Past Events

Suppose mu is a probability measure which is shift invariant on {0,1}^{Z^d} and we know that for almost every configuration x in {0,1}^{Z^d} there are connected components of 1s which are infinite. In this talk, we will follow a paper by Burton and...

A random planar map is a canonical model for a discrete random surface which is studied in probability, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2d Riemannian manifold with roots...

Measuring the impact of scientific articles is important for evaluating the research output of individual scientists, academic institutions, and journals. While citations are raw data for constructing impact measures, there exist biases and potential...

Abstract We say that \(G\to (F, H)\) if, in every edge colouring \(c : E(G) \to \{1, 2\}\), we can find either a 1-coloured copy of \(F\) or a 2-coloured copy of \(H\). The well-known Kohayakawa-Kreuter conjecture states that the threshold for the...

For k a perfect field of characteristic p > 0 and G a split reductive group over k with p a non-torsion prime for G, we compute the mod p motivic cohomology of the geometric classifying space BG_(r), where G_(r) is the rth Frobenius kernel of G. Our...

A neural code C on n neurons is a collection of subsets of the set of integers {1,2,...,n}. Usually, C is paired with a collection of n open subsets of some Euclidean space, with C encoding how those open sets intersect. A central problem concerning...

TBC

We consider the restriction to the unit circle of random degree-n polynomials with iid normalized coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows...

A classical problem in algebraic geometry asks what rational cuspidal curves can be realised in the complex projective plane. In the last few years some substantial advancement regarding this problem have been made, also based on the methods of...

In 1958, Fine and Herstein proved that the an n by n matrix over the finite field F_q has a probability of q^{-n} to be nilpotent. A clever application of this result can lead to the formula \sum_{H: abelian p-group} 1/|Aut(H)| = 1/((1-p^-1)(1-p^-2)...