I will discuss polynomial approximation problems on the n-dimensional hypercube, focusing on quantitative estimates of the approximation error as n grows. This topic represents a burgeoning area in the analysis of …

We consider a sparse Erdős–Rényi graph G(n,λ/n) where each edge is assigned a random and independent signed weight. For two uniformly chosen vertices, we study the joint distribution of the total weights and …

In their 2022 work, Bowden, Hensel, and Webb associate to a surface its fine curve graph, which is a Gromov hyperbolic space. The homeomorphisms of the surface act as isometries on the fine curve graph, either …

Modeling the impact of co-variates upon the transition from one hidden state to another may improve both estimation and prediction in hidden hidden Markov and semi-Markov models. However, the problem of the …

Quid of dynamical degrees ? The dynamical degree of a polynomial endomorphism f of K^n measures the exponential growth of its degree under iteration. Using weighted degrees, I will construct a space of Tame …

Knot theory has a long history yet remains a vibrant field today. One of its central questions is how to distinguish knots up to isotopy. In this talk, we focus on combinatorial approaches. We study knots through …

In 1913, De Franchis proved that the number of surjective holomorphic maps from $X$ to $Y$ is finite when $X$ and $Y$ are compact Riemann surfaces and $Y$ has genus at least 2. This result was extended to higher …