Archivio 2025

2025
05 febbraio
Gautam Pai
nell'ambito della serie: NEUROMATEMATICA
Seminario di analisi matematica, sistemi dinamici
The roto-translation group SE(2) has been of active interest in image analysis due to methods that lift the image data to multi-orientation representations defined in this Lie group. This has led to impactful applications of crossing-preserving flows for image de-noising, geodesic tracking, and roto-translation equivariant deep learning. In this talk, I will enumerate a computational framework for optimal transportation over Lie groups, with a special focus on SE(2). I will describe several theoretical aspects such as the non-optimality of group actions as transport maps, invariance and equivariance of optimal transport, and the quality of the entropic-regularized optimal transport plan using geodesic distance approximations. Finally, I will illustrate a Sinkhorn-like algorithm that can be efficiently implemented using fast and accurate distance approximations of the Lie group and GPU-friendly group convolutions. We report advancements with the experiments on 1) 2D shape/ image barycenters, 2) interpolation of planar orientation fields, and 3) Wasserstein gradient flows on SE(2). We observe that our framework of lifting images to SE(2) and optimal transport with left-invariant anisotropic metrics leads to equivariant transport along dominant contours and salient line structures in the image and leads to meaningful interpolations compared to their counterparts on R^2. *Joint work with Daan Bon, Gijs Bellaard, Olga Mula, and Remco Duits from CASA – TU/e. Preprint: https://arxiv.org/abs/2402.15322 (to appear in SIAM Journal in Imaging Sciences 2025)
2025-02-05
Dino Zardi
Relazione all'interno del convegno: Matematica e Clima
Seminario interdisciplinare
2025-02-05
Franco Flandoli
Relazione all'interno del convegno: Matematica e Clima
Seminario interdisciplinare
2025
04 febbraio
Carlo Gasparetto
Seminario di analisi matematica
Allard’s theorem roughly states that a minimal surface, that is close enough to a plane, coincides with the graph of a smooth function which enjoys suitable a priori estimates. In this talk we will show how one can prove this result by exploiting viscosity technique and a weighted monotonicity formula. -Seminario per il ciclo ASK -
2025
04 febbraio
Elena Collacciani
Seminario di algebra e geometria
In this talk, I will provide an elementary introduction to the Local Langlands Correspondence, focusing on the key concepts and definitions of the objects involved. We will build intuition by examining some simpler instances of the correspondence, including local class field theory, the case of GLn , and the split case, before presenting the general statement. In the second part, we will explore a conjecture proposed by Vogan, which suggests a reduction of the Local Langlands Correspondence from p-adic fields to finite fields. Particular emphasis will be placed on the GLn case, where the conjecture has an easier formulation and has been established through the work of Macdonald, Silberger, and Zink. Finally, I will briefly discuss the conjecture for SLn, talking about my research contributions to this area.
2025
04 febbraio
Lorenzo Vecchi
Seminario di algebra e geometria, interdisciplinare
Three decades ago, Stanley and Brenti initiated the study of the Kazhdan–Lusztig–Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In this talk we present a theory that parallels the KLS theory. To each kernel in a given poset, we associate a function in the incidence algebra that we call the Chow function. The Chow function often exhibits remarkable properties, and sometimes encodes the graded dimensions of a cohomology or Chow ring. The framework of Chow functions provides natural polynomial analogs of graded module decompositions that appear in algebraic geometry, but that work for arbitrary posets, even when no graded module decomposition is known to exist. In this general framework, we prove a number of unimodality and positivity results without relying on versions of the Hard Lefschetz theorem. Our framework shows that there is an unexpected relation between positivity and real-rootedness conjectures about chains on face lattices of polytopes by Brenti and Welker, Hilbert–Poincaré series of matroid Chow rings by Huh, and enumerations on Bruhat intervals of Coxeter groups by Billera and Brenti. This is joint work with Luis Ferroni and Jacob Matherne https://arxiv.org/abs/2411.04070.
