Past Events

Products of permutations are used to model problems in fields ranging from representation theory and algebraic geometry to topological graph theory. I will show how probability can be used to study such problems, with a focus on how graphs may be...

I will describe a new approach for exhaustively generating combinatorial objects by combining a satisfiability (SAT) solver with an isomorph-free exhaustive generation method such as orderly generation. The SAT solver is able to limit the search to...

What is the structure of the set of the last few points visited by a random walk on a graph? We show that on vertex-transitive graphs of bounded degree, this set is decorrelated (it is close to a product measure in total variation) if and only if a...

We improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowing a smooth truncation inside the procedure, and an estimate due to Barban-Vehov and...

What happens to a progressively dilating body when folding the space in which it lives? For a start, we shall examine the problem in a Euclidean context, surveying results of Randol and Strichartz through a classical Fourier-analytic approach...

For r ≥ 1, a graph has r-friendship property if every pair of vertices has exactly r common neighbours. The motivation for this definition is from the friendship theorem, which is on the graphs with 1-friendship property. The friendship theorem...

I will describe a new approach for exhaustively generating combinatorial objects by combining a satisfiability (SAT) solver with an isomorph-free exhaustive generation method such as orderly generation. The SAT solver is able to limit the search to...

We introduce a model of a controlled random process. In this model, the vertices of a hypergraph are ordered randomly and then revealed, one by one, to an algorithm. The algorithm must decide, immediately and irrevocably, whether to keep each...

It is well-known that a function 𝑢=𝑢(𝑡,𝑥)u=u(t,x) describing the behavior of acoustic or electromagnetic waves in time and space can often be decomposed as an infinite sum 𝑢(𝑡,𝑥)=∑𝑛=1∞𝑐𝑛(𝑡)𝜓𝑛(𝑥) ,u(t,x)=∑n=1∞cn(t)ψn(x) , where each term in the sum is...

In general Topological Quantum Field Theories are very diverse, but we may focus on low dimensional cases. As a starting point, we'll give a complete classification of 1-dimensional TQFTs. To this end, I'll present a review of dualization in a...