Prossimi seminari del Dipartimento di Matematica

tra circa un'ora
Martedì
19 marzo
Chenyu Bai
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 11:00
presso Aula Vitali
The opening segment will explore the conjectural relationships between Hodge structures and Chow groups. The Bloch-Beilinson conjecture suggests a functorial filtration on the Chow groups of smooth projective varieties, underpinned by natural axioms. We anticipate refined structures of Bloch-Beilinson filtrations, particularly within projective hyper-Kähler and Calabi-Yau manifolds, as proposed by Beauville and Voisin. Linking these to the generalized Hodge conjecture allows the formation of explicit conjectures. Verifying these for specific Calabi-Yau manifolds or projective hyper-Kähler manifolds could substantiate both the Bloch-Beilinson and generalized Hodge conjectures. **Part 2 title:** *Voisin's Conjecture and Voisin's Map* Voisin's work, which crafts a series of K-trivial varieties from cubic hype-resurfaces and self-rational maps on them, called the Voisin's map will be the focus here. Notable among these is the Fano variety of lines of a cubic fourfold, a dimension 4 hyper-Kähler manifold. The Voisin's map in this case has been extensively studied. We'll examine higher-dimensional examples, which are all Calabi-Yau manifolds. This session aims to study the geometry of these manifolds and apply their structural insights to the conjectures on algebraic cycles discussed in Part 1, utilizing Voisin's self-rational map as a pivotal analytical tool.
Mercoledì
20 marzo
In this paper, we introduce a novel observation-driven model for high-dimensional correlation matrices, wherein the largest conditional eigenvalues are modelled dynamically. We impose equal correlations for any pair of assets from the same sector(s), which facilitates the use of a highly efficient alternative expression of the likelihood of a tν-distributed random vector. This alternative expression utilises the canonical form for block correlation matrices by Archakov and Hansen (2020). The dynamics of the eigenvalues is obtained from the Generalised Autoregressive Score (GAS) framework by Creal et al. (2011). We provide an empirical application by constructing Global Minimum Variance (GMV) portfolios using daily returns of 200 assets. In its simplest form, where just a single eigenvalue is updated, our model is extremely fast to estimate. It surpasses the Dynamic Equicorrelation (DECO) model model by Engle and Kelly (2012) and rivals their Block DECO (BDECO) model’s performance in achieving low variance in GMV portfolio returns. Joint work with: Stan Thijssen and Andre Lucas.
We will discuss some recent results concerning weak and strong well-posedness of nonlinear stable driven SDEs with convolution interaction kernel, where the kernel belongs to a suitable Besov space. We will in particular characterize how singular the kernel can be in function of the stability index of the driving noise. In connection with some concrete models, some convergence rates for an approximating particle system will be discussed.
Mercoledì
20 marzo
The many-body Schrödinger equation may be considered a triumph of reductionism: a vast variety of phenomena has been reduced to a single linear partial differential equation. Unfortunately the Schrödinger equation can in general not be solved efficiently, since entanglement suffers from the curse of exponentially growing dimensionality. So this triumph has created a new challenge: revealing the macroscopic behavior from the microscopic equation. I will present recent advances on the emergence of nonlinear equations through the analysis of scaling limits, and then discuss current challenges in the description of interacting fermionic quantum systems. In particular I will discuss the role of non-trivial correlations in the ground state.
Giovedì
21 marzo
Lunedì
25 marzo
Francisco Pereira
Seminario di analisi numerica
ore 11:00
presso Seminario I
The Evolutionary and Complex Systems Group (ECOS) is an Artificial Intelligence research group of the Centre for Informatics and Systems of the University of Coimbra (CISUC), Portugal. ECOS research is based on the development of bio-inspired optimization algorithms and on the application of machine learning methods to extract useful knowledge and patterns from different data sources. Our group has a strong tradition for collaborations with national and international research groups, aiming at developing methods that can effectively address real problems arising in different areas. In this presentation we will provide a general overview of several problems that have been addressed in the areas of chemistry, biochemistry, and life sciences.
