Past Events

In this talk I will present a series of works derived from the framework of physics inspired graph neural networks (GNN). The central premise is a GNN can be seen as the discretisation of a learnable dynamical system over a graph, this allows to...

An n-by-n matrix A=[a_{ij}] is said to be a pairwise comparison matrix (PC matrix) or a reciprocal matrix if it is positive and a_ij=1/a_ji, for all i,j=1,...,n. If, in addition, a_ika_kj=a_ij for all i,j,k, the matrix is said to be consistent. There...

A ring spectrum (a.k.a. a multiplicative cohomology theory) E is complex-orientable if every complex vector bundle admits a Thom class in E . While many familiar spectra are complex-orientable, notable examples fail to be so — such as real K-theory...

For a complex projective variety, the Lefschetz standard conjectures predict the existence of algebraic self-correspondences that are inverse to the hard Lefschetz isomorphisms. They have broad implications for Hodge theory and the theory of motives...

Triangular modular curves are a generalization of modular curves and arise as quotients of the complex upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves naturally parameterize hypergeometric abelian varieties...

The Turan density of a forbidden hypergraph F is the largest edge density a large hypergraph H can have without containing any copy of F, and determining this number for various F is a notoriously difficult problem. One on-ramp to this question (from...

‘Reef halos’ are rings of sand, barren of vegetation, encircling reefs. However, the extent to which various biotic (e.g., herbivory) and abiotic (e.g., temperature, nutrients) factors drive changes in halo prevalence and size remains unclear. The...

Fix a positive integer n and a graph F . A graph G with n vertices is called F -saturated if G contains no subgraph isomorphic to F but each graph obtained from G by joining a pair of nonadjacent vertices contains at least one copy of F as a subgraph...

In this talk we will introduce the modular method, the approach followed by Wiles to prove Fermat’s Last Theorem. We will explain the role of elliptic curves, modular forms, and Galois representations in this framework, and discuss how the method has...

The fact that |z|.|w| = |zw| for complex numbers z and w leads to a "sums of squares identity of type (2,2,2)", namely [x1^2 + x2^2] [y1^2 + y2^2] = [x1y1 - x2y2]^2 + [x1y2 + x2y1]^2. Similarly, quaternion and octonion numbers lead to analogous...