Abstracts

I am a postdoctoral researcher in Statistics at the Department of Environmental Sciences Informatics and Statistics at Ca' Foscari University of Venice. I obtained my bachelor's and master's degrees in Mathematics from the University of Trento, and subsequently, I completed a PhD in Statistics at the University of Padua. My research focuses on semi-parametric models, with a particular emphasis on Generalized Additive Models, gradient boosting and survival analysis.

Abstract: Feature engineering, the process of applying a scalar transformation to some covariates, is a commonly used practice in data analysis aimed at reducing the number of variables or improving their informational content. This often results in a model that is both parsimonious and easier to interpret. The method generally involves a two-stage procedure that is iterated until the model reaches optimality. Initially, transformation parameters are selected, often by cross-validation or expert knowledge, followed by model fitting. In this talk, we propose a novel and computationally efficient modelling approach within the Generalized Additive Models for Location Scale and Shape framework, aimed at estimating model parameters as well as feature engineering parameters together. By simultaneously estimating all parameters, the resulting model incorporates uncertainties from both feature engineering and model coefficients, thus integrating these uncertainties into the inferential procedures. We will illustrate the application of the proposed framework with examples related to UK power demand and house prices.

My name is Laura Perelli and I am a PhD student in Mathematics at the University of Milan, where I also completed both my Bachelor's and Master's degrees in Mathematics. During my Master's studies, I specialized in probability, stochastic calculus and mathematical finance. Currently, as a PhD student, my research focuses on stochastic optimal control, more precisely on optimal stopping theory. 

Abstract: We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems arise, for instance, in the pricing of American options when the underlying asset follows a McKean-Vlasov dynamics. Due to the time inconsistency of these problems, we provide a suitable reformulation of the original problem for which a dynamic programming principle can be established. To accomplish this, we first enlarge the state space and then introduce the so-called extended value function. We prove that the Snell envelope of the original problem can be written in terms of the extended value function, from which we can derive a characterization of the smallest optimal stopping time. On the enlarged space, we restore time-consistency and in particular establish a dynamic programming principle for the extended value function. Finally, we derive the associated Hamilton-Jacobi-Bellman equation, which turns out to be a second-order variational inequality on the product space  [0, T] × Rd × P2(Rd), where P2(Rd) is the set of probability measures on  Rd with finite second moment. Under suitable assumptions, we also prove that the extended value function is a viscosity solution to this equation.

I'm a PhD student at the Department of Mathematics in the University of Milan, where I obtained both my Bachelor and my Master degree. My field of research is stochastic modeling, focusing on particle systems in porous media and singular McKean Vlasov SDEs. I am also interested in propagation of chaos and mean field limits. 

Abstract : We present a new stochastic model for the sulphation process of calcium carbonate at the microscale, focusing on the chemical reaction that leads to the formation of gypsum and to the consequent marble degradation, which is relevant in Cultural Heritage conservation. The Langevin dynamics of the sulfuric acid particles is described via first order stochastic differential equations (SDEs) of Itô type, while calcium carbonate and gypsum are modelled as underlying random fields evolving according to random ODEs. Furthermore, particles interact pairwise via a strongly singular potential of Lennard Jones type. The system is finally coupled with a marked Poisson compound point measure for realizing the chemical reactions. We discuss the well-posedness of the system for a broad class of singular potentials, including Lennard Jones, by proving that, almost surely, particle collisions do not occur in a finite time.

This is a joint work with Daniela Morale, Stefania Ugolini (University of Milano) and Adrian Muntean, Nicklas Javergard (University of Karlstad).

I obtained my master’s degree in mathematics at the University of Milano-Bicocca. Now, I’m a PhD student at the University of Milano. I am currently working in the field of numerical analysis. My main interest is the study of the virtual element methods for solving problems in solid mechanics, such as the obstacle and contact problem. 

Abstract: Virtual Element Methods (in short, VEMs) are a recent family of numerical methods widely employed today for approximating partial differential equations (see [1]). This class of Galerkin methods naturally adapts to arbitrary polygonal decompositions of the domain, due to the choice of suitable discrete spaces that are no longer restricted to polynomials. This flexibility makes VEMs particularly well-suited for dealing with variational problems with complex geometries and non-standard boundary conditions. In this talk, we will explore the application of the Stokes-like virtual element method (see [2]) to address a fundamental problem in solid mechanics, known as the contact problem (see [3]). After a brief introduction to the mathematical framework of VEMs, we will focus on the displacement-pressure formulation of a frictionless contact problem between two elastic bodies, specifically in the nearly incompressible regime (see [4]). We will discuss results related to the existence and uniqueness of the solution for the continuous problem. Furthermore, we will present an explicit construction of the VEM discretization for this problem, along with the corresponding convergence results. Finally, we will highlight the key advantages of VEMs in the discrete treatment of contact conditions compared to classical FEMs and we will show some numerical tests that validates theoretical estimates.