I will review some longstanding open problems concerning the notion of spatial localization of quantum particles in relativistic regime and I will present some recent achievements on the subject, also in relation with the so-called causal logic of the Minkowski space-time.
2025
31 gennaio
Nicholas Meadows
Seminario di logica, teoria delle categorie
A series of recent papers by Bergfalk, Lupini and Panagiotopoulus developed the foundations of a field known as 'definable algebraic topology,' in which classical cohomological invariants are enriched by viewing them as groups with a Polish cover. This allows one to apply techniques from descriptive set theory to the study of cohomology theories. In this talk, we will establish a 'definable ' version of a classical theorem from obstruction theory, and use this to study the potential complexity of the homotopy relation on the space of continuous maps $C(X, |K|)$, where $X$ is a locally compact Polish space, and K is a locally finite countable simplicial complex. We will also characterize the Solecki Groups of the Cech cohomology of X, which are canonical approximations of a Polishable subgroup of a Polish group.
2025
31 gennaio
Nicholas Meadows
Seminario di algebra e geometria, logica, teoria delle categorie
Sarah Hopkins is an Associate Professor in Mathematics Education at Monash University (Melbourne, Australia). In this presentation, Sarah will provide a brief overview of a paper she co-authored that was recently published; she will then describe the journey involved in getting it published. Reviewers' comments and replies will be examined and strategies for navigating the publication process will be discussed.
2025
30 gennaio
Marco Caroccia
Seminario di analisi matematica
The classical Plateau problem asks which surface in three-dimensional space spans the least area among all the surfaces with boundary given by an assigned curve S. This problem has many variants and generalizations, along with (partial) answers, and has inspired numerous new ideas and techniques. In this talk, we will briefly introduce the problem in both its classical and modern contexts, and then we will focus on a specific vectorial (planar) type of the Plateau problem. - Given a curve S in the plane, we can ask which diffeomorphism T of the disk D maps the boundary of D to S and spans the least area, computed as the integral of the Jacobian of T, among competitors with the same boundary condition. For simply connected curves, the answer is provided by the Riemann map, and the minimal area achieved is the Lebesgue measure of the region enclosed by S. For more complex curves, possibly self-intersecting, new analysis is required. I will present a recent result in this sense, obtained in collaboration with Prof. Riccardo Scala from the University of Siena, where the value of the minimum area is computed with an explicit formula that depends on the topology of S.
2025
28 gennaio
Nicholas Meadows
Seminario di logica, teoria delle categorie
A series of recent papers by Bergfalk, Lupini and Panagiotopoulus developed the foundations of a field known as 'definable algebraic topology,' in which classical cohomological invariants are enriched by viewing them as groups with a Polish cover. This allows one to apply techniques from descriptive set theory to the study of cohomology theories. In this talk, we will establish a 'definable ' version of a classical theorem from obstruction theory, and use this to study the potential complexity of the homotopy relation on the space of continuous maps $C(X, |K|)$, where $X$ is a locally compact Polish space, and K is a locally finite countable simplicial complex. We will also characterize the Solecki Groups of the Cech cohomology of X, which are canonical approximations of a Polishable subgroup of a Polish group.
2025
28 gennaio
Elia Fioravanti
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
Given a (nice) group G, we are interested in how fast the length of a group element can grow when we apply powers of a given outer automorphism of G. If the group G is free or the fundamental group of a closed surface, classical train-track techniques give a complete and precise picture. This can be extended to automorphisms of all negatively curved (a.k.a. Gromov hyperbolic) groups G, using Rips-Sela theory and the canonical JSJ decomposition. Very little seems to be known beyond this setting. We study this problem for a broad class of non-positively curved groups: "special" groups in the Haglund-Wise sense. In this setting, we prove that: (1) the top exponential growth rate of any automorphism is an algebraic integer; (2) if the automorphism is untwisted, then it admits only finitely many growth rates, and each of these is polynomial-times-exponential.
