Abstracts

I am a PhD student at the University of Milan, where I also earned my Bachelor’s and Master’s degrees. My research interests lie in the analysis of PDE systems arising from medical-biological problems.

Title of the talk: Asymptotic behavior of local and nonlocal Cahn-Hilliard systems

Abstract: The Cahn-Hilliard equation has been extensively studied over the past decades, as it plays a fundamental role in various fields, ranging from materials science and physics to biology and engineering.

In this talk we will present equations of this type in both their local and nonlocal formulations, highlighting the main similarities and differences between these models. Particular attention will be devoted to the role of boundary conditions depending on appropriate parameters and the boundary equations arising in the two settings.

We will then discuss convergence results for these boundary equations and illustrate how they lead to a large variety of applications.

I am a PhD student at the University of Padova, where I am attending the third year of the PhD program in Mathematics under the supervision of Prof. Valentina Franceschi and Dott. Mattia Fogagnolo. My research is related to Mean Curvature Flow in Riemannian and sub-Riemannian settings. I previously studied at the University of Milano-Bicocca, where I obtained both my Bachelor’s and Master’s degrees.

Title of the talk: Mean Curvature Flow: Geometry and Singularities

Abstract: How do shapes evolve when driven by their mean curvature? The Mean Curvature Flow (MCF) is the natural gradient flow of the area functional. In Euclidean space, Huisken's classical theorem ensures that convex surfaces "round up" and become spherical as they shrink to a point.

In this talk, we introduce the fundamental geometric properties of the MCF, focusing on the formation of singularities where the curvature blows up. We will emphasize the classification of these singular points and their deep connection with self-similar solutions, which describe the flow's asymptotic profile. Finally, we will discuss different approaches to extend the flow through the singularity, allowing for a description of the evolution beyond topological changes.

I'm Urmila Bosisio, second year PhD student at the University of Milan. I studied in this University both in the Bachelor and Master's years, time during which I discovered my passion for Numerical Analysis. Currently, i'm researching on Constructive Approximation of functions using a tree structure, in view of various and relevant applications to adaptive finite element methods (AFEM) for approximating the solution of PDEs. Hope to see you at my talk, so we can further discuss some details of my work!

Title of the talk: Adaptive tree approximation

Abstract: This talk’s main topics are instance optimal algorithms for the adaptive approximation of a function where the degrees of freedom (DOFs) are organized in trees. When approximating a function f from a functional space V , we substitute it with another simpler function s from a finite dimensional, not necessarily linear, subspace. The parameters to be specified in order to uniquely identify such an element are called degrees of freedom (DOFs).

I’ll outline the differences between an adaptive and a nonadaptive technique, identifying suitable local errors and introducing an infinite master tree T∞, following an idea from 2004 by Binev and DeVore. The potential ways of adaptively introducing the degrees of freedom may thus be seen as the transition from a node, called parent, to other connected nodes, called children. Such a structure identifies the crucial operation of adding DOFs with growing a subtree of T∞.

My main research interests lie in Numerical Analysis for the approximation of partial differential equations, with a particular focus on the Finite Element Method (FEM), Virtual Element Methods (VEM), and their implementation.

Title of the talk: Virtual Brick Elements for Nonlinear Solid Mechanics

Abstract: The Virtual Element Method (VEM) extends the classical finite element framework to general polygonal and polyhedral meshes, overcoming the geometric restrictions of standard discretizations. In this talk we present a VEM formulation for 3D eight-node hexahedral elements, called Virtual Bricks, as an extension of the classical Q1 element. The local functional space is constructed as the harmonic extension of isoparametric bilinear face functions, yielding a space of dimension eight with vertex degrees of freedom analogous to classical Q1 elements. The method relies on a computable nabla projector and a suitable stabilization term to assemble the discrete bilinear form. We apply the proposed formulation to a nonlinear hyperelastic problem comparing the Virtual Brick approach with standard isoparametric Q1 finite elements.

I completed my Bachelor’s and Master’s degrees in Mathematics at the University of Turin, where I am currently a PhD student under the supervision of Prof. Elena Issoglio. My research focuses on numerical approximation schemes for stochastic differential equations with distribution-valued drift, in both the Brownian and fractional-noise settings.

