Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 15-01-2024 al 21-01-2024
Lunedì 15 gennaio 2024
Ore 14:00, Aula E, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso dottorato
Alberto Cogliati (Università di Pisa)
Stodia della geometria iperbolica (I)
Lunedì 15 gennaio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Francois Hamel (Aix-Marseille Université)
Parallel flows in infinite cylinders
In this talk, I will discuss some rigidity results for steady incompressible flows away from stagnation in infinite cylinders with tangential boundary conditions. In two-dimensional strips, Euler flows turn out to be parallel flows. In any dimension, Euler or Navier-Stokes potential flows turn out to be constant. I will also discuss various counter-examples without the main assumptions. The proofs rely on the study of the geometric properties of the streamlines and a combination of ODE and PDE arguments. The talk is based on some joint works with A. Karakhanyan and N. Nadirashvili. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 16 gennaio 2024
Ore 13:00, aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso dottorato
Alberto Cogliati (Università di Pisa)
Storia della geometria iperbolica (II)
Martedì 16 gennaio 2024
Ore 14:00, Sala di Consiglio , Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Michele Salvi (Università di Tor Vergata)
From the Uniform to the Minimum Spanning Tree
A spanning tree of a graph G is a connected subset of G without cycles. The Uniform Spanning Tree (UST) is obtained by choosing one of the possible spanning trees of G at random. The Minimum Spanning Tree (MST) is realised instead by putting random weights on the edges of G and then selecting the spanning tree with the smallest weight. These two models exhibit markedly different behaviours: for example, their diameter on the complete graph with n nodes transitions from n^1/2 for the UST to n^1/3 for the MST. What lies in between? We introduce a model of Random Spanning Trees in Random Environment (RSTRE) designed to interpolate between UST and MST. In particular, when the environment disorder is sufficiently low, the RSTRE on the complete graph has a diameter of n^1/2 as the UST. Conversely, when the disorder is high, the diameter behaves like n^1/3 as for the MST. We conjecture a smooth transition between these two values for intermediate levels of disorder. This talk is based on joint work with Rongfeng Sun and Luca Makowiec (NUS Singapore).
Per informazioni, rivolgersi a: faggiona@mat.uniroma1.it
Martedì 16 gennaio 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Katharina Müller (Universität der Bundeswehr München)
On towers of isogeny graphs with full level structure
Let k be a finite field of chracteristic q. Let p,l be primes corpime to q and let N be a positive integer coprime to pql. In this talk we will define graphs \(X_l^q(Np^n)\) whose vertices are tuples (E,P,Q), where E/k is an elliptic curves and P,Q is a basis for \(E[Np^n]\). The edges are given by degree l isogenies. We will discuss when \(X_l^q(Np^n)/X_l^q(Np^{n-1})\) is Galois and will describe the structure of these graphs as volcanos. This is joint work with Antonio Lei.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Mercoledì 17 gennaio 2024
Ore 14:00, Aula G, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso dottorato
Alberto Cogliati (Università di Pisa)
Storia della geometria iperbolica (III)
Mercoledì 17 gennaio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Salvatore Floccari (Universität Bielefeld)
The Hodge conjecture for sixfolds of generalized Kummer type
The Hodge conjecture is a central problem in modern algebraic geometry. It is notoriously difficult to attack, and we still lack general evidence towards its validity. In my talk I will present a proof of the Hodge conjecture for all six-dimensional hyper-Kähler varieties of generalized Kummer type, i.e. those arising via deformation of Beauville's generalized Kummer varieties built from abelian surfaces. The result presented yields the first complete families of projective hyper-Kähler varieties of dimension larger than two for which the Hodge conjecture is verified. As I will explain, a key ingredient for the proof is the construction of a K3 surface naturally associated to a sixfold of generalized Kummer type.
Mercoledì 17 gennaio 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario Vito Volterra
Alessia Nota (Università dell'Aquila)
On the Smoluchowski equation for aggregation phenomena under non-equilibrium conditions
In this talk I will first discuss some fundamental properties of the Smoluchowski’s coagulation equation, an integro-differential equation of kinetic type, which provides a mean-field description for mass aggregation phenomena. I will then present some recent results on the problem of existence or non-existence of stationary solutions, both for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomenon: they localize along a line in the composition space as the total size of the particles increase. This localization is a universal property of multicomponent systems and it has also been recently proved to occur in time dependent solutions to mass conserving coagulation equations. (Based on joint works with M.Ferreira, J.Lukkarinen and J. Velázquez)
Giovedì 18 gennaio 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Antonella Grassi (Bologna)
The Noether-Lefschetz locus in families of (singular) Fano threefolds
The Noether-Lefschetz locus parametrizes families of surfaces in threefolds whose rank of the Neron-Severi group (the Picard rank) is higher than that of the ambient space. I will present work in progress (joint with with K. DeVleming and J. Rana) on the behavior in families of this locus. We will discuss “modularity properties” of components of both maximal and minimal codimension and present many examples.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 18 gennaio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Paolo Piccione (Universidade de São Paulo)
Algebraic and topological methods for Yamabe-type problems
A Yamabe-type problem addresses the inquiry into the existence of metrics within a specified conformal class, characterized by a constant higher-order, possibly fractional, Q-curvature. I will present some results on the multiplicity of complete solutions for Yamabe-type problems on noncompact manifolds, obtained using algebraic and topological techniques.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 19 gennaio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Ricccardo Aragona (U L'Aquila)
Normalizer chain, modular idealizer chain and partitions
In recent joint works with Civino, Gavioli and Scoppola, we studied the conjugacy classes of an elementary abelian regular subgroup T of the symmetric group on 2^n elements. In particular, we computed, via GAP software package, a chain of normalizers in a Sylow 2-subgroup of this symmetric group defined iteratively starting from T. We noticed that the logarithm of the index of the (i-1)-th normalizer in the i-th normalizer of our chain is equal to the i-th partial sum of the sequence of the numbers of partitions of an integer in at least two distinct parts. In this talk, we present some techniques developed in order to prove this result, including the notion of a special family of elements of Sylow 2-subgroup, called rigid commutators. Finally, some generalizations to Lie algebras are given, considering similar results for an idealizer chain.
Venerdì 19 gennaio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Tommaso Rossi (U Roma Tor Vergata)
Homology operations for gravity algebras
In the early nineties, Getzler discovered a nice algebraic structure on the equivariant homology of a topological conformal field theory. He called this algebraic structure a "gravity algebra" and showed that it is governed by an operad which is closely related to the homology of M_{0,n+1}, the moduli space of genus zero Riemann surfaces with n+1 marked points. A gravity algebra can be thought as a generalization of a (dg) Lie algebra, in the sense that other than the Lie bracket we also have higher arity operations which satisfies a "generalized Jacobi identity". In this talk, we will first give an introduction to gravity algebras, providing many interesting examples from both algebra (cyclic cohomology of a Frobenius algebra) and topology (S^1-equivariant homology of the free loop space on a manifold). Then I will briefly explain that any class in the S^1-equivariant homology of the (unordered) configuration spaces of points in the plane H_*^{S^1}(C_n(R^2); F_p) (with coefficients in a field F_p of p elements) gives rise to a homology operation for gravity algebras. After that we will see how to compute this equivariant homology, and if time permits we will see some applications.
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