Room: 202 ed IV 
 
Abstract: Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are the main mathematical attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. APN and AB functions are important not only for the purpose of constructing new block ciphers in cryptography, but for other areas of computer science and discrete mathematics (such as combinatorics, sequence design, coding theory, design theory) in which APN functions correspond to some optimal objects. In this talk we address some longstanding problems related to APN and AB monomials.

More information available here.

We investigate an eigenvalue problem involving the 1-Laplacian operator on bounded domains with Neumann boundary conditions. The problem is not well posed in standard Sobolev spaces and must be studied in the space of functions of bounded variation, using tools from nonsmooth analysis. We give a geometrical characterization of this eigenvalue in terms of a relative isoperimetric problem. This connection allows us to characterize eigenfunctions in several relevant situations, including C^2 strictly convex domains, and to highlight both uniqueness and symmetry phenomena.

Abstract: In this talk I will give an overview of what is known about conjugacy growth and the formal series associated with it in infinite discrete groups. I will highlight how the rationality (or rather lack thereof) of these series is connected to both the algebraic and the geometric nature of groups such as (relatively) hyperbolic or nilpotent, and how tools from analytic combinatorics can be employed in this context. I will also mention results about the languages of conjugacy representatives in various groups.

Title: Self-Organized Spreading Dynamics near Criticality
Speaker: Viola Priesmann, Max Planck Institute for Dynamics and Self-Organization
& Georg-August-University Göttingen.

Date | Time: March 20, 2026 | from 14:00 to 14:50.

Place: Room 3 - Building Hangar II.

Abstract: Many living systems, from virus spread in societies to information spread in neural networks, are characterized by stochastic spreading of discrete events on complex networks. This spread then does not occur on a static network, but on an adaptive one, where the spreading proper influences the network’s coupling strength. This feedback loop between spreading activity and coupling strength can generate either stabilize and optimize information flow, or it can generate catastrophic resonance effects. We will investigate how these different phases emerge, and how they shape disease spread and information flow in complex networks.

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Title: Near-Threshold Stochastic Dynamics and Arbovirus Emergence in Non-Endemic Regions.

Speaker: Maíra Aguiar, Basque Center for Applied Mathematics (BCAM).

Date | Time: March 20, 2026 | from 14:50 to 15:40.

Place: Room 3 - Building Hangar II.

Abstract: Arboviruses such as dengue and chikungunya are increasingly reported in temperate and non-endemic regions, driven by climate variability, global mobility, and the expansion of competent mosquito vectors. Most risk assessments, however, rely on deterministic metrics like the basic reproduction number (R₀), assuming sustained transmission is unlikely when R₀ < 1. Under this framework, areas with low mosquito abundance, short transmission windows, and sporadic viral importation are considered low-risk.

We show that this approach can underestimate outbreak potential. Many non-endemic settings operate near the transmission threshold, where stochastic effects dominate and rare introductions can trigger substantial outbreaks despite subcritical average conditions. Using the 2024 dengue outbreak in Fano, Italy, we demonstrate that stochastic transmission models reproduce observed outbreak timing and magnitude, whereas deterministic models predict rapid extinction.
This mechanism extends beyond specific case studies: near-threshold stochasticity can generate outbreak patterns resembling supercritical dynamics wherever competent vectors and episodic viral introductions occur. Recognizing these dynamics is crucial for improving epidemic intelligence and public health preparedness. Integrating stochastic models with high-resolution mosquito surveillance, climate data, and human mobility enables more realistic outbreak risk assessments, informing early warning systems and targeted interventions in emerging epidemic settings.

In this talk, I will present a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions, the latter is better-behaved for initial data at lower regularities. In particular, the admissible regularities go beyond the $H^{-1}$-scale, which is a well-known threshold for KdV. As a byproduct, by reversing the gauge transform, we are able to improve on the theory for KdV. Additionally, our method is totally independent of the KdV complete integrability structure, and extends to other non-integrable models with quadratic nonlinearities. 
I will focus mainly on the derivation of the gauged equation: using tree graphs and some basic combinatorics, we will uncover a hidden structure which then gives rise to the announced gauge transform. This is joint work with Andreia Chapouto (CNRS, Monash University, Australia) and João Pedro Ramos (IMPA, Brazil).