Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 21-11-2022 al 27-11-2022

Lunedì 21 novembre 2022
Ore 11:30, Aula 009, Dipartimento di Matematica e Fisica, Roma Tre
Seminario di Fisica Matematica
Margherita Disertori (Bonn University)
Vertex reinforced jump process on a hierarchical lattice
The vertex reinforced jump process is a history dependent continuous time process introduced by Werner, which can be mapped into a certain nonlinear sigma model, where spins take values on a supersymmetric hyperbolic manifold. We consider the model on a complete graph with hierarchical interactions and show that in this setting the problem reduces to study a one-dimensional chain with non-constant interactions. This is joint work with S. Rolles and F. Merkl. Ci sara' la possibilita' di seguire il seminario in remoto, cliccando sul seguente link
Per ulteriori informazioni si può contattare gli organizzatori all'email alessandro.giuliani@uniroma3.it.


Lunedì 21 novembre 2022
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di analisi
Pierre-Damien Thizy (Università di Lyon)
Large blow-up sets for Q-curvature equations
On a bounded domain of the Euclidean space \(\mathbb{R}^{2m}, m>1\), Adimurthi, Robert and Struwe pointed out that, even assuming a volume bound \(\int e^{2mu} dx\le C\), some blow-up solutions for prescribed Q-curvature equations \((-\Delta)^m u= Q e^{2m u}\) without boundary conditions may blow-up not only at points, but also on the zero set of some nonpositive nontrivial polyharmonic function. This is in striking contrast with the two dimensional case (m=1). During this talk, starting from a work in progress with Ali Hyder and Luca Martinazzi, we will discuss the construction of such solutions which involves (possible generalizations of) the Walsh-Lebesgue theorem and some issues about elliptic problems with measure data.


Martedì 22 novembre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Mauro Mariani (HSE University (Moscow))
Long time asymptotic of action functionals
I will provide a self-contained variational approach to state some classical and new results in the framework of Aubry-Mather theory. More precisely, I will discuss the expansion by Gamma-convergence of the action functional of classical mechanics, as the time-scale diverges. Joint work with Carlo Orrieri.


Martedì 22 novembre 2022
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di geometria
Stefano Filipazzi (EPFL)
On the boundedness of elliptic Calabi-Yau threefolds
In this talk, we will discuss the boundedness of Calabi-Yau threefolds admitting an elliptic fibration. First, we will review the notion of boundedness in birational geometry and its weak forms. Then, we will switch focus to Calabi-Yau varieties and discuss how the Kawamata-Morrison cone conjecture comes in the picture when studying boundedness properties for this class of varieties. To conclude, we will see how this circle of ideas applies to the case of elliptic Calabi-Yau threefolds. This talk is based on work joint with C.D. Hacon and R. Svaldi.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it


Martedì 22 novembre 2022
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Giuseppe Orlando (Politecnico di Milano)
A filtering monotonization technique for DG discretizations of hyperbolic problems
In this talk, I will introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. After a brief overview of classical monotonization techniques, I will present an approach which reduces the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not, following an approach already proposed for the Hamilton-Jacobi equations by other authors. The method has been implemented in the framework of the deal.II numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. The potentialities of the proposed filtering technique are shown in a number of numerical experiments.
Per informazioni, rivolgersi a: giuseppe.visconti@uniroma1.it


Martedì 22 novembre 2022
Ore 16:00, Aula Dal Passo, Università degli Studi di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Massimiliano Berti (SISSA - Trieste)
Benjamin-Feir instability of Stokes waves
A classical subject in fluid mechanics regards the spectral instability of traveling periodic water waves, called Stokes waves. Benjamin, Feir, Whitam and Zhakarov predicted, through experiments and formal arguments, that Stokes waves in sufficiently deep water are unstable, finding unstable eigenvalues near the origin of the complex plane, corresponding to small Floquet exponents \(\mu\) or equivalently to long-wave perturbations. The first rigorous mathematical results have been given by Bridges-Mielke (’95) in finite depth and by Nguyen-Strauss (’20) in infinite depth. On the other hand, it has been found numerically that when the Floquet number \(\mu\) varies, two eigenvalues trace an entire figure-eight. I will present a novel approach to prove this conjecture fully describing the unstable spectrum. This is joint work with A. Maspero and P. Ventura. Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006.
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it