2025
27 gennaio
Liwei Hu
nell'ambito della serie: SCUBE
Seminario di analisi numerica
Accurately estimating landslides’ failure surface depth is essential for hazard prediction. However, most of the classical methods rely on overly simplistic assumptions [1]. In this work, we will present the landslide thickness estimation problem as an inverse problem Aw = b, obtained from discretization of the thickness equation [2]: ∂(hf vx)/∂x + ∂(hf vy)/∂y = − ∂ζ/∂t , (1) where the forward operator A contains information on the surface velocity (v_x, v_y), the right-hand side b corresponds to the surface elevation change ∂ζ/∂t, and w is the thickness hf . By employing a regularization approach, the inverse problem is reformulated as an optimization problem. In real-world scenarios, often no information on neither the noise type nor the noise level affecting data is available. In this context, the correct choice of the regularization parameter becomes a pressing issue. We propose a method to determine this parameter in a fully automatic way for the thickness inversion problem. Results obtained on both synthetic data generated by landslide simulation software and data measured from real-world landslides will be shown. [1] Jaboyedoff M., Carrea D., Derron M.H., Oppikofer T., Penna I.M., Rudaz B. (2020): A review of methods used to estimate initial landslide failure surface depths and volumes. Engineering Geology, 267, 105478 [2] Booth A. M. ; Lamb M. P. ; Avouac J.P. ; Delacourt C. (2013): Landslide velocity, thickness, and rheology from remote sensing: La Clapière landslide, France. Geophysical Research Letters, Vol. 40, 4299 - 4304.
2025
24 gennaio
Francesco Milizia
Seminario di algebra e geometria, analisi matematica, interdisciplinare
The simplicial volume is a homotopy invariant of manifolds; this talk is about the simplicial volume of a Davis' manifolds, obtained from the so-called reflection group trick, which is a powerful method for constructing aspherical manifolds. I will describe an approach based on the study of triangulations of spheres and simplicial maps between them. This approach also presents connections with the theory of graph minors. No knowledge about simplicial volume or Davis' reflection group trick is expected from the audience.
2025
23 gennaio
Francesca Corni, assegnista di ricerca dell'Università di Bologna
Seminario di analisi matematica
In this talk we present an explicit area formula to compute the spherical Hausdorff measure of an intrinsic regular graph in an arbitrary homogeneous group. We assume the intrinsic graph to be intrinsically differentiable at any point with continuous intrinsic differential. The key aspect of the result lies in the introduction of a suitable notion of intrinsic Jacobian and in the computation of an explicit expression for this object. Eventually, we present recent results about the symmetries of some homogeneous distances for which the area formula takes a simplified expression. This is a joint work with V. Magnani (Unipi). Attività di ricerca supportata dal progetto INDAM-GNAMPA-2024: "Free boundary problems in noncommutative structures and degenerate operators" CUP E53C23001670001
2025
21 gennaio
Pierpaola Santarsiero
TBA
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
2025
20 gennaio
Lorenzo Luperi Baglini
Seminario di logica
We introduce the concept of Ramsey pairs, and show how they can be prove several infinitary results in combinatorics.
2025
17 gennaio
2025
16 gennaio
Luigi Ambrosio
nel ciclo di seminari: MATEMATICI NELLA STORIA
Seminario di analisi matematica, storia della matematica
Dopo alcuni cenni biografici sulla vita di Ennio De Giorgi e alcuni ricordi personali, nel seminario verrà illustrato l'impatto che egli ha avuto e continua ad avere nella ricerca matematica, nel ricordo di tante generazioni di studenti che, anche se non hanno avuto la fortuna di conoscerlo, ne riconoscono l'eredita'.
15/01/2025
17/01/2025
Kieran O'Grady
General polarized varieties of type K3^[n] as moduli spaces of vector bundles.