Lunedì
25 marzo
Luca Decembrotto; Giulia De Rocco; Andrea Maffia
Seminario di didattica della matematica, interdisciplinare
ore 14:30
presso Seminario I
seminario on line • collegamento al meeting
La didattica in contesto penitenziario è regolata da una specifica normativa, che prevede un complesso intreccio di responsabilità tra istituzione detentiva e scuola, tra esigenze di sicurezza e diritto allo studio. Comprendere i diritti e i doveri dello studente ristretto è requisito fondamentale per progettare interventi educativi e didattici in contesti penitenziari. Il seminario formativo, organizzato dal Dipartimento di Matematica e dal Dipartimento di Scienze dell’Educazione dell’Università di Bologna all’interno del progetto Learning Math in Prison (LeMP), ha lo scopo di introdurre ricercatori, studenti e altri soggetti interessati a queste tematiche, in particolare al contesto in cui è collocata la scuola in carcere e, quindi, l’insegnamento della matematica.
An elementary argument (for sure well-known to the operator theory community) allows to compare the orthogonal projection of a Hilbert space H onto a given closed subspace of H, with (any) bounded non-orthogonal projection acting among the same spaces: this yields an operator identity that is valid in the Hilbert space H. This paradigm has deep implications in analysis, at least in two settings: -in the specific context where the Hilbert space consists of the square-integrable functions along the boundary of a rectifiable domain D in Euclidean space, taken with with respect to, say, induced Lebesgue measure ds (the Lebesgue space L^2(bD)), and the closed subspace is the holomorphic Hardy space H^2(D). In this context the orthogonal projection is the Szego projection, and the non-orthogonal projection is the Cauchy transform (for planar D), or a so-called Cauchy-Fantappie’ transform (for D in C^n with n¥geq 2). -in the specific context where the Hilbert space is the space of square-integrable functions on a domain D in Euclidean space taken with respect to Lebesgue measure dV, and the closed subspace is the Bergman space of functions holomorphic in D that are square-integrable on D. Here the orthogonal projection is the Bergman projection, and the non-orthogonal projection is some ``solid’’ analog of the Cauchy (or Cauchy-Fantappie’) transform. A prototypical problem in both of these settings is the so-called ``L^p-regularity problem’’ for the orthogonal projection where p¥neq 2. This is because the Szego and Bergman projections, which are trivially bounded in L^2 (by orthogonality), are also meaningful in L^p, p¥neq 2 but proving their regularity in L^p is in general a very difficult problem which is of great interest in the theory of singular integral operators (harmonic analysis). Three threads emerge from all this: (1) a link between the (geometric and/or analytic) regularity of the ambient domain and the regularity properties of these projection operators. (2) applications to the numerical solution of a number of boundary value problems on a planar domain D that model phenomena in fluid dynamics. For a few of these problems there can be no representation formula for the solution: numerical methods are all there is. (3) the effect of dimension: for planar D the projection operators are essentially two and can be studied either directly or indirectly via conformal mapping (allowing for a great variety of treatable domains); as is well known, in higher dimensional Euclidean space there is no Riemann mapping theorem: conformal mapping is no longer a useful tool. On the other hand the basic identity in L^2 (see above) is still meaningful but geometric obstructions arise (the notion of pseudoconvexity) that must be reckoned with.
Martedì
26 marzo
Angelo Vistoli
nel ciclo di seminari: MATEMATICI NELLA STORIA
Seminario di algebra e geometria, storia della matematica
ore 16:00
presso Aula Pincherle
Enrico Betti non in realtà non ha mai definito quelli che ora si chiamano numeri di Betti. Durante la conferenza verrà illustrato in modo elementare una connessione veramente notevole tra numeri di Betti e l'aritmetica delle varietà algebriche.
