Abstracts

Gabriela Jeronimo

29/01/2026

Algorithmic equidimensional decomposition of affine varieties defined by sparse polynomials

The study of polynomial systems with specific structure has gained significant attention in the last decades. In particular, systems of sparse polynomials (namely, polynomials with nonzero coefficients only at prescribed sets of monomials) have become a central topic in the computer algebra framework. In this talk, we will discuss recent work on polynomial system solving in the sparse setting, with a special focus on a new symbolic probabilistic algorithm that, given a system of sparse polynomials, characterizes completely all the equidimensional components of the set of their common zeros. This is joint work with María Isabel Herrero (Universidad Torcuato Di Tella, Argentina) and Juan Sabia (Universidad de Buenos Aires and CONICET, Argentina).

Panagiotis Spanos

19/02/2026

Criticality in Spread-Out Percolation

In this talk we discuss a special model of percolation called spread-out percolation. Let  G be a vertex-transitive graph equipped with the graph metric and let  r be a range parameter. The spread-out lattice  is the graph G_r with the same vertex set as G, where two vertices are connected by an edge whenever their distance in G  is at most  r .

In joint work with Tointon, we study the asymptotic behavior of the critical parameter for the existence of an infinite cluster as the range  tends to infinity, for vertex-transitive graphs of superlinear polynomial growth. The spread-out model was originally introduced for Z^d by Hara and Slade in the study of mean-field phenomena. We will discuss connections with critical exponents and branching random walks and present several open problems.

Michael Hinz

05/03/2026

Non-local differential complexes

On smooth manifolds, the deRham complex is a powerful tool, its cohomology encodes topological information. In the Riemannian case the associated elliptic operator is the (Hodge) Laplacian. On metric measure spaces Laplacians are notoriously difficult to construct, but non-local operators, e.g., bounded integral operators or (truncated) fractional

Laplacians, are often easy to define. We talk about differential complexes associated with such non-local operators, their cohomology encodes metric information. We briefly comment on nonlocal Hodge Laplacians, nonlocal-to-local convergence, removable sets, and a deRham theorem in the compact manifold case. These results are joint with Jörn Kommer. If time permits, we will mention latest results, joint with Angelica Pachon, on probabilistic representations for discrete Hodge Laplacians. 

Alexander B. Vladimirsky 

12/03/2026

Stochastic switching systems: abrupt context changes and structured uncertainty 

Piecewise-deterministic Markov processes (PDMPs) provide an excellent framework for modelling non-diffusive random perturbations. They are particularly useful for modelling abrupt changes in global environment (e.g., an onset of El Niño or an outcome of elections), changes in capabilities of the controlled systems (e.g., a partial breakdown of a robot on Mars), or uncertainty due to time-structured data acquisition (e.g.,  a just discovered location of an emergency). Both the optimality and robustness of system performance require advance planning, using statistical information about possible and likely context switches to prepare before those switches actually happen. (E.g., should a fully functional rover take a shorter risky path on Mars if it might lead to a breakdown? Should it ever stop and run diagnostics along that path to reassess the likelihood of such breakdowns? Should a foraging animal plan to visit the most food-rich part of the forest if an encounter with predators is likely along the way? How much of a detour might be justified? Should an idle ambulance be repositioned in between the emergency calls to improve the response time to the next call? ) In this talk, I will provide an introduction to the challenges of controlling PDMPs, illustrating them with simple examples motivated by robotics, sailboat racing, behavioral ecology, and surveillance-evasion applications.