Title of the talk: Martingale problems with Distributional Drift via Regularisation

Abstract: Stochastic differential equations with irregular drifts arise naturally in models with highly singular interaction, but in this setting even the meaning of the drift term becomes unclear. In particular, when the drift is only a distribution in space, the expression ∫ᵗ₀ b(s, Xₛ) ds is not classically well-defined, since the drift b may only exist as a distribution in the space variable.

The goal of this talk is to explain how one can nevertheless give a rigorous meaning to such an integral along the trajectories of a solution. I will present the construction of an integral operator associated with the martingale problem for a stochastic differential equation with distributional drift. The idea is to start from smooth approximations of the drift, study the corresponding classical integrals, and show that they converge to a limit that is stable and depends continuously on the rough coefficient.

A central role is played by a backward parabolic PDE with rough drift. Its solution provides a representation formula for the approximating integrals and makes it possible to pass to the limit. This yields a robust notion of integral along the process, which coincides with the usual one in the smooth setting and extends the class of test functions available in the martingale problem.

I'm a PhD student at the University of Milan, working with Prof. F. Binda. I've been doing arithmetic geometry since undergraduate, obtaining a Bachelor's degree from University of Chinese Academy of Sciences and an ALGANT master's degree from University of Essen and Concordia University in Montreal. Currently I work on noncommutative stacks with arithmetic significance.

Title of the talk: Condensed mathematics

Abstract: In this short talk I will introduce some simple aspects of condensed mathematics, a framework recently developped by Clausen and Scholze for better accommondating topological structures in algebra. The basic objects of the theory, the (light) condensed sets, will be defined together with various examples.

The talk will be targeted at general mathematical audience, especially analysts who want another perspective towards the notion of convergence. The ultimate goal of the talk is to convince everyone that the condensed formalism is not terribly difficult. No prior knowledge of abstract nonsense will be needed.

I am a second-year PhD student at the Department of Mathematics of the University of Milan, where I also earned both my Bachelor’s and Master’s degrees, specializing in stochastic analysis. My research focus is on the study of symmetries of SDEs, with particular interest in the connections with the symmetries of the associated Kolmogorov equations and the study of integration-by-parts formulas for stochastic processes derived from invariance principles.

Title of the talk: Symmetries of SDEs: from invariance properties to integration by parts formulas

Abstract: The study of symmetries in differential equations, pioneered by Sophus Lie, constitutes a fundamental geometric approach to understand the invariance properties governing a dynamical system. By identifying the groups of transformations that preserve the equation’s structure, this framework provides systematic tools for order reduction, the construction of exact solutions, and the simplification of complex problems. Although symmetry analysis stands as a classical pillar for deterministic differential equations (ODEs and PDEs), supported by extensive literature, its extension to Stochastic Differential Equations (SDEs) represents a relatively recent field of research.

Recent literature has also highlighted significant connections with the symmetries of the associated Fokker-Planck or Kolmogorov equations. Furthermore, the application of Lie symmetry theory to SDEs enables the derivation of integration by parts formulas inspired by Bismut’s variational approach to Malliavin calculus, with notable applications to the analysis of the law and regularity of the processes, as well as to the development of a stochastic calculus of variations.

In this talk, we will discuss various notions of symmetry for SDEs, highlighting their connections to established invariance properties of well-known stochastic models and the symmetries of Kolmogorov PDEs. We will analyze how a geometric approach, inspired by Lie’s deterministic framework, enables the development of powerful computational tools for symmetry calculation. Subsequently, we will demonstrate how applying this geometric theory allows for the constructive derivation of an integration by parts formula for SDEs, rooted in Bismut’s approach. Finally, we will show how this integration by parts formula acts as a generating identity for well-known probability formulas, and discuss its connections to Stein’s identities.

I am a PhD student at the Institute of Science and Technology Austria in Robert Seiringer’s group.

I have obtained my bachelor and master in physics at the University of Milan under the supervision of Niels Benedikter. My research in mathematical physics focuses on quantum many-body systems.

Title of the talk: The Polaron Problem

Abstract: A charged particle travelling through a crystal generates a polarization field that induces lattice oscillations. A polaron is a quasiparticle defined as the coupling between the charged particle and the quantized lattice oscillations modelled by bosonic fields. The starting point to describe the energy spectrum and the dynamics of a polaron is the introduction of an Hamiltonian operator in second quantization. In recent times, significant advances have been made toward the understanding of the mathematical properties of polarons and, in particular, for the Fröhlich polaron where the coupling is described by a dipolar interaction. The mathematical description of polarons admits both an analytic and a probabilistic approach. In fact, the spectral properties of a polaron Hamiltonian can be derived through the analysis of the partition function of the model by means of the theory of Brownian motion or by means of methods purely from functional analysis and the spectral calculus. In this talk, I will introduce the mathematics of polaron problems and discuss the state of the art.