Mercoledì 23 novembre 2022
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Algebra e Geometria
Gabriella Tarantello (Università di Roma "Tor Vergata")
On a Donaldson functional for CMC-immersions of surfaces into hyperbolic 3-manifolds
We discuss a parametrization for the moduli space of Constant Mean Curvature (CMC)immersions of a closed surface S (orientable and of genus at least 2) into hyperbolic 3-manifolds by elements of the tangent bundle of the Teichmüller space of S. Namely, by pairs formed of a given conformal structure X on S and a Dolbeault cohomology class of (0,1)-forms valued in the holomorphic tangent bundle of X. For any such pair, we determine uniquely the pullback metric and the second fundamental form of the immersion by solving the Gauss-Codazzi equations. The Gauss-Codazzi equations can be viewed as the Hitchin’s self-duality equations for a suitable nilpotent SL(2;C)-Higgs bundle, and have been handled in this way in case of minimal immersions. However, they correspond also to the Euler-Lagrange equation of a suitable Donaldson functional [see Gonsalves-Uhlenbeck ( 2007)] and their unique solvability is attained [in collaboration with M. Lucia an Z. Huang (2022)] by showing that such functional admits a global minimum as its unique critical point. Eventually, we can extend such a uniqueness result to more general situations previously treated via the Higgs-bundle approach, including minimal Lagrangian immersions. In addition, we are able to analyze the asymptotic behavior of those minimizers along a whole ray of cohomology classes and obtain “convergence” in terms of the Kodaira map. For example in case of genus 2, we are able to catch at the limit “regular “ CMC 1-immersions, except in the rare situation where the projective representative of given cohomology class belongs to the image, through the Kodaira map, of the six Weierstrass points of S. If time permits, we shall mention further recent progress for higher genus obtained in collaboration with S. Trapani.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it


Mercoledì 23 novembre 2022
Ore 14:30, Aula 311, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Analisi
Massimiliano Berti (SISSA, Trieste)
Quasi-periodic vortex patches of 2d-Euler
I will discuss the bifurcation of time quasi-periodic vortex patch solutions of the 2d-Euler equations close to rotating Kirchhoff ellipses, for a Borel set of eccentricities of asymptotically full Lebesgue measure. Joint work with Z. Hassaina and N. Masmoudi.


Giovedì 24 novembre 2022
Ore 14:00, Aula Seminari (in RM004, ex palazzina E, via Scarpa), Dipartimento SBAI, Sapienza Università di Roma
Seminario di Analisi Matematica
Giovanni Franzina (CNR)
Large time behaviour of non-local filtration and fractional Lane-Emden equations with sub-linear power
We consider a Lane-Emden equation involving the fractional Laplacian, with a concave power function as a non-linearity. We prove that the least energy solution is isolated from all other critical points of the non-local energy and we discuss some applications to the qualitative analysis of the fractional porous media equation at large times.
Per informazioni, rivolgersi a: Isabella.ianni@uniroma1.it


Venerdì 25 novembre 2022
Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Giovanni Gaiffi (Università di Pisa)
Combinatorial aspects of the cohomology of compactifications of toric arrangements
I will describe how to construct monomial bases for the integer cohomology rings of compact wonderful models of toric arrangements. In the description of the monomials various combinatorial objects come into play: building sets, nested sets, and the fan of a suitable toric variety. In particular, I will focus on the case of the toric arrangements associated with root systems of type A. Here the combinatorial description of these basis offers a geometrical point of view on the relation between some eulerian statistics on the symmetric group. This is a joint work with Oscar Papini and Viola Siconolfi.


Venerdì 25 novembre 2022
Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Alessandro Iraci (Università di Pisa)
Delta and Theta operators expansions
Delta and Theta operators are two families of operators on symmetric functions that show remarkable combinatorial properties. Delta operators generalise the famous nabla operator by Bergeron and Garsia, and have been used to state the Delta conjecture, an extension of the famous shuffle theorem proved by Carlsson and Mellit. Theta operators have been introduced in order to state a compositional version of the Delta conjecture, with the idea, later proved successful, that this would have led to a proof via the Carlsson-Mellit Dyck path algebra. We are going to give an explicit expansion of certain instances of Delta and Theta operators when t=1 in terms of what we call gamma Dyck paths, generalising several results including the Delta conjecture itself, using interesting combinatorial properties of the forgotten basis of the symmetric functions.


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