This is a joint work with Prof. C. Lovadina.

References

[1] L. Beirão Da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini and A.Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199-214.

[2] L. Beirão Da Veiga, C. Lovadina, G. Vacca, Divergence free virtual elements for the Stokes problem on polygonal meshes, ESAIM: M2AN, 51 (2017) 509-535.

[3] B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problem, Acta Numerica, Cambridge University Press, 2011, pp.569-734.

[4] F. Ben Belgacem, Y. Renard, L. Slimane, A mixed formulation for the Signorini problem in nearly incompressible elasticity, Applied Numerical Mathematics, 54 (2005), 1-22.

My name is Federico Achini, and I am a PhD student in Mathematics at Università degli Studi of Milano – the same where I got my Master’s degree about five years ago. Before starting my PhD, I worked as a software engineer and a scientific researcher for two companies in the tomography industry. Currently, my research is about developing new algorithms for inverse problems in tomography with the aid of neural networks.

Abstract: Deep Neural Networks (DNNs) are regarded as a powerful and versatile tool in machine learning; for example, for tasks such as object detection. Despite their proven capabilities, they remain mostly black-boxes: explaining the reasons that drive the decisions of a model is extremely difficult. This constitutes an obstacle in several applications, both from a legal and an ethical point of view, besides being quite unsatisfactory for the theory itself. Moreover, this complexity is exacerbated by the lack of understanding of what to explain should really mean. Saliency maps come into play as an attempt to address these issues, at least for those tasks where the model inputs are images. They typically take the form of heat maps highlighting the area of the input that contributed the most to the model decision. Nowadays, they constitute an active field of research.

Research Experience

• Research Fellow, University of Modena and Reggio Emilia (2024-Present)

• Visiting Researcher, University of Bath (2022)

Education

• PhD in Mathematics, University of Bologna (2020-2024)

• MSc Applied Mathematics, University of Bologna (2017-2020)

Research Interests

My research focuses on the intersection of deep learning and computational imaging, with a particular emphasis on solving inverse problems in medical imaging. I am interested in developing physics-informed machine learning techniques that integrate prior knowledge from imaging physics to improve image quality, robustness, and interpretability of the resulting techniques. My work combine model-based and data-driven approaches to enhance the reliability of deep learning algorithms in real-world medical applications. Currently, I am a research fellow in the Department of Physics, Informatics, and Mathematics at the University of Modena and Reggio Emilia, working on the project “Advanced optimization METhods for automated central veIn Sign detection in multiple sclerosis from magneTic resonAnce imaging (AMETISTA)”.

Abstract: Inverse problems in imaging arise in many applications, where the goal is to reconstruct an unknown image from indirect or noisy measurements. Traditional deep learning methods have shown remarkable success in addressing such problems, but they often lack stability, interpretability and struggle with data scarcity. In medical imaging, inverse problems play a crucial role in modalities such as MRI and CT, where high-quality image reconstruction is essential for accurate diagnosis and treatment planning. However, data availability is often limited due to acquisition constraints, patient safety considerations (e.g., reducing radiation dose in CT), and high costs of data labeling. In this talk, we explore the integration of physical models with deep learning techniques to overcome these limitations, with a particular focus on limited-data CT. We will discuss recent advancements in self-supervised approaches, combining the knowledge of physical acquisition model within an interpretable neural network architecture.

I obtained my Master’s degree in Mathematics at the University of Milan, where I’m currently pursuing my PhD. My research focuses on the analysis of PDEs, with a particular interest in symmetry and stability in nonlinear problems.

Abstract: In this seminar, we will explore a possible interpretation of the term ‘stability’ in the realm of PDEs, focusing on two well-known problems – the Gidas-Ni-Nirenberg problem and the classification of positive solutions to the critical p-Laplace equation. These problems will serve as guiding examples to illustrate classical results and recent developments, providing new insights into their stability properties.

I am a PhD student in SISSA, in Trieste, where I’m attending the third year of the PhD course in mathematical analysis, modelling and applications, under the supervision of prof.  Alberto Maspero and doc. Beatrice Langella. My research is related to long-time behavior of solutions of some dispersive PDEs.

I previously studied in Palermo for my bachelor and then I did the master in Trieste, starting working with prof. Alberto Maspero already with my master thesis.