I am a PhD student at the Research Institute of Mathematics and Physics at the Université catholique de Louvain in Louvain-la-Neuve, Belgium. I obtained my Bachelor’s degree in Mathematical Physics and my Master’s degree in Mathematics from the University of Würzburg, Germany. My doctoral research lies in categorical algebra. I study internal structures such as internal categories, 2-categories and double categories in algebraic categories, including Mal’tsev and semi-abelian categories, via categorical Galois theory.

Title of the talk: Internal Structures in Algebraic Categories

Abstract: The notions of (small) category and functor can be internalized in any category C  with pullbacks. In this way, one obtains the category Cat(C ) whose objects are internal categories in C  and whose morphisms are internal functors in C . If C  is the category Ab of abelian groups, the category Cat(Ab) is equivalent to the arrow category Arr(Ab) whose objects are morphisms in Ab and whose morphisms are commutative squares in Ab. This is more generally true for any abelian category. If C  is the category Grp of groups, the category Cat(Grp) is equivalent to the category XMod(Grp) of crossed modules whose objects are group homomorphisms d: X → B together with a group action of B on X such that the so-called equivariance and Peiffer conditions hold. This is more generally true for any semi-abelian category. In this talk, I would like to give an overview of the categorical properties of Cat(C ) when C  is a category with "algebraic flavour" (as the categories Ab and Grp), and of its relations with other internal structures such as internal reflexive graphs, internal groupoids, internal double categories and internal 2-categories.

I obtained my master's degree in mathematics at the University of Milano-Bicocca. Now, I am a PhD student at the same institution, working in the field of numerical analysis. My main research focuses on the study of finite and virtual element methods for partial differential equations (PDEs) arising in physical models, with an emphasis on their robustness with respect to certain parameters.

Title of the talk: A Péclet-Robust Discontinuous Galerkin Method For Nonlinear Diffusion With Advection

Abstract: This talk provides an accessible, step-by-step introduction to Discontinuous Galerkin (DG) methods for Partial Differential Equations introduced in the 70s [1]. The first part of the presentation will explore the basic intuition behind discontinuous approximations.

Building on these foundations, we will then focus on a specific, challenging model: a problem combining linear advection with nonlinear p-type diffusion. Convergence analyses for various DG schemes applied to the pure p-type diffusion setting can be found, e.g., in [3,4]. However, to the authors’ knowledge, an investigation of model problems including both advection and nonlinear diffusion is missing in the literature of DG elements. Especially if one aims at developing sharp estimates which respect the local nature of diffusion and convection, the interaction between the (linear) advection and the nonlinear diffusion cannot be accounted for through a simple combination of known techniques, as the estimate of each term becomes dependent on the local regime.

In the last part of the talk, based on [2], after presenting the model and the numerical method, we will outline the theoretical results. Finally, a set of numerical tests supporting the theory will be shown. 

This is a joint work with Lourenço Beirão da Veiga (University of Milano-Bicocca) and Daniele A. Di Pietro (University of Montpellier).

References

[1] G. A. Baker. Finite element methods for elliptic equations using nonconforming elements. Math. Comp. 31.137, pp. 45–49, 1977.

[2] L. Beirão da Veiga, D. A. Di Pietro, and K. B. Haile. A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection. Math. Models Methods Appl. Sci. 34.09, pp. 1781-1807, 2024.

[3] E. Burman, and A. Ern. Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian. C. R. Math. Acad. Sci. Paris 346.17-18, pp. 1013–1016, 2008.

[4] T. Malkmus, M. Ruzicka, S. Eckstein, and I. Toulopoulos. Generalizations of SIP methods to systems with p-structure. IMA J. Numer. Anal. 38.3, pp. 1420–1451, 2018.

I got my bachelor and master degrees at the ENS Rennes in France, and now I am a PhD candidate in Milan. My main interests are broadly at the intersection between homotopy theory and motives in algebraic geometry. The heart of my research is in the non-𝔸¹-invariant flavors of stable motivic homotopy theory.

