Notiziario Scientifico

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

Settimana dal 02-03-2020 al 08-03-2020

Lunedì 02 marzo 2020
Ore 14:00, Aula Conversi, Dipartimento di Fisica, Università di Roma La Sapienza
Seminario delle meccaniche
Irene Giardina (Università di Roma La Sapienza)
Collective behavior and dynamic scaling in biological groups
Recent findings on flocks of birds and swarms of insects show that these groups exhibit strong correlations and obey static and dynamic scaling laws, thereby supporting a statistical physics approach. Experiments also indicate that a crucial ingredient - behavioral inertia - is needed to reproduce the observed phenomenology. In this talk, after reviewing the experimental facts, I will introduce a new model of collective motion with behavioral inertia. The related field theory, including both dissipative and reversible dynamical terms, displays flock-like propagation in the ordered phase, and - as revealed by a RG analysis - dynamic scaling laws consistent with the ones of natural swarms.


Martedì 03 marzo 2020
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Chiara Simeoni (Università di Nizza Sophia-Antipolis)
Analysis and numerics of the propagation speed for hyperbolic reaction-diffusion models
We briefly discuss different types of modeling reaction-diffusion phenomena, supporting the idea of the advantages of a description based on hyperbolic equations. Three basic numerical schemes are presented, two of which can be applied for general hyperbolic systems (at the price of reduced performances when dealing with discontinuous initial data). The kind of underlying mechanism prescribes that, in the long-run, also these approaches are reliable. Then, we focus on a class of 2x2 systems corresponding to second order PDEs in one space dimension, adapted for simplified modeling of reaction-diffusion equations and focus on propagating fronts. Special cases where the speed of propagation can be explicitly computed are also provided. We introduce the phase-plane algorithm, which bears a reliable approximation of the propagation speed, assessing its validity in the case with damping where an explicit formula is available. Then, we propose two PDE-based algorithms to approximate the propagation speed, named the scout&spot algorithm and the LeVeque–Yee formula, and we conclude by showing that the second one is a more efficient tool in the determination of the velocity. Joint work with Corrado Lattanzio (DISIM - University of L'Aquila), Corrado Mascia (Sapienza University of Rome), Ramon G. Plaza (IIMAS - National Autonomous University of Mexico)


Mercoledì 04 marzo 2020
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario Algebra e Geometria
Giovanni Cerulli Irelli (Sapienza Università di Roma)
On quiver Grassmannians
A quiver Grassmannian is a projective variety which parametrizes the subrepresentations of a fixed dimension of a quiver representation. It is easy to show that every projective variety can be realized in this way. One hence restricts the study of such projective varieties to relevant classes of quivers and of quiver representations. In a joint work with F. Esposito, H. Franzen and M. Reineke we prove geometric and cohomological properties of these varieties in the case of quivers of finite and tame type and in the case of representations which are rigid, i.e. whose Ext^1 is zero. I will illustrate the results, give examples and provide an idea of the techniques of proofs.


Venerdì 06 marzo 2020
Ore 11:00, aula 2001, Dipartimento di Matematica, Università di Roma Tor Vergata
Corso di Dottorato (prima lezione)
Giulio Codogni (Tor Vergata)
Fano varieties: Kaehler-Einstein metrics, K-stability and moduli spaces
The Yau-Tian-Donaldson conjecture predicts that a Fano variety admits a Keahler- Einstein metric if and only if it is K-stable. K-stability is an algebraic notion modeled on geometric invariant theory. It is also expected that K-stable Fano varities have a good moduli space. By now, the Yau-Tian-Donaldson has been fully proved for smoothable Fano varieties, and partially for all Fano varities. Thanks to a surprising and deep relation with the Minimal Model Program, building on the proof of the BAB conjecture by Birkar, the existence of the moduli space of K-stable varieties has been recently established. However, its projectivity is still an open problem. This result also opens the way to the study of specific interesting examples of moduli spaces. Preliminary program: (1) Algebraic definition of K-stability (2) K-stable Fano varieties are klt (following Odaka) (3) sketch of the variational proof of the Yau-Tian-Donaldson conjecture (4) special test configuration (following Li and Xu) (5) K-stability via filtrations and valuations (following Fujita, Li and Xu) (6) relation between K-stability and Birkar’s theory of complements (following Blum and Xu) (7) existence of the good moduli space of K-stable Fano varities (following Alper, Blum, Halpern-Leistner, Liu and Xu ) The course will be held every friday, from 6th of March to 22nd of May, from 11:00 to 13:00. Web site of the course: http://www.mat.uniroma2.it/~codogni/Kstability.html


Venerdì 06 marzo 2020 - CANCELLATO
Ore 14:00, Aula "Claudio D'Antoni", Università di Roma "Tor Vergata" - dipartimento di Matematica
Algebra and Representation Theory Seminar (ARTS)
Mattia COLOMA (Università di Roma “Tor Vergata”)
The Hirzebruch-Riemann-Roch theorem in the fancy language of Spectra
The category of spectra indubitably is the best of possible worlds for cohomology theories. For instance in spectra one can start with a few basic morphisms, be confident that every natural diagram built from them will commute, and end up with a proof of the Hirzebruch-Riemann-Roch theorem. As in every good story we'll have a deus ex machina: Atiyah's identi-fication of the Spanier-Whitehead dual of a manifold with the Thom spectrum of minus its tangent bundle. I will try to gently introduce all of these tools assuming basic notions of topology, geometry and algebra. Based on joint work with Domenico Fiorenza and Eugenio Landi.


Venerdì 06 marzo 2020
Ore 15:15, Aula D'Antoni (1101), Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Geometria Algebrica
Andreas L. Knutsen (University of Bergen (NO))
Moduli of polarized Enriques surfaces
Moduli spaces of polarized Enriques surfaces have several irreducible components, even if one fixes the degree of the polarization. I will present some results concerning these spaces. In particular I will answer a question of Gritsenko and Hulek concerning connectedness of the étale double covers from the moduli spaces of polarized Enriques surfaces to the moduli spaces of numerically polarized such surfaces, and I will give a way to determine all irreducible components of these moduli spaces.


Venerdì 06 marzo 2020
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminario per docenti (PLS)
Elena Possamai (Liceo Nomentano), Patrizia Berneschi (Liceo Nomentano), Maria Puzio (Liceo De Sanctis), Elena Savinelli (Liceo De Sanctis), Enrico Rogora (Sapienza Università di Roma)
Sequenze binarie 1 (Macchine di Turing e teorema di Van der Waerden)


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