelos Georgakopoulos - TBA
|13 Oct||Gábor Pete (Rényi Institute and TU Budapest)||Noise sensitivity questions in bootstrap percolation|
|20 Oct||Paul Russell (Cambridge)||Monochromatic infinite subsets|
|27 Oct||Ben Barber (Bristol)||Isoperimetry in integer lattices|
|3 Nov||Eoin Long (Oxford)||TBA|
|10 Nov||Christian Reiher (Hamburg)||TBA|
|17 Nov||Johannes Carmesin (Cambridge)||Embedding simply connected 2-complexes in 3-space|
|24 Nov||Jakub Sosnovec (Warwick)||TBA|
|1 Dec||Andrew Granville (UCL)||TBA|
|8 Dec||Jakub Konieczny (Oxford)
It is well known that there is a finite colouring of the natural numbers such that there is no infinite set X with X+X (the pairwise sums from X, allowing repetition) monochromatic. It is easy to extend this to the rationals. Hindman, Leader and Strauss showed that there is also such a colouring of the reals, and asked if there exists a space 'large enough' that for every finite colouring there does exist an infinite X with X+X monochromatic. We show that there is indeed such a space. Joint work with Imre Leader.
The edge isoperimetric problem for a graph G is to find, for each n, the minimum number of edges leaving any set of n vertices. Exact solutions are known only in very special cases, for example when G is the usual cubic lattice on Zd, with edges between pairs of vertices at l1 distance 1. The most attractive open problem was to answer this question for the "strong lattice" on Zd, with edges between pairs of vertices at l∞ distance 1. Whilst studying this question we in fact solved the edge isoperimetric problem asymptotically for every Cayley graph on Zd. I'll talk about how to go from the specification of a lattice to a corresponding near-optimal shape, for both this and the related vertex isoperimetric problem, and sketch the key ideas of the proof. Joint work with Joshua Erde.
We characterise the embeddability of simply connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász and Wagner.