201718
The seminars are held on Friday at 2pm3pm 
Organisers:

Term 1 2017/18  Room MS.04
Date  Name  Title 

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 2complexes in 3space 
24 Nov  Jakub Sosnovec (Warwick)  TBA 
1 Dec  Andrew Granville (UCL)  TBA 
8 Dec  Jakub Konieczny (Oxford) 
TBA 
Noise sensitivity questions in bootstrap percolation (Gábor Pete)
Monochromatic infinite subsets (Paul Russell)
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.
Isoperimetry in integer lattices (Ben Barber)
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 Z^{d}, with edges between pairs of vertices at l_{1} distance 1. The most attractive open problem was to answer this question for the "strong lattice" on Z^{d}, 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 Z^{d}. I'll talk about how to go from the specification of a lattice to a corresponding nearoptimal shape, for both this and the related vertex isoperimetric problem, and sketch the key ideas of the proof. Joint work with Joshua Erde.
Embedding simply connected 2complexes in 3space (Johannes Carmesin)
We characterise the embeddability of simply connected 2dimensional simplicial complexes in 3space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lovász and Wagner.