Junior Seminars

Taming Adaptive Security and New Access Structures in Evolving Secret Sharing

by Sara Giammusso

February 25, 2026 – 14:00 – Room B (Physics Dept.)

Abstract. Secret sharing is a fundamental cryptographic primitive that allows a secret to be distributed among multiple parties so that only authorized subsets can reconstruct it. Traditional secret sharing schemes assume that the set of participants and the access policy are fixed in advance. However, in many real-world scenarios —such as dynamic networks or long-lived systems— participants may join over time, and the access structure may not be known beforehand. Evolving secret sharing, introduced by Komargodski, Naor, and Yogev, addresses this challenge by allowing a dealer to distribute shares online, without knowing the total number of participants or the final access structure in advance, and without ever modifying previously distributed shares. In this seminar, we study evolving secret sharing in the computational setting, where security is required only against computationally bounded adversaries. We present new constructions of evolving secret sharing schemes for rich classes of access structures, including dynamic weighted threshold policies and all evolving monotone functions in NP. Furthermore, we initiate the study of adaptive security in this setting, where an adversary can choose which participants to corrupt as the system evolves. We show how to achieve adaptive security for dynamic weighted thresholds and for evolving monotone circuits. Overall, this work significantly expands the scope of evolving secret sharing and provides new tools for building secure systems in dynamic and unpredictable environments.

Functional Inequalities in Euclidean and Non-Euclidean Settings

by Lorenzo D'Arca

January 28, 2026 – 14:00 – Room B (Physics Dept.)

Abstract. This seminar presents an overview of Hardy type inequalities and their role in analysis and geometry. After recalling the classical Euclidean Hardy inequality and its connection with the uncertainty principle, we briefly outline the main ideas underlying its proof. We then discuss why Hardy type inequalities become more delicate in non-Euclidean and degenerate frameworks, focusing on the Heisenberg group as a prototypical example. Particular attention is given to the role of geometric features such as degeneracy and anisotropy. We conclude by describing a unified approach that extends Hardy type inequalities to more general geometric contexts and to \(L^p\) settings.

Single Image Super Resolution via Wavelets and Transformers

by Pietro Cestola

December 3, 2025 – 14:00 – Room B (Physics Dept.)

Abstract. Single Image Super Resolution (SISR) is an ill-posed problem: the lack of an intrinsic notion of “same content” across resolutions motivates its statistical formulation. We begin by clarifying this viewpoint and its relevance to our medical imaging setting. We then present an approach based on the additive refinement of the wavelet coefficients of a classically upsampled image. Building on this formulation, we introduce a super-resolution architecture that implements it by combining two-dimensional discrete wavelet transforms with the Swin Transformer. We conclude by discussing the training strategy and the use of knowledge distillation, along with quantitative and qualitative results on medical datasets.

From Kauffman States to BMS States: A Framework in Combinatorics and Quiver Representation Theory

by Michele Matteucci

November 5, 2025 – 14:00 – Room B (Physics Dept.)

Abstract. Inspired by recent works exploring the interconnections between formal knot theory and quiver representation theory, we introduce new combinatorial objects generalizing the notion of a Kauffman state. A BMS state consists of a graph \(G\) embedded in an orientable surface, endowed with a nonnegative weight on the edges and a pair of integer-valued functions on the set of angles satisfying a balancing condition. Such an object is naturally associated with a representation of the Jacobian algebra of the medial quiver of \(G\). After defining two symmetric notions of partial order for BMS states, we study the structure of the category in which these objects live, in connection with the lattices of subrepresentations arising from them. Furthermore, we address questions of decomposability. Finally, we discuss polynomial aspects and outline some open problems currently under investigation.

Junior Seminars

Academic Year 2024/25

Partecipants.

• Wei Chen – On tangent curves
• Sara Galatro – Efficient certifying algorithms for linear classification
• Rocco Brunelli – Machine learning meets differential cryptanalysis
• Simone Marrocco – Hamiltonian methods for the Kirchhoff equation
• Mario Morellini – Nonlinear spin system
• Martina Miseri – The Prym-canonical Clifford index
• Lorenzo Baroni – Linear flow on the infinite torus

Junior Seminars

Academic Year 2023/24

Partecipants.

• Zakaria Brahimi – Cubic fourfolds: some rational examples
• Adrien Ragot – Realisability: from constructive proofs to program specification
• Muhammad Usman – 3D Human Pose Estimation: Real-time Performance and Applications
• Federico Pieroni – An overview on Coble surfaces, their moduli, and the Coble conjecture
• Luca Ferrigno – Unlikely Intersections in diophantine geometry
• Elena Sammarco – The rationality problem for the cubic fourfold

Junior Seminars

Academic Year 2022/23

Organised by Armando Capasso and Elia Onofri
with the participation of Martina Miseri and Bruno Renzi.

Partecipants.

• Armando Capasso – What is... a Higgs Bundle?
• Elia Onofri – How machine learning can improve macroscopic models for traffic state estimation and forecast
• Simone Pesatori – Coincident root loci and the moduli space of rational elliptic surfaces
• F. C. Simon Schirren – Virtual Cycles: An Introduction
• Bruno Renzi – The dimer model: phase diagram and universality

G.T.M. – General Topics in Mathematics (informal seminars)

Academic Year 2021/22

Organised by Armando Capasso and Elia Onofri

Partecipants.

• Elia Onofri – On tweakable black-box polinomials: the cube attacks family
• Armando Capasso – Numerically flatness for Higgs bundles over compact Kähler manifolds
• Luca Ferrigno – An Overview of Diophantine Geometry
• Muhammad Usman – Symbol-based preconditioning for Riesz distributed-order space-fractional diffusion equations
• Elia Onofri – Attribute-based colouring and its applications in reducing problem's size
• Armando Capasso – Algebraic hypersurfaces with vanishing Hessian and CW-complexes
• Elia Onofri – The role of the applied mathematician: optimisation of pedestrian flows in crowded museums