Sunlight constitutes an abundant and endless natural fuel, available worldwide. In a society where a substantial part of the global energy yield is being directly expended at the city scale, urban areas appear as serious candidates for the production of solar energy. Their intrinsic complexity yet makes it challenging. The morphological heterogeneity between urban geometries and intricacy of their materials optical properties especially contribute together to causing important spatiotemporal variations in the distribution of incident solar radiations. The field of irradiance received by a specific urban region (e.g. façade, building, district) may thus rapidely become the result of complex miscellaneous interactions between many degrees of freedom. Besides, Principal Component Analysis (PCA) has been widely validated as an efficient algorithm to identify the principal behavioural features, or modes of variability, of a high-dimensional phenomenon. An approach is proposed here for analysing the variations in space and time of the solar resource within an urban context by means of PCA. A parametric investigation is conducted on a set of theoretical 100×100 m² urban districts, defined as arrangements of cuboid-like buildings, with various typological indicators (Total Site Coverage, Average Building Height) and surface materials (Lambertian, highly-specular) at three different latitudes. For each configuration, the distribution of irradiance incident on the facets of the central building is modelled via backwards Monte-Carlo ray tracing over a full year and under clear sky conditions, with a 15 min timestep and 1 m spatial resolution. PCA is subsequently applied to the simulated radiative fields to extract dominant modes of variation. First results validate energy-based orthogonal decompositions like PCA as efficient tools for characterising the variability distribution of multivariate phenomena in this context, allowing for the identification of district areas subjected to important spatial and temporal variations of the solar resource. Characteristic time scales are clearly represented across successive orders of decomposition. Information about the district morphology is also obtained, with the contribution of surrounding geometries being portrayed by specific spatial modes. Similar prevalent variables are further repetitively encountered across multiple evaluated surfaces, but at different modal ranks.
Giovedì
04 aprile
Lunedì
08 aprile
Piotr M. Hajac
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria, fisica matematica
ore 10:00
presso Dipartimento di Fisica, Aula teorici
seminario on line •
A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra B. We prove that principality is a piecewise property: given N comodule-algebra surjections P->Pi whose kernels intersect to zero, P is principal if and only if all Pi's are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with B. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such N-families of surjections P->Pi and such that the comodule algebra of global sections is P.
TBA
Martedì
09 aprile
Claudio Procesi
nel ciclo di seminari: MATEMATICI NELLA STORIA
Seminario di algebra e geometria, storia della matematica, analisi matematica
ore 16:00
presso Aula Pincherle
Verranno discusse la vita e i lavori di Riemann e si accennerà ai Matematici con cui ha avuto contatti, fra cui molti italiani.
Giovedì
11 aprile
Daniela Di Donato
TBA
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
15/04/2024
19/04/2024
Conference
da lunedì 15 aprile 2024 a venerdì 19 aprile 2024
Lunedì
15 aprile
Gianmarco Todesco
Seminario di didattica della matematica, interdisciplinare, storia della matematica
ore 15:00
presso Aula Tonelli
seminario on line •
Nel 1958 l'artista olandese M. C. Escher fu profondamente colpito da uno schema di triangoli curvilinei presente in un libro del matematico canadese H.S.M. Coxeter. Escher rielaborò la figura a modo suo, creando la splendida serie di incisioni "Limite del Cerchio". La matematica intessuta nelle quattro opere è un buon punto di partenza per esplorare diversi concetti interessanti: il piano iperbolico, le geometrie non euclidee e i rapporti fra curvatura e geometria di una superficie.
Martedì
16 aprile
Pietro Beri
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 11:00
presso Aula Vitali
Martedì
16 aprile
Philippe Ellia
nel ciclo di seminari: MATEMATICI NELLA STORIA
Seminario di algebra e geometria, storia della matematica
ore 16:00
presso Aula Pincherle
Un veloce ed informale racconto della vita, dei metodi e dell'eredità matematica (specie in teoria dei numeri) di Pierre de Fermat. Si cercherà anche di sfatare un mito riguardo alla sua famosa congettura.