Seminario di algebra e geometria
15/01/2025
17/01/2025
Valeria Bertini
Terminalizations of quotients of compact hyperkähler manifolds by induced symplectic automorphisms
Seminario di algebra e geometria
15/01/2025
17/01/2025
Chiara Camere
Logarithmic Enriques Varieties
Seminario di algebra e geometria
15/01/2025
17/01/2025
Salvatore Floccari
The hyper-Kummer construction and applications
Seminario di algebra e geometria
15/01/2025
17/01/2025
Lucas Li Bassi
Schemi di Hilbert su superfici simplettiche irriducibili
Seminario di algebra e geometria
15/01/2025
17/01/2025
Francesco Meazzini
Deformations of monomial ideals
Seminario di algebra e geometria
15/01/2025
17/01/2025
Antonio Rapagnetta
Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces
Seminario di algebra e geometria
15/01/2025
17/01/2025
Gianluca Pacienza
Regenerations and applications
Seminario di algebra e geometria
2025
10 gennaio
Tamas Katay
Seminario di algebra e geometria, logica
Group operations on a fixed countably infinite universe form a Polish space G. Thus we can view group properties as isomorphism-invariant subsets of G, and it makes sense to ask: what properties are generic (in the sense of Baire category)? In my talk, I will address this question and if time permits, I may also say a few words about generic properties of compact groups.
2025
09 gennaio
Ivan Di Liberti
Seminario di algebra e geometria, logica, teoria delle categorie
Inspired by a recent characterisation of coherent topoi as a class of Kan injectives, we provide a tentative definition of fragment of geometric logic. We treat them as mathematical objects, and study them from the point of view of Lindstrom-type theorems.
2025
09 gennaio
Angelina Zheng
Seminario di algebra e geometria
2025
09 gennaio
Giovanni Seraghiti
nell'ambito della serie: SCUBE
Seminario di analisi numerica
In this seminar, I will talk about Objective Function Free Optimization (OFFO) in the context of pruning the parameter of a given model. OFFO algorithms are methods where the objective function is never computed; instead, they rely only on derivative information, thus on the gradient in the first-order case. I will give an overview of the main OFFO methods, focusing on adaptive algorithms such as Adagrad, Adam, RMSprop, ADADELTA, which are gradient methods that share the common characteristic of depending only on current and past gradient information to adaptively determine the step size at each iteration. Next, I will briefly discuss the most popular pruning approaches. As the name implies, pruning a model, typically a neural networks, refers to the process of reducing its size and complexity, typically by removing certain parameters that are considered unnecessary for its performance. Pruning emerges as an alternative compression technique for neural networks to matrix and tensor factorization or quantization. Mainly, I will focus on pruning-aware methods that uses specific rules to classify parameters as relevant or irrelevant at each iteration, enhancing convergence to a solution of the problem at hand, which is robust to pruning irrelevant parameters after training.Finally, I will introduce a novel deterministic algorithm which is both adaptive and pruning-aware, based on a modification Adagrad scheme that converges to a solution robust to pruning with complexity of $\log(k) \backslash k$. I will illustrate some preliminary results on different applications.
06/01/2025
10/01/2025
Roberto Frigerio
Relazione all'interno del convegno: Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups
Seminario di algebra e geometria
Constructing higher degree non-trivial bounded coho- mology classes is a very challenging task. For surface groups and free groups, bounded cohomology is very rich in degree 2 and 3, and a natural question is whether one can build non-trivial classes in higher degrees by taking the cup product of lower-dimensional classes. For hyperbolic manifolds, there exists a well defined map Ψ• associating to every closed differential form a bounded coho- mology class via integration over straight simplices. Classes in the image of this map are usually called De Rham classes, and, in de- gree 2, they span an infinite-dimensional subspace of the bounded cohomology space of the manifold. We prove that, in suitable degrees, Ψ• is a homomorphism of al- gebras, i.e. it sends the wedge product of closed differential forms to the cup product of the associated bounded cohomology classes. As a corollary, the cup product of two De Rham classes vanishes, provided that its degree exceeds the dimension of the manifold. This result complements several recent vanishing results for the cup product of De Rham classes.