Title of the talk: There is a better way to count than with integers

Abstract: In 1849, Cayley and Salmon [1] proved that on a smooth complex projective cubic surface, there always lie 27 straight lines. This result has been adapted a few years later by Schläfli [5] to real cubic surfaces (where there are 3, 7, 15 or 27 lines) and more recently by Finashin and Kharlamov [2] to cubic surfaces defined on finite fields.

Much later, Morel [4] computed the motivic π₀ of spheres as the Milnor-Witt K-theory of the base field. He insightfully deduced that the “motivic Brouwer degree” of an endomorphism of a sphere should live in the Grothendieck-Witt ring GW(k), i.e. the isomorphism classes of non-degenerate quadratic forms on k, endowed with ⊕, then completed to a group, and finally endowed with ⊗.

This suggested that one should actually count the lines on a cubic surface not with integers, but rather with quadratic forms inside GW(k)! This was done by Kass and Wickelgren [3], yielding the beautiful generalization

∑ ₗ ₗᵢₙₑ Tr ʟ∕ₖ[l] = 15 · ⟨1⟩ + 12 · ⟨−1⟩

which implies all the aforementioned results.

References

[1] A. Cayley. On the Triple Tangent Planes of Surfaces of the Third Order. The Collected Mathematical Papers. Vol.1. Cambridge Library Collection - Mathematics. Cambridge: Cambridge University Press, 1849, pp. 445-456. ISBN: 978-1-108-00493-0. DOI: 10.1017/CBO9780511703676.077.

[2] S. Finashin and V. Kharlamov. Abundance of real lines on real projective hypersurfaces. International Mathematics Research Notices 2013.16 (2013), pp. 3639-3646. ISSN: 1687-0247, 1073-7928. DOI: 10.1093/imrn/rns135. arXiv: 1201.2897 [math].

[3] J. Kass and K. Wickelgren. An Arithmetic Count of the Lines on a Smooth Cubic Surface. Compositio Mathematica 157.4 (2021), pp. 677–709. ISSN: 0010-437X, 1570-5846. DOI: 10.1112/S0010437X20007691. arXiv: 1708.01175 [math].

[4] F. Morel. 𝔸¹-Algebraic Topology over a Field. Vol. 2052. Lecture Notes in Mathematics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. ISBN: 978-3-642-29513-3 978-3-642-29514-0. DOI: 10.1007/978-3-642-29514-0.

[5] L. Schläfli. On the Distribution of Surfaces of the Third Order into Species, in Reference to the Absence or Presence of Singular Points, and the Reality of Their Lines. Philosophical Transactions of the Royal Society of London 153 (1863), pp. 193–241. ISSN: 0261-0523.

I got my Bachelor and Master degree in Mathematics from Università degli Studi di Milano, and now I am a second year PhD student at Università degli Studi di Milano-Bicocca. My research interests are in Riemannian Geometry and Geometric Analysis.

Title of the talk: Harmonic functions on Riemannian manifolds

Abstract: A function u ∈ C∞(M) on a Riemannian manifold (M, g) is harmonic if it satisfies the equation ∆g u = 0, where ∆g denotes the Laplace-Beltrami operator of M with respect to the metric g. Despite the simple defining equation, the theory of harmonic functions is very rich and lies at the intersection of several branches of mathematics, including PDEs, complex analysis, probability and geometry. In this talk, we will discuss some examples where harmonic functions theory is used to deduce geometric information in the context of Riemannian manifolds and minimal surfaces. The common thread linking these examples will be the Liouville theorem, and we will discuss conditions that guarantee its validity on a general Riemannian manifolds. If time permits, we will also discuss Liouville-type results for other operators that arise naturally in geometric contexts.

I am a PhD Student in algebraic geometry both in Universitat de Barcelona and Università degli Studi di Milano. My research topics are bridgeland stability and generation for geometric triangulated categories. Besides Maths, I like cinema and Valencian folkloric dances. I do not consider myself Spanish so it would be very appreciated if you don't refer to me as it.

Title of the talk: Generation in geometric derived categories

Abstract: In this talk we will discuss the concept and applications of generation in triangulated categories as well as some results on the geometric side. To be more specific, we'll see give the definition and why do we care and the we will move to some theorem-examples that can be found through the literature.