Abstract: The behavior of solutions of dispersive PDEs is a widely studied topic, full of open questions already in the linear setting. The main challenge is to identify indicators of different behaviors as well as effective ways to capture them. In this talk I will consider a class of linear, time-dependent, Schrödinger equations and give sufficient conditions to prove existence of unstable solutions. First I will introduce Sobolev norms as a tool to examine how the energy of solutions spreads over time. In particular, I will explain why the unbounded growth in time of positive Sobolev norms is an indicator of instability of the solution. Next, I will discuss some recent results related to growth of Sobolev norms and, if time permits, I will outline the main ingredients needed in their proofs and the key difficulties typically encountered. 

I studied mathematics at the University of Rome Tor Vergata, where I earned both my bachelor's and master's degrees. I am currently in my third year of a PhD at the University of Rome Tre. My research focuses primarily on Hamiltonian PDE's, with a particular emphasis on the Kirchhoff equation, a nonlinear version of the wave equation. 

Abstract: The Kirchhoff equation with periodic boundary conditions provides a beautiful model for describing the transverse oscillations of a nonlinear elastic medium. Since its introduction in 1876, it has continued to fascinate and challenge mathematicians from all over the world. In this presentation, we analyze its properties, highlighting both its physical motivations and mathematical implications. In particular, we discuss key theoretical questions, such as local well-posedness and the lifespan of solutions, emphasizing the challenges posed by its quasi-linear structure. A central focus of our analysis is its Hamiltonian formulation, which provides a powerful theoretical framework for understanding the dynamics of solutions. Our goal is to offer a clear overview of the open challenges and the main techniques used to tackle them, with particular emphasis on the so-called normal form techniques.

I am a PhD student here at Statale and I study quantum many-body systems, specifically Fermion many-body systems. Before arriving here, I pursued a master in mathematical physics at the University of Tübingen and before that I did my bachelor in India.

 Abstract: I will start with an introduction to Quantum many-body systems. Next I will present a brief description of systems of interest. Then present the most important results in the field while giving a brief list of preliminary knowledge required. Then I will talk about our result on the momentum distribution of an interacting Fermi gas on a 3D torus in the mean field regime. The key tool for deriving the distribution is a rigorous bosonization method. I will start with the construction of a natural trial state and then show the implementation of the bosonization procedure. The expression for the momentum distribution contains the contribution from the collective excitations above the Fermi-surface going beyond the precision of Hartree-Fock theory.

I am Lucas Li Bassi, I did my bachelor and master in UniMi and my PhD was in a joint project between Milano and Poitiers, where I obtained my PhD degree on December 2023. Right now I am doing a postdoc in Genova. My work and interests are in algebraic geometry, more specifically in hyperkähler geometry with a view on moduli spaces and the singular world. 

Abstract: In the study of singular versions of smooth irreducible holomorphic symplectic varieties, topological properties play a key role, especially how quasi- étale covers behave. A recent result by Garbagnati, Penegini, and Perego classifies all primitive symplectic surfaces and shows that their Hilbert square is also a primitive symplectic variety. In this talk, I will present ongoing joint work with F. Papallo on how coverings can be induced on the Hilbert square of a complex surface. We will also explore some cohomological and differential properties that arise in this setting.

I am currently a doctoral student at the University of Milan working in complex algebraic geometry and derived category. I received a Bachelor degree from Jilin University and a Master degree from the University of Bonn.

Abstract: In this short talk, we will see a brief survey on stability conditions on K3 surfaces constructed by Bridgeland in [4] and the associated moduli spaces studied in [2, 3, 7]. In particular, we will mention Bridgeland’s conjecture [1] and its application [5, 6] on the geometry of K3 surfaces.

References

[1] Arend Bayer, Tom Bridgeland. Derived automorphism groups of K3 surfaces of Picard rank 1. Duke Mathematical Journal, 166(1): 75-124, 2017.

[2] Arend Bayer, Emanuele Macrì. Projectivity and birational geometry of Bridgeland moduli spaces. Journal of the American Mathematical Society, 27(3): 707-752, 2014.

[3] Arend Bayer, Emanuele Macrì. MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations. Inventiones mathematicae, 198(3): 505-590, 2014.

[4] Tom Bridgeland. Stability conditions on K3 surfaces. Duke Mathematical Journal, 141(2): 241-291, 2008.

[5] Yu-Wei Fan, Kuan-Wen Lai. Nielsen realization problem for derived automorphisms of generic K3 surfaces. Preprint, 2302.12663v3, 2023.

[6] Ziqi Liu. Derived-natural automorphisms on Hilbert schemes of points on generic polarized K3 surfaces. Preprint, 2501.08854v1, 2025.

