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.  

Bertrand Gauthier

19/03/2026

Coordinate descent and information-geometry-driven graph sequential growth 

The conditional dependence structure of a multivariate Gaussian vector is encoded by the non-zero entries of its precision matrix (that is, the inverse of its covariance matrix). This structure can naturally be described by a graph, and recovering this graph from observations is the fundamental motivation behind graphical modelling. In graphical lasso for instance, graph recovery is achieved by minimising the negative log-likelihood of the observations in combination to a sparsity-inducing regularisation term. 

In this talk, we will present a class of regularisation-free approaches for graphical modelling based on the sequential growth of initially edgeless graphs. Building on the analogy between edge activation and coordinate update, we will characterise the fully-corrective descents corresponding to information-optimal growths, and discuss numerically efficient strategies for the approximation of such growths. The ability of the proposed procedures to reliably extract sparse graphs while limiting the number of false detections will be demonstrated on a series of examples. We will also illustrate how the considered framework can be combined with the notion of stability selection to assist the extraction of relevant graphical models in practical situations. 

This is a joint work with Harry Bond (Cardiff University) and Kirstin Strokorb (University of Bath); a preprint is available at https://arxiv.org/abs/2601.22106 

Khoa Le

23/04/26

Rough stochastic differential equations 

Rough stochastic differential equations are differential equations driven by a Brownian motion and a rough path. It is a simultaneous generalization of Itô’s theory of stochastic and Lyons’ theory of rough differential equations. The interest in such a unification comes from a variety of applications, including pathwise stochastic filtering-control and the conditional analysis of stochastic systems with common noise. I will discuss some recent progress and open problems along this line of research.

Natashe Blivic

30/04/26

Permutation Patterns

In the area of combinatorics known as ‘permutation patterns’, seemingly innocuous questions can conceal a surprising degree of difficulty, giving rise to combinatorial problems that range from trivial to unsolved (despite decades of work). In this talk, we will explore several ways in which permutation pattern questions interface with probability. We will examine generalizations of known processes, propose new constructions at this interface, and put forward several conjectures. The techniques we employ exploit natural connections between consecutive permutation patterns and posets. In particular, we examine posets arising from packings of consecutive permutation patterns and show that they lead to natural classification problems while also yielding new enumerative results, including explicit integer sequences, generating functions, integrals and matrix products. This is based on forthcoming joint work with Slim Kammoun and Einar Steingrimsson. 

Sabine Jansen

14/05/2026

Duality and intertwining for continuum interacting particle systems

Studying the time-evolution of a many-particle system is a difficult task. For some interacting particle systems in Z^d, duality and intertwining allow to map the time evolution of one- or two-point correlation functions of a many-particle system to the time evolution of a one- or two-particle system, a considerable simplification. Often duality functions are products of univariate orthogonal polynomials, one for each site of the lattice. In the talk I will explain how to

generalize these dualities, and the algebraic approach with representations of Lie algebras, to particles in R^d. This brings in Lévy point processes and infinite-dimensional orthogonal polynomials.

Based on joint work with Simone Floreani, Frank Redig and Stefan Wagner. 

Liu Peng

21/05/2026

Robust distortion risk metrics and portfolio optimization

We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are  characterized by four key features of the underlying  distribution: mean, variance, unimodality, and Wasserstein distance to a reference distribution.

We first examine a broad class of distortion functions, assuming only finite variation and imposing neither continuity nor monotonicity. This class includes important examples such as the Gini deviation, the mean–median deviation, and inter-quantile differences. When the uncertainty set is defined by a fixed mean, variance, and Wasserstein distance, we derive the worst- and best-case values of the distortion risk metric and identify the corresponding extremal distributions. 

We then impose an additional unimodality constraint.  In this case, for absolutely continuous distortion functions, we again characterize the worst- and best-case values and explicitly determine the optimal distributions attaining these bounds. Moreover, an algorithm is developed to compute sharp upper bounds and the worst-case quantiles.

We apply our results to a robust portfolio optimization problem of interest.