I am a second year PhD student at SISSA, in Trieste, and I previously obtained my Master's degree in Mathematics at Sapienza University of Rome. My research focuses on quantum many-body problems arising from condensed matter physics.

Title of the talk: ℤ₂-lattice gauge theory coupled to fermionic matter

Abstract: In this talk, I will discuss a system of spinless fermions on the lattice coupled to dynamical ℤ₂ gauge fields, living on the bonds of the lattice. The model displays a rich phase diagram, as shown by numerical simulations. Following Lieb’s proof, I will show how the ground state, within certain regions of the parameters, belongs to the so-called pi-flux phase. Such result relies on reflection positivity and the resulting chessboard estimates. Time permitting, I will discuss how to characterize such phase, by computing some physical quantities, such as the susceptibility.

I obtained my Master’s degree from University of Pavia in Theoretical physics where I focused on the themes of stochastic analysis and stochastic quantization. Currently, I am a PhD Student at Heriot-Watt University and Univeristy of Milan. My main research interest lies in Stochastic homogenization, particularly exploring the homogenization of high-contrast elliptic systems with partial degeneracy.

Title of the talk: Spectral Analysis of high-contrast degenerate random systems

Abstract: In this talk, we introduce the notion of homogenization and two-scale convergence in the periodic setting for an elliptic PDE. We then move to the stochastic setting, where the coefficients of the Laplacian operator are given by stochastic functions on an ergodic probability space. The latter setting allows us to delve into the specific research topic of the PhD.

We examine the homogenization and spectral theory of a double-porosity model arising in random systems of elliptic partial differential equations with isolated inclusions. As last we analyse the homogenized operator and discuss how the high-contrast structure and partial degeneracy influence the spectral properties of the system.

I am a third-year PhD student in Mathematics and Data Analytics for Finance at the University of Verona. Since October 2025, I have been a visiting PhD student at Université Paris Cité, within the Laboratoire Jacques-Louis Lions. I obtained my Bachelor's and Master's degrees in Mathematics from the University of Milan.

My research focuses on neural network-based approximation methods for stochastic optimal control problems, mean field games and mean field control, and mathematical finance.

Title of the talk: Neural Network-Based Approximation for Stochastic Control Problems

Abstract: We consider numerical approximations of stochastic optimal control (SOC) and mean field control (MFC) problems using deep neural networks. First, we establish explicit error bounds and convergence results for the SOC value function in an averaged sense, accommodating degenerate diffusions. We then extend the analysis to MFC problems, learning the value function globally across the infinite-dimensional Wasserstein domain. By leveraging the propagation of chaos to approximate the mean field limit via a finite-player cooperative game, our approach reduces the MFC problem to a high-dimensional task efficiently handled by neural architectures. Numerical simulations illustrate the effectiveness and scalability of the proposed approaches.

The talk is based on a series of joint works with O. Bokanowski (LJLL, Université Paris Cité), J. F. Chassagneux (ENSAE, CREST and Institut Polytechnique de Paris), A. Picarelli (University of Verona), J. Tam (University of Oxford), and X. Warin (EDF/R&D). 

I obtained a Master’s degree in Mathematics at the University of Milan, where I am currently a PhD student. My research interests include categorical logic, algebraic logic, and duality theory.

Title of the talk: Duality Theory

Abstract: The Stone representation theorem for Boolean algebras, due to Marshall H. Stone in the 30s, is the starting point of duality theory. Although it arose in the context of functional analysis,the theorem is relevant to logic. For a fixed set of formulas of a classical propositional language, the set of formulas deducible from it in a complete and sound proof system, regarded up to the Tarski-Lindenbaum equivalence relation, is a Boolean algebra, whilst its set of models can be endowed with a topology—the Stone topology—in a canonical way. In the language of category theory, the Stone representation theorem states that the category of Boolean algebras and Boolean homomorphisms is dually equivalent to the category of Stone spaces and continuous maps. It thus describes the connection between provable formulas and their models in classical propositional logic.

Since the Stone representation theorem, duality theory developed in logical contexts through dual equivalences between categories related to the syntax and the semantics of logical languages, respectively. However, categorical dualities arise all over different fields of mathematics, with analysis, geometry and universal algebra providing the richest sources of examples. Our research falls within this extra-logical prospective, and draws motivations from polyhedral and toric geometry. Specifically, we are developing a duality between the category of rational affine polytopes with ℤ-maps as morphisms and the category of polytopal groups with monotone unital group homomorphisms as morphisms. To indicate the connection with toric varieties, we point out that a rational polyhedron yields an associated rational polyhedral by homogeneisation; and the resulting cone, in turn, determines in the usual manner an affine toric variety over a ground field of choice.