[7] Yukinobu Toda. Moduli stacks and invariants of semistable objects on K3 surfaces. Advances in Mathematics, 217: 2736-2781, 2008.

I got my bachelor and master degree in Sapienza University and now I’m a PhD candidate in the same university. My research interest is in Algebraic geometry and more specifically in the study of vector bundles and their positivity.

Abstract: A vector bundle can be thought of as a family of vector spaces varying continuously along over a given variety. These objects offer a valuable point of view in order to better understand the geometry and the topology of algebraic varieties. After reviewing some classical applications of the theory of vector bundles in algebraic geometry, we will introduce Ulrich bundles and glimpse the recent results and conjectures on this special class of vector bundles.

I am currently a PhD student in University of Milano, and mainly work in algebraic and arithmetic geometry. More precisely , I study motivic theory in algebraic, analytic and logarithmic geometry, and its application in p-adic cohomologies and K-theory. 

Abstract: Log geometry provides a language system, in which we can treat  geometric spaces that have mild singularity as "smooth" objects in some sense. On the other hand, derived geometry can be regarded as a kind of higher deformation theory of classical algebraic geometry.  In this talk, we firstly review the basic definitions in both log and derived settings. Then we will introduce the moduli stack of derived log structures. If time permits, we will consider the realization of log motivic invariants and log motivic categories from the stacky perspective. 

I obtained a master's degree in mathematics at the University of Milan, where I am currently a PhD student. My research interests are differential and Riemannian geometry and geometric analysis. 

Abstract: Many of the so-called canonical (or special) metrics arise as critical points of suitable Lp -norms of the components of the Riemann curvature tensor. This object encodes all the information about the curvature of the manifold and, in dimension 4, it admits a peculiar decomposition. Throughout the talk, we will explore some known results and open problems concerning Riemannian functionals and critical metrics in dimension 4 and beyond.

After earning a Bachelor’s and a Master’s degree in Mathematics at the University of Torino, I am currently a PhD student at the same institution under the supervision of Luciano Mari and Alessandro Iacopetti. My research focuses on the problem of prescribing mean curvature in Lorentzian manifolds, particularly on the regularity of hypersurfaces in curved spacetime whose mean curvature is a Radon measure, and on the existence of entire graphs in Minkowski spacetime that are asymptotic to a light cone. At the moment, and throughout the spring, I am a visiting PhD student at the Université libre de Bruxelles under the supervision of Denis Bonheure.

Abstract: The study of hypersurfaces with prescribed mean curvature in Lorentzian geometry is motivated by both mathematical interest and its relevance in physics, particularly in general relativity and non-linear electrodynamics. This talk will provide an overview of key results in the field, discussing classical approaches as well as more recent advances. Time permitting, some new developments and open problems will be presented, focusing on challenges and potential research directions.

I am a PhD student at the Mathematics Department of the University of Milan, where I also attained my Bachelor's and Master's degrees. My research interests are in Categorical Algebra, and I am currently working in Non-Abelian Cohomology Theory. 

Abstract: It is a classical result in Homological Algebra (due to N. Yoneda) that the Extn groups, which are usually defined by means of right derived functors in the fairy world of abelian categories, admit a description in terms of n-extensions, i.e. (equivalence classes of) exact sequences: this extension approach has proved to be succesful also to understand and develop (co)homological theories for some highly frequented, but alas non abelian, algebraic structures such as groups, rings, associative or Lie algebras. A seminal paper by D. Bourn (1999) showed that a unified treatment of these and many other non-abelian cohomological theories is possible, by means of a very general construction which he called the direction functor. It is the aim of this talk to give a (gentle) introduction to this functor, showing for instance how its properties allow for a conceptual description of the Baer sums, in the familiar case of groups. Time permitting, we shall also discuss some recent developments of these techniques, which will hopefully result in a cohomological theory for monoids.

I am a third year PhD student at the University of Turin where I obtained my Master degree. My research concerns abstract and categorical algebra. More precisely, I am mainly interested in Hopf algebras, their categorical features and generalizations and related topics: braided monoidal categories, semi-abelian categories, Yang-Baxter equations and noncommutative geometry. 

Abstract: In this introductory talk, we briefly discuss Hopf algebras, braidings, and semi-abelian categories, explaining how these notions can be connected. By considering the notion of Hopf brace, one can use Hopf algebras to produce solutions of the famous quantum Yang–Baxter equation. Moreover, under the assumption of cocommutativity, Hopf braces form a semi-abelian category, sharing so many interesting properties with groups and Lie algebras.