17/04/2024
19/04/2024
Conference
da mercoledì 17 aprile 2024 a venerdì 19 aprile 2024
The aim of this workshop is to bring together young researchers working in low-dimensional topology and geometric group theory in a broad sense. The event consists in main lectures and shorter talks in order to give the opportunity to young researchers to present their own research.
Mercoledì
17 aprile
We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority (conformism) and the aspiration of sticking with the own type (stubbornness). We also consider a quadratic cost related to the rate at which a change in the state happens: changing opinion may be a costly operation. Depending on the parameters of the model, the game may have more than one Nash equilibrium, even though the corresponding N-player game does not. Moreover, it exhibits a very rich phase diagram, where polarized/unpolarized, coherent/incoherent equilibria may coexist, except for T small, where the equilibrium is always unique. We fully describe such phase diagram in closed form and provide a detailed numerical analysis of the N-player counterpart of the mean field game. Joint work with Paolo Dai Pra (Verona) and Elena Sartori (Padova).
Mercoledì
17 aprile
Jonas Tölle
TBA
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore 12:00
presso Aula Arzelà
TBA
Giovedì
18 aprile
Ermanno Lanconelli
TBA
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
seminario on line •
TBA
We study the limiting behavior of minimizing p-harmonic maps from a bounded 3d Lipschitz domain O to a compact connected Riemannian manifold without boundary and with finite fundamental group as p goes to 2 from below. We prove that there exists a closed set S of finite length such that minimizing p-harmonic maps converge to a locally minimizing harmonic map in O\S. We prove that locally inside O the singular set S is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains. Furthermore, we establish local and global estimates for the limiting singular harmonic map. Under additional assumptions, we prove that globally in the closure of O the set S is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains, which is defined by a given boundary datum and O. This is a joint work with Jean Van Schaftingen and Benoît Van Vaerenbergh.
Lunedì
22 aprile
Orthogonal modular varieties are locally symmetric varieties associated to integral quadratic forms of signature (2,n). They are related to various branches of Mathematics such as Algebraic Geometry (especially as moduli spaces of K3 surfaces and hyperKahler manifolds), Number theory and Representation theory. In these lectures, I will give an introduction to the geometry of orthogonal modular varieties, with focus on the topics such as toroidal compactifications, Kodaira dimension and mixed Hodge structures.
Martedì
23 aprile
Shouhei Ma
Seminario di algebra e geometria
ore 14:00
presso - Aula Da Stabilire -
Orthogonal modular varieties are locally symmetric varieties associated to integral quadratic forms of signature (2,n). They are related to various branches of Mathematics such as Algebraic Geometry (especially as moduli spaces of K3 surfaces and hyperKahler manifolds), Number theory and Representation theory. In these lectures, I will give an introduction to the geometry of orthogonal modular varieties, with focus on the topics such as toroidal compactifications, Kodaira dimension and mixed Hodge structures.
Mercoledì
24 aprile
Orthogonal modular varieties are locally symmetric varieties associated to integral quadratic forms of signature (2,n). They are related to various branches of Mathematics such as Algebraic Geometry (especially as moduli spaces of K3 surfaces and hyperKahler manifolds), Number theory and Representation theory. In these lectures, I will give an introduction to the geometry of orthogonal modular varieties, with focus on the topics such as toroidal compactifications, Kodaira dimension and mixed Hodge structures.