Although arising from integral polyhedral geometry, the duality we are exploring also displays various interesting connections to logic. Indeed, the investigation of rational affine polytopes and their ℤ-maps turns out to be equivalent to the study of a dualised affine fragment of Lukasiewicz’s many-valued logic. Further, one of the applications of the duality concerns its algebraic side. The category of polytopal groups is equivalent to a certain category of pointed affine monoids, and these affine monoids form a quasi-variety. The duality is thereby related with a central field of research in both logic and universal algebra, namely, the theory of quasi-varieties.

I am a PhD student at the University of Florence under the supervision of Daniele Angella and Fiammetta Battaglia. My research focuses on non-Kähler complex geometry and, in particular, on special metrics and cohomological properties of LVMB manifolds: a broad class of non-Kähler complex manifolds related to toric geometry. I’m very pleased to take part in this event since the University of Milan is the institution where I obtained my Master’s degree.

Title of the talk: Complex invariants of Generalized Calabi–Eckmann threefolds

Abstract: The existence of a Kähler metric on a complex manifold imposes topological and cohomological constraints, such as b₂ > 0. Therefore any classification of manifolds admitting a complex structure must take non-Kähler examples into account.

The absence of the Kähler condition makes the non-Kähler setting richer: new Hermitian connections appear, new cohomology theories arise, and “special metrics” are characterized by conditions weaker than dω = 0.

Classical examples are Hopf manifolds and Calabi–Eckmann manifolds. Their construction has recently been generalized with the introduction of the so-called LVMB manifolds, a class of complex manifolds constructed from a combinatorial datum.

Among them are Generalized Calabi–Eckmann threefolds. By applying general results on LVMB manifolds, in this talk we present some of their complex invariants, leading to a complete classification.

I am a PhD student under joint supervision between Milan and Freiburg, and I obtained both my bachelor's and master's degrees in Pisa. My field of research is mathematical logic, with a focus on applications to Ramsey theory and additive combinatorics.

Title of the talk: Colors and big numbers

Abstract: You have a bunch of colors, and you start painting all the natural numbers (ok, you have a lot of free time!): you may wonder whether or not you can always spot some arithmetic structure painted with the same color. This question is the core of arithmetic Ramsey theory; structures, or configurations, which we always encounter in one of the colors are called partition regular, and examples of partition regular patterns are arithmetic progressions and solutions to certain polynomial equations.

In this talk, I will present an approach based on the use of the hypernaturals *ℕ, an elementary extension of ℕ containing infinite numbers: we will see how a special relation between these numbers yields partition regularity and, time permitting, we will discuss concrete applications to polynomial configurations.

I am an algebraic geometry PhD student, currently enrolled at the University of Poitiers (France) and also pursuing a cotutelle PhD with the University of Milan (Italy). I obtained both my Bachelor's and Master's degrees in Bordeaux, France. My main interests include the study of Borcea-Voisin Calabi-Yau varieties and the cone conjecture. 

Title of the talk: The Borcea-Voisin Construction

Abstract: In this talk, I will introduce Calabi–Yau varieties and discuss some ways to construct them. After presenting some motivations, I will look at a few simple examples. I will then explain the main ideas of the Borcea–Voisin construction and aim to give some intuition for this construction.

I am a PhD student in the Department of Mathematics at the University of Milan. My research interests are in Categorical Algebra, more specifically in Categorical Galois Theory. Before arriving here, I obtained my bachelor’s and master’s degrees at the University of Turin.

Title of the talk: An Excursion into Galois Theories

Abstract: Galois theory is one of the most powerful tools in modern field theory. Its cornerstone is the Fundamental Theorem of Galois Theory, which establishes a deep connection between field theory and group theory. The wide range of applications of this theorem has led mathematicians to seek analogous characterizations in more general contexts. One of the most influential developments in this direction is Grothendieck’s Galois theory for algebras over a field. The aim of this talk is to introduce the further generalization developed by G. Janelidze, which, using the language and tools of category theory, provides a conceptual and unifying description of Galois-type correspondences.