Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma

Settimana dal 25 settempre al 1 ottobre 2017

Martedì 26 settembre 2017
Ore 15:00, aula D'Antoni, dipartimento di Matematica, Università di Roma Tor Vergata
Lara Bossinger (University of Cologne)
Toric degenerations of Grassmannians: birational sequences and the tropical variety
As toric varieties are well understood due to their rich combinatorial structure, a toric degeneration allows to deduce properties of the original variety. For Grassmannians, such degenerations can be obtained from birational sequences and the tropical Grassmannian. The first were recently introduced by Fang, Fourier, and Littelmann. They originate from the representation theory of Lie algebras and algebraic groups. In our case, we use a sequence of positive roots for the Lie algebra sln to define a valuation on the homogeneous coordinate ring of the Grassmannian. Nice properties of this valuation allow us to define a filtration whose associated graded algebra (if finitely generated) is the homogeneous coordinate ring of the toric variety. The second was defined by Speyer and Sturmfels and is an example of a tropical variety: a discrete object (a fan) associated to the original variety that shares some of its properties and in nice cases, as the one of Grassmannians, provides toric degenerations. In this talk, I will briefly explain the two approaches and establish a connection between them.

Martedì 26 settembre 2017
Ore 16:00, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata
Gonzalo Tornaria (Universidad de la Republica, Montevideo)
Explicit modularity for typical genus 2 curves
I will describe the computations we used to prove the (para)modularity of the genus 2 curve of conductor 277. Joint work with Armand Brumer, Ariel Pacetti, Cris Poor, John Voight and David Yuen.

Mercoledì 27 settembre 2017
Ore 12:00, aula I, Dipartimento di Chimica edificio L. Caglioti
Attività della facoltà di Scienze MFN per la Notte Europea dei Ricercatori 2017
Domenica Fiorenza (Sapienza Università di Roma)
Mai vista una testuggine... Però ho capito che intende - Algoritmi che apprendono (con un po' d'aiuto)

Giovedì 28 settembre 2017
Ore 11:00, aula 311, Dipartimento di Matematica e Fisica, Università di Roma Tre, largo san L. Murialdo 1
seminario di Analisi Matematica
Davide Gabrielli (Università de L'Aquila)
Gibbsian stationary non-equilibrium states
I will discuss the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular I will discuss two different discrete geometric constructions. Both of them are applied to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions it is possible to generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated to functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and I will use this decomposition to construct models having a fixed invariant measure. Joint work with L. De Carlo

Giovedì 28 settembre 2017
Ore 16:00, aula 311, Dipartimento di Matematica e Fisica, Università di Roma Tre, largo san L. Murialdo 1
seminario di Analisi Matematica
J.P. Marco (Paris VI)
Integrability and complexity of geodesic flows on ellipsoids : from the finite dimensional case to the infinite dimensional one
Starting from the geodesic flow on finite dimensional Euclidean ellipsoids, for which we will recall the classical constructions of complete sets of first integrals and describe their singularities and dynamical complexity, we will examine the possibility of extensions to the infinite dimensional case. This could possibly make a bridge between integrability in the finite dimensional Hamiltonian case and that of Hamiltonian PDE's.

Venerdì 29 settembre 2017
Ore 14:00, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata
Zhi Jiang (SCMS & Fudan University, Shanghai)
Generic vanishing and pluricanonical maps of irregular varieties
Generic vanishing is a powerful tool to study the geometry of irregular varieties. I will give some examples where we can apply generic vanishing to understand the pluricanonical systems of irregular varieties.

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