Mercoledì
24 aprile
Irene Benedetti
Seminario di analisi matematica
ore 16:00
presso Seminario II
seminario on line •
In questa presentazione verranno mostrati risultati sull'esistenza e la localizzazione delle soluzioni per problemi differenziali non locali in spazi astratti. In particolare, verrà illustrato un procedimento basato su teoremi di punto fisso associati alle cosiddette condizioni di trasversalità. Una particolare attenzione verrà dedicata ad alcune tecniche che permettono di indebolire le ipotesi di compattezza classiche spesso presenti in letteratura per lo studio di equazioni differenziali in spazi astratti con metodi topologici. Questo approccio fornisce un metodo unificante per lo studio di modelli che descrivono processi di diffusione in diversi contesti. Permette di considerare condizioni periodiche e condizioni iniziali non locali più generali come ad esempio condizioni multipoint oppure condizioni iniziali di tipo integrale, e di gestire nonlinearità con crescite superlineari, ad esempio polinomi cubici o mappe che dipendono dall'integrale della soluzione, includendo così comportamenti di diffusione non locale.
Martedì
30 aprile
Susanna Terracini, Università di Torino
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
seminario on line •
Giovedì
02 maggio
Francesca Da Lio
TBA
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
Mercoledì
08 maggio
Francesco Leonetti
TBA
Seminario di analisi matematica
ore 16:00
presso Seminario II
seminario on line •
TBA
Giovedì
09 maggio
Luigi De Pascale
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
2024-05-15
Conference
da mercoledì 15 maggio 2024 a mercoledì 15 maggio 2024
Since their birth to the present day, spin glasses remain a vibrant area of research. This enduring vitality can be attributed to two primary factors. Firstly, certain conjectures continue to pose significant challenges for mathematical physicists, despite decades of concerted effort. Secondly, their distinctive feature lies in the universality of the approaches used to describe their theory, which has permeated numerous other disciplines, including social sciences, information theory, high-dimensional probability, and notably, machine learning, a domain currently experiencing a resurgence following the AI winter of the previous century. The workshop aims to illustrate the key milestones in the consolidation of the mathematical and physical theory of spin glasses by showcasing the firsthand experiences of leading researchers in the field, while also acknowledging the many possibilities it still holds for exploration. The event will take place in the Ulysses room of the Bologna Academy of Sciences, a prestigious venue traditionally reserved for top-tier conferences and seminars, adorned with Pellegrino Tebaldi’s frescoes depicting the exploits of the Homeric hero.
Giovedì
16 maggio
Alberto Parmeggiani
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
Mercoledì
22 maggio
Francesco Russo
TBA
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore 11:00
presso Aula Arzelà
TBA
Mercoledì
22 maggio
Fabrizio Lillo
TBA
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di finanza matematica
ore 12:00
Giovedì
30 maggio
Marco Squassina
Seminario di analisi matematica
ore 16:00
presso Aula Vitali
seminario on line • collegamento al meeting
We present some new results about the concavity (up to a transformation) of positive solutions for some classes of quasi-linear elliptic problems, including nonautonomous cases.
Martedì
04 giugno
Andrea Di Lorenzo
nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA
Seminario di algebra e geometria
ore 11:00
presso - Aula Da Stabilire -
Blow-ups are fundamental tools in algebraic geometry, and there are several results (e.g the famous Castelnuovo's theorem) that can be used to determine when a variety is obtained as a blow-up of a smooth variety along a smooth center. Weighted blow-ups play a similar role for stacks. In this talk I will present a criterion for finding out if a smooth DM stack is a weighted blow-up. I will apply this result for showing that certain alternative compactifications of moduli of marked elliptic curves are obtained via weighted blow-ups (and blow-downs). This in turn will prove to be useful in order to compute certain invariants, like Chow rings or Brauer groups. First part of this talk is a joint work with Arena, Inchiostro, Mathur, Obinna and Pernice; the second part of this talk is a joint work with L. Battistella.
Mercoledì
19 giugno
Katia Colaneri
TBA
nell'ambito della serie: STOCHASTICS AND APPLICATIONS
Seminario di probabilità
ore 12:00
presso Aula Arzelà
TBA
Giovedì
20 giugno
Simone Ciani
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
Giovedì
27 giugno
Kanishka Perera
TBA
Seminario di analisi matematica
ore 16:00
presso - Aula Da Stabilire -
seminario